罗斯 公司理财 英文第九版Chap005
《公司理财》斯蒂芬A罗斯英文》PPT课件讲义
5.1 Definition and Example of a Bond
• A bond is a legally binding agreement between a borrower and a lender: – Specifies the principal amount of the loan. – Specifies the size and timing of the cash flows:
• In dollar terms (fixed-rate borrowing) • As a formula (adjustable-rate borrowing)
5.1 Definition and Example of a Bond
• Consider a U.S. government bond listed as 6 3/8 of December 2009.
N I/Y PV PMT FV
12
5
– 1,070.52
31.875 = 1,000
1,000×0.06375 2
5.3 Bond Concepts
1. Bond prices and market interest rates move in opposite directions.
2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond)
英文版罗斯公司理财习题答案Chap005
CHAPTER 5INTEREST RATES AND BOND VALUATIONAnswers to Concepts Review and Critical Thinking Questions1.No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasurysecurities have substantial interest rate risk.2.All else the same, the Treasury security will have lower coupons because of its lower default risk,so it will have greater interest rate risk.3. No. If the bid were higher than the ask, the implication would be that a dealer was willing to sell abond and immediately buy it back at a higher price. How many such transactions would you like to do?4.Prices and yields move in opposite directions. Since the bid price must be lower, the bid yieldmust be higher.5.There are two benefits. First, the company can take advantage of interest rate declines by callingin an issue and replacing it with a lower coupon issue. Second, a company might wish toeliminate a covenant for some reason. Calling the issue does this. The cost to the company is ahigher coupon. A put provision is desirable from an investor’s standpoint, so it helps the company by reducing the coupon rate on the bond. The cost to the company is that it may have to buy back the bond at an unattractive price.6. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds areused to establish the coupon rate necessary for a particular issue to initially sell for par value.Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them. The coupon rate is fixed and simply determines what the bond’s coupon payments will be.The required return is what investors actually demand on the issue, and it will fluctuate throughtime. The coupon rate and required return are equal only if the bond sells for exactly at par.7.Yes. Some investors have obligations that are denominated in dollars; i.e., they are nominal.Their primary concern is that an investment provides the needed nominal dollar amounts. Pension funds, for example, often must plan for pension payments many years in the future. If thosepayments are fixed in dollar terms, then it is the nominal return on an investment that is important.8. Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell;many large investors are prohibited from investing in unrated issues.9.Treasury bonds have no credit risk since it is backed by the U.S. government, so a rating is notnecessary. Junk bonds often are not rated because there would be no point in an issuer paying arating agency to assign its bonds a low rating (it’s like paying someone to kick you!).10.The term structure is based on pure discount bonds. The yield curve is based on coupon-bearingissues.11.Bond ratings have a subjective factor to them. Split ratings reflect a difference of opinion amongcredit agencies.12.As a general constitutional principle, the federal government cannot tax the states without theirconsent if doing so would interfere with state government functions. At one time, this principlewas thought to provide for the tax-exempt status of municipal interest payments. However,modern court rulings make it clear that Congress can revoke the municipal exemption, so the only basis now appears to be historical precedent. The fact that the states and the federal government do not tax each other’s securities is referred to as “reciprocal immunity.”13. Lack of transparency means that a buyer or seller can’t see recent transactions, so it is muchharder to determine what the best bid and ask prices are at any point in time.14.One measure of liquidity is the bid-ask spread. Liquid instruments have relatively small spreads.Looking at Figure 7.4, the bellwether bond has a spread of one tick; it is one of the most liquid of all investments. Generally, liquidity declines after a bond is issued. Some older bonds, including some of the callable issues, have spreads as wide as six ticks.panies charge that bond rating agencies are pressuring them to pay for bond ratings. When acompany pays for a rating, it has the opportunity to make its case for a particular rating. With an unsolicited rating, the company has no input.16. A 100-year bond looks like a share of preferred stock. In particular, it is a loan with a life thatalmost certainly exceeds the life of the lender, assuming that the lender is an individual. With ajunk bond, the credit risk can be so high that the borrower is almost certain to default, meaningthat the creditors are very likely to end up as part owners of the business. In both cases, the“equity in disguise” has a significant tax advantage.17.a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate used in valuing the cash flows from a bond.b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate.c. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return.18. A long-term bond has more interest rate risk compared to a short-term bond, all else the same. Alow coupon bond has more interest rate risk than a high coupon bond, all else the same. Whencomparing a high coupon, long-term bond to a low coupon, short-term bond, we are unsure which has more interest rate risk. Generally, the maturity of a bond is a more important determinant of the interest rate risk, so the long-term high coupon bond probably has more interest rate risk. The exception would be if the maturities are close, and the coupon rates are vastly different.Solutions to Questions and ProblemsNOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.NOTE: Most problems do not explicitly list a par value for bonds. Even though a bond can have any par value, in general, corporate bonds in the United States will have a par value of $1,000. We will use this par value in all problems unless a different par value is explicitly stated.Basic1.The price of a pure discount (zero coupon) bond is the present value of the par. Even though the bond makes no coupon payments, the present value is found using semiannual compounding periods, consistent with coupon bonds. This is a bond pricing convention. So, the price of the bond for each YTM is:a. P = €1,000/(1 + .03)20 = €553.68b. P = €1,000/(1 + .05)20 = €376.89c. P = €1,000/(1 + .07)20 = €258.422.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond at each YTM will be:a.P = £40({1 – [1/(1 + .04)]40 } / .04) + £1,000[1 / (1 + .04)40]P = £1,000.00When the YTM and the coupon rate are equal, the bond will sell at par.b.P = £40({1 – [1/(1 + .05)]40 } / .05) + £1,000[1 / (1 + .05)40]P = £828.41When the YTM is greater than the coupon rate, the bond will sell at a discount.c.P = £40({1 – [1/(1 + .03)]40 } / .03) + £1,000[1 / (1 + .03)40]P = £1,231.15When the YTM is less than the coupon rate, the bond will sell at a premium.We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIF R,t = 1 / (1 + r)twhich stands for Present Value Interest FactorPVIFA R,t= ({1 – [1/(1 + r)]t } / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key.3.Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:P = 元970 = 元43(PVIFA R%,20) + 元1,000(PVIF R%,20)Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find:R = 4.531%Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so:YTM = 2 4.531% = 9.06%4.Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:P = $1,145 = C(PVIFA3.75%,29) + $1,000(PVIF3.75%,29)Solving for the coupon payment, we get:C = $45.79Since this is the semiannual payment, the annual coupon payment is:2 × $45.79 = $91.58And the coupon rate is the coupon rate divided by par value, so:Coupon rate = $91.58 / $1,000 = 9.16%5.The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is:R = r + hApproximate r = .06 –.045 =.015 or 1.50%The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)(1 + .06) = (1 + r)(1 + .045)Exact r = [(1 + .06) / (1 + .045)] – 1 = .0144 or 1.44%6.The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)R = (1 + .04)(1 + .025) – 1 = .0660 or 6.60%7. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)h = [(1 + .15) / (1 + .09)] – 1 = .0550 or 5.50%8.The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)r = [(1 + .134) / (1.045)] – 1 = .0852 or 8.52%9.This is a bond since the maturity is greater than 10 years. The coupon rate, located in the first column of the quote is 6.125%. The bid price is:Bid price = 116:05 = 116 5/32 = 116.15625%⨯$1,000 = $1,161.5625The previous day’s ask price is found by:Previous day’s asked price = T oday’s asked price – Change = 116 5/32 – (–932) = 116 14/32 The previous day’s price in dollars was:Previous day’s dollar price = 116.4375%⨯$1,000 = $1,164.37510.This is a premium bond because it sells for more than 100% of face value. The current yield is:Current yield = Annual coupon payment / Price = $75/$1,320.9375 = 5.68%The YTM is located under the “ASK YLD” column, so the YTM is 4.93%.The bid-ask spread is the difference between the bid price and the ask price, so:Bid-Ask spread = 132:03 – 132:02 = 1/32Intermediate11.Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The bond price equation is:P = C(PVIFA R%,t) + £1,000(PVIF R%,t)Miller Corporation bond:P0= £40(PVIFA3%,26) + £1,000(PVIF3%,26) = £1,178.77P1= £40(PVIFA3%,24) + £1,000(PVIF3%,24) = £1,169.36P3= £40(PVIFA3%,20) + £1,000(PVIF3%,20) = £1,148.77P7= £40(PVIFA3%,12) + £1,000(PVIF3%,12) = £1,099.54P12= £40(PVIFA3%,2) + £1,000(PVIF3%,2) = £1,019.13P13= £1,000Modigliani Company bond:Y: P0= £30(PVIFA4%,26) + £1,000(PVIF4%,26) = £840.17P1= £30(PVIFA4%,24) + £1,000(PVIF4%,24) = £847.53P3= £30(PVIFA4%,20) + £1,000(PVIF4%,20) = £864.10P7= £30(PVIFA4%,12) + £1,000(PVIF4%,12) = £906.15P12= £30(PVIFA4%,2) + £1,000(PVIF4%,2) = £981.14P13= £1,000All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths.Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond.12.Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 10 percent. If the YTM suddenly rises to 12 percent: P Evans= €50(PVIFA6%,4) + €1,000(PVIF6%,4) = €965.35P Troxel= €50(PVIFA6%,30) + €1,000(PVIF6%,30) = €862.35The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Evans% = (€965.35 – 1,000) / €1,000 = – 3.47%∆P Troxel% = (€862.35 – 1,000) / €1,000 = – 13.76%If the YTM suddenly falls to 8 percent:P Evans= €50(PVIFA4%,4) + €1,000(PVIF4%,4) = €1,036.30P Troxel= €50(PVIFA4%,30) + €1,000(PVIF4%,30) = €1,172.92∆P Evans% = (€1,036.30 – 1,000) / €1,000 = + 3.63%∆P Troxel% = (€1,172.92 – 1,000) / €1,000 = + 17.29%All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates.13.Initially, at a YTM of 7 percent, the prices of the two bonds are:P Busan= ฿25(PVIFA3.5%,16) + ฿1,000(PVIF3.5%,16) = ฿879.06P Iksan= ฿55(PVIFA3.5%,16) + ฿1,000(PVIF3.5%,16) = ฿1,241.88If the YTM rises from 7 percent to 9 percent:P Busan= ฿25(PVIFA4.5%,16) + ฿1,000(PVIF4.5%,16) = ฿775.32P Iksan= ฿55(PVIFA4.5%,16) + ฿1,000(PVIF4.5%,16) = ฿1,112.34The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Busan% = (฿775.32 – 879.06) / ฿879.06 = – 11.80%∆P Iksan% = (฿1,112.34 – 1,241.88) / ฿1,241.88 = – 10.43%If the YTM declines from 7 percent to 5 percent:P Busan= ฿25(PVIFA2.5%,16) + ฿1,000(PVIF2.5%,16) = ฿1,000.000P Iksan= ฿55(PVIFA2.5%,16) + ฿1,000(PVIF2.5%,16) = ฿1,391.65∆P Busan% = (฿1,000.00 – 879.06) / ฿879.06 = + 13.76%∆P Iksan% = (฿1,391.65 – 1,241.88) / ฿1,241.88 = + 12.06%All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.14.The bond price equation for this bond is:P0 = $1,040 = $45(PVIFA R%,18) + $1,000(PVIF R%,18)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.179%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 4.179% = 8.359%The current yield is:Current yield = Annual coupon payment / Price = $90 / $1,040 = 8.65%The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter:Effective annual yield = (1 + 0.04179)2– 1 = 8.532%15.The company should set the coupon rate on its new bonds equal to the required return. The required return can be observed in the market by finding the YTM on outstanding bonds of the company. So, the YTM on the bonds currently sold in the market is:P = 元1,100 = 元40(PVIFA R%,40) + 元1,000(PVIF R%,40)Using a spreadsheet, financial calculator, or trial and error we find:R = 3.5295%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 3.5295% = 7.059%16. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so one month has passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $72/2 × 2/6 = $12And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $1,140 – 12 = $1,12817. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are three months until the next coupon payment, so three months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = €65/2 × 3/6 = €16.25And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = €865 + 16.25 = €881.2518.To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as:Current yield = .0906 = $110/P0P0 = $110/.0906 = $1,214.13Now that we have the price of the bond, the bond price equation is:P = $1,214.13 = $110[(1 – (1/1.085)t ) / .085 ] + $1,000/1.085tWe can solve this equation for t as follows:$1,214.13 (1.085)t = $1,294.12 (1.085)t– 1,294.12 + 1,000294.12 = 79.99(1.085)t3.6769 = 1.085tt = log 3.6769 / log 1.085 = 15.96 ≈ 16 yearsThe bond has 16 years to maturity.19.The bond has 10 years to maturity, so the bond price equation is:P = $769.355 = $36.875(PVIFA R%,20) + $1,000(PVIF R%,20)Using a spreadsheet, financial calculator, or trial and error we find:R = 5.64%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 5.64% = 11.28%The current yield is the annual coupon payment divided by the bond price, so:Current yield = $73.75 / $769.355 = 9.59%The “EST Spread” column shows the difference between the YTM of the bond quoted and the YTM of the U.S. Treasury bond with a similar maturity. The column lists the spread in basis points. One basis point is one-hundredth of one percent, so 100 basis points equals one percent. The spread for this bond is 468 basis points, or 4.68%. This makes the equivalent Treasury yield:Equivalent Treasury yield = 11.28% – 4.68% = 6.60%20.We found the maturity of a bond in Problem 18. However, in this case, the maturity is indeterminate. A bond selling at par can have any length of maturity. In other words, when we solve the bond pricing equation as we did in Problem 18, the number of periods can be any positive number.Challenge21.To find the capital gains yield and the current yield, we need to find the price of the bond. Thecurrent price of Bond P and the price of Bond P in one year is:P: P0 = $100(PVIFA8%,5) + $1,000(PVIF8%,5) = $1,079.85P1 = $100(PVIFA8%,4) + $1,000(PVIF8%,4) = $1,066.24Current yield = $100 / $1,079.85 = 9.26%The capital gains yield is:Capital gains yield = (New price – Original price) / Original price Capital gains yield = ($1,066.24 – 1,079.85) / $1,079.85 = –1.26%The current price of Bond D and the price of Bond D in one year is:D: P0 = $60(PVIFA8%,5) + $1,000(PVIF8%,5) = $920.15P1 = $60(PVIFA8%,4) + $1,000(PVIF8%,4) = $933.76Current yield = $60 / $920.15 = 6.52%Capital gains yield = ($933.76 – 920.15) / $920.15 = +1.48%All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 8%, but this return is distributed differently between current income and capital gains.22.a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is theYTM. The bond price equation for this bond is:P0 = €1,150 = €80(PVIFA R%,10) + €1,000(PVIF R%,10)Using a spreadsheet, financial calculator, or trial and error we find:R = YTM = 5.97%b. To find our HPY, we need to find the price of the bond in two years. The price of the bond intwo years, at the new interest rate, will be:P2 = €80(PVIFA4.97%,8) + €1,000(PVIF4.97%,8) = €1,196.41To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were €80 each year for two years, and the price of the bond when we sold it. The equation to find our HPY is:P0 = €1,150 = €80(PVIFA R%,2) + €1,196.41(PVIF R%,2)Solving for R, we get:R = HPY = 8.89%The realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall.23.The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is:P M= €1,200(PVIFA5%,16)(PVIF5%,12) + €1,500(PVIFA5%,12)(PVIF5%,28) + €20,000(PVIF5%,40) P M= €13,474.20Notice that for the coupon payments of €1,500, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a €20,000 par value, therefore, the price of the bond is the PV of the par, or:P N= €20,000(PVIF5%,40) = €2,840.9124.To calculate this, we need to set up an equation with the callable bond equal to a weighted average of the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is: C2 = C1 X + C3(1 – X)8.25 = 6.50 X + 12(1 – X)8.25 = 6.50 X + 12 – 12 XX = 0.68182So, we invest about 68 percent of our money in Bond 1, and about 32 percent in Bond 3. This combination of bonds should have the same value as the callable bond, excluding the value of the call. So: P2= 0.68182P1 + 0.31819P3P2= 0.68182(106.375) + 0.31819(134.96875)P2= 115.4730The call value is the difference between this implied bond value and the actual bond price. So, the call value is:Call value = 115.4730 – 103.50 = 11.9730Assuming $1,000 par value, the call value is $119.73. 25.In general, this is not likely to happen, although it can (and did). The reason this bond has a negative YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not receive all the cash flows promised. A better measure of the return on a callable bond is the yield to call (YTC). The YTC calculation is the basically the same as the YTM calculation, but the number of periods is the number of periods until the call date. If the YTC were calculated on this bond, it would be positive.26.To find the present value, we need to find the real weekly interest rate. To find the real return, we need to use the effective annual rates in the Fisher equation. So, we find the real EAR is:(1 + R) = (1 + r)(1 + h)1 + .104 = (1 + r)(1 + .039)r = .0626 or 6.26%Now, to find the weekly interest rate, we need to find the APR. Using the equation for discrete compounding:EAR = [1 + (APR / m)]m– 1We can solve for the APR. Doing so, we get:APR = m[(1 + EAR)1/m– 1]APR = 52[(1 + .0626)1/52– 1]APR = .0607 or 6.07%So, the weekly interest rate is:Weekly rate = APR / 52Weekly rate = .0607 / 52Weekly rate = .0012 or 0.12%Now we can find the present value of the cost of the roses. The real cash flows are an ordinary annuity, discounted at the real interest rate. So, the present value of the cost of the roses is:PVA = C({1 – [1/(1 + r)]t } / r)PVA = $5({1 – [1/(1 + .0012)]30(52)} / .0012)PVA = $3,588.6627.To answer this question, we need to find the monthly interest rate, which is the APR divided by 12. We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate, so, the real effective annual interest rates, and the monthly interest rates for each account are:Stock account:(1 + R) = (1 + r)(1 + h)1 + .11 = (1 + r)(1 + .04)r = .0673 or 6.73%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0673)1/12– 1]APR = .0653 or 6.53%Monthly rate = APR / 12Monthly rate = .0653 / 12Monthly rate = .0054 or 0.54%Bond account:(1 + R) = (1 + r)(1 + h)1 + .07 = (1 + r)(1 + .04)r = .0288 or 2.88%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0288)1/12– 1]APR = .0285 or 2.85%Monthly rate = APR / 12Monthly rate = .0285 / 12Monthly rate = .0024 or 0.24%Now we can find the future value of the retirement account in real terms. The future value of each account will be:Stock account:FVA = C {(1 + r )t– 1] / r}FVA = £700{[(1 + .0054)360 – 1] / .0054]}FVA = £779,103.15Bond account:FVA = C {(1 + r )t– 1] / r}FVA = £300{[(1 + .0024)360 – 1] / .0024]}FVA = £170,316.78The total future value of the retirement account will be the sum of the two accounts, or:Account value = £779,103.15 + 170,316.78Account value = £949,419.93Now we need to find the monthly interest rate in retirement. We can use the same procedure that we used to find the monthly interest rates for the stock and bond accounts, so:(1 + R) = (1 + r)(1 + h)1 + .09 = (1 + r)(1 + .04)r = .0481 or 4.81%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0481)1/12– 1]APR = .0470 or 4.70%Monthly rate = APR / 12Monthly rate = .0470 / 12Monthly rate = .0039 or 00.39%N ow we can find the real monthly withdrawal in retirement. Using the present value of an annuity equation and solving for the payment, we find:PVA = C({1 – [1/(1 + r)]t } / r )£949,419.93 = C({1 – [1/(1 + .0039)]300 } / .0039)C = £5,388.21This is the real pound amount of the monthly withdrawals. The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal pound amount of the last withdrawal, we can increase the real pound withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal. So, the last withdrawal in nominal terms will be:FV = PV(1 + r)tFV = £5,388.21(1 + .04)(30 + 25)FV = £46,588.4228.In this problem, we need to calculate the future value of the annual savings after the five years of operations. The savings are the revenues minus the costs, or:Savings = Revenue – CostsSince the annual fee and the number of members are increasing, we need to calculate the effective growth rate for revenues, which is:Effective growth rate = (1 + .10)(1 + .03) – 1Effective growth rate = .1330 or 13.30%The revenue for the current year is the number of members times the annual fee, or:Current revenue = 500(元400)Current revenue = 元200,000The revenue will grow at 13.30 percent, and the costs will grow at 2 percent, so the savings each year for the next five years will be:Year Revenue Costs Savings1 元 226,600.00 元 81,600.00 元 145,000.002 256,737.80 83,232.00 173,505.803 290,883.93 84,896.64 205,987.294 329,571.49 86,594.57 242,976.925 373,404.50 88,326.46 285,078.03Now we can find the value of each year’s savings using the future value of a lump sum equation, so:FV = PV(1 + r)tYear Future Value1 元145,000.00(1 + .08)4 = 元197,270.902 元173,505.80(1 + .08)3 = 218,567.343 元205,978.29(1 + .08)2 = 240,263.574 元242,976.92(1 + .08)1 = 262,415.075 285,078.03Total future value of savings = 元1,203,594.91He will spend 元500,000 on a luxury boat, so the value of his account will be:Value of account = 元1,203,594.91 – 500,000Value of account = 元703,594.91Now we can use the present value of an annuity equation to find the payment. Doing so, we find:PVA = C({1 – [1/(1 + r)]t } / r )元703,591.51 = C({1 – [1/(1 + .08)]16 } / .08)C = 元79,489.57。
罗斯《公司理财》第9版笔记和课后习题(含考研真题)详解[视频详解](折现现金流量估价)【圣才出品】
【圣才出品】](https://img.taocdn.com/s3/m/810ed282482fb4daa58d4bf0.png)
罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第4章折现现金流量估价[视频讲解]4.1复习笔记当前的1美元与未来的1美元的价值是不同的，因为当前1美元用于投资，在未来可以得到更多，而且未来的1美元具有不确定性。
这种区别正是“货币的时间价值”。
货币的时间价值概念是金融投资和融资的基石之一，资本预算、项目决策、融资管理和兼并等领域均有涉及。
因此有必要理解和掌握相关的现值、终值、年金和永续年金的概念和计算公式。
1．现值与净现值现值是未来资金在当前的价值，是把未来的现金流按照一定的贴现率贴现到当前的价值。
以单期为例，一期后的现金流的现值：其中，C1是一期后的现金流，r是适当贴现率。
在多期的情况下，求解PV的公式可写为：其中，C T是在T期的现金流，r是适当贴现率。
净现值的计算公式为：NPV=-成本+PV。
也就是说，净现值NPV是这项投资未来现金流的现值减去成本的现值所得的结果。
一种定量的财务决策方法是净现值分析法。
产生N期现金流的投资项目的净现值为：NPV=其中，-C0是初始现金流，由于它代表了一笔投资，即现金流出，因而是负值。
2．终值一笔投资在多期以后终值的一般计算公式可以写为：FV=C0×（1+r）T其中，C0是期初投资的金额，r是利息率，T是资金投资持续的期数。
一项投资每年按复利计息m次的年末终值为：其中：C0是投资者的初始投资；r是名义年利率。
当m趋近于无限大时，则是连续复利计息，这时T年后的终值可以表示为：C0×e rT。
连续复利在高级金融中有广泛的应用。
3．名义利率和实际利率名义年利率是不考虑年内复利计息的，不同的银行或金融机构有不同的称谓，比较通用的是年百分比利率（APR）；实际利率（EAR）是指在年内考虑复利计息的，然后折算成一年的利率。
名义利率和实际利率之间的差别在于名义利率只有给出计息间隔期下才有意义。
4．年金年金是指一系列稳定有规律的，持续一段固定时期的现金收付活动，即在一定期间内，每隔相同时期（一年、半年或一季等）收入或支出相等金额的款项。
罗斯《公司理财》英文习题答案DOCchap004
公司理财习题答案第四章Chapter 4: Net Present Value4.1 a. $1,000 ⨯ 1.0510 = $1,628.89b. $1,000 ⨯ 1.0710 = $1,967.15c. $1,000 ⨯ 1.0520 = $2,653.30d. Interest compounds on the I nterest already earned. Therefore, the interest earnedin part c, $1,653.30, is more than double the amount earned in part a, $628.89.4.2 a. $1,000 / 1.17 = $513.16b. $2,000 / 1.1 = $1,818.18c. $500 / 1.18 = $233.254.3 You can make your decision by computing either the present value of the $2,000 that youcan receive in ten years, or the future value of the $1,000 that you can receive now.Present value: $2,000 / 1.0810 = $926.39Future value: $1,000 ⨯ 1.0810 = $2,158.93Either calculation indicates you should take the $1,000 now.4.4 Since this bond has no interim coupon payments, its present value is simply the presentvalue of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.PV = $1,000 /1.125 = $92.304.5 PV = $1,500,000 / 1.0827 = $187,780.234.6 a. At a discount rate of zero, the future value and present value are always the same.Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV.Therefore, the values of the options are $10,000 and $20,000, respectively. Youshould choose the second option.b. Option one: $10,000 / 1.1 = $9,090.91Option two: $20,000 / 1.15 = $12,418.43Choose the second option.c. Option one: $10,000 / 1.2 = $8,333.33Option two: $20,000 / 1.25 = $8,037.55Choose the first option.d. You are indifferent at the rate that equates the PVs of the two alternatives. Youknow that rate must fall between 10% and 20% because the option you wouldchoose differs at these rates. Let r be the discount rate that makes you indifferentbetween the options.$10,000 / (1 + r) = $20,000 / (1 + r)5(1 + r)4 = $20,000 / $10,000 = 21 + r = 1.18921r = 0.18921 = 18.921%4.7 PV of Joneses’ offer = $150,000 / (1.1)3 = $112,697.22Since the PV of Joneses’ offer is less than Smiths’ offer, $115,000, you should chooseSmiths’ offer.4.8 a. P0 = $1,000 / 1.0820 = $214.55b. P10 = P0 (1.08)10 = $463.20c. P15 = P0 (1.08)15 = $680.594.9 The $1,000 that you place in the account at the end of the first year will earn interest for sixyears. The $1,000 that you place in the account at the end of the second year will earninterest for five years, etc. Thus, the account will have a balance of$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3= $6,714.614.10 PV = $5,000,000 / 1.1210 = $1,609,866.184.11 a. The cost of investment is $900,000.PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123= $875,865.52Since the PV of cash inflows is less than the cost of investment, you should notmake the investment.b. NPV = -$900,000 + $875,865.52= -$24,134.48c. NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000 / 1.113= $-4,033.18Since the NPV is still negative, you should not make the investment.4.12 NPV = -($340,000 + $10,000) + ($100,000 - $10,000) / 1.1+ $90,000 / 1.12 + $90,000 / 1.13 + $90,000 / 1.14 + $100,000 / 1.15= -$2,619.98Since the NPV is negative, you should not buy it.If the relevant cost of capital is 9 percent,NPV = -$350,000 + $90,000 / 1.09 + $90,000 / 1.092 + $90,000 / 1.093+ $90,000 / 1.094 + $100,000 / 1.095= $6,567.93Since the NPV is positive, you should buy it.4.13 a. Profit = PV of revenue - Cost = NPVNPV = $90,000 / 1.15 - $60,000 = -$4,117.08No, the firm will not make a profit.b. Find r that makes zero NPV.$90,000 / (1+r)5 - $60,000 = $0(1+r)5 = 1.5r = 0.08447 = 8.447%4.14 The future value of the decision to own your car for one year is the sum of the trade-invalue and the benefit from owning the car. Therefore, the PV of the decision to own thecar for one year is$3,000 / 1.12 + $1,000 / 1.12 = $3,571.43Since the PV of the roommate’s offer, $3,500, is lower than the aunt’s offer, you shouldaccept aunt’s offer.4.15 a. $1.000 (1.08)3 = $1,259.71b. $1,000 [1 + (0.08 / 2)]2 ⨯ 3 = $1,000 (1.04)6 = $1,265.32c. $1,000 [1 + (0.08 / 12)]12 ⨯ 3 = $1,000 (1.00667)36 = $1,270.24d. $1,000 e0.08 ⨯ 3 = $1,271.25公司理财习题答案第四章e. The future value increases because of the compounding. The account is earninginterest on interest. Essentially, the interest is added to the account balance at theend of every compounding period. During the next period, the account earnsinterest on the new balance. When the compounding period shortens, the balancethat earns interest is rising faster.4.16 a. $1,000 e0.12 ⨯ 5 = $1,822.12b. $1,000 e0.1 ⨯ 3 = $1,349.86c. $1,000 e0.05 ⨯ 10 = $1,648.72d. $1,000 e0.07 ⨯ 8 = $1,750.674.17 PV = $5,000 / [1+ (0.1 / 4)]4 ⨯ 12 = $1,528.364.18 Effective annual interest rate of Bank America= [1 + (0.041 / 4)]4 - 1 = 0.0416 = 4.16%Effective annual interest rate of Bank USA= [1 + (0.0405 / 12)]12 - 1 = 0.0413 = 4.13%You should deposit your money in Bank America.4.19 The price of the consol bond is the present value of the coupon payments. Apply theperpetuity formula to find the present value. PV = $120 / 0.15 = $8004.20 Quarterly interest rate = 12% / 4 = 3% = 0.03Therefore, the price of the security = $10 / 0.03 = $333.334.21 The price at the end of 19 quarters (or 4.75 years) from today = $1 / (0.15 ÷ 4) = $26.67The current price = $26.67 / [1+ (.15 / 4)]19 = $13.254.22 a. $1,000 / 0.1 = $10,000b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus,the value of the perpetuity is $5,000 / 1.1 = $4,545.45.c. $2,420 / 0.1 = $24,200 is the value two years from now of the perpetual stream.Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.4.23 The value at t = 8 is $120 / 0.1 = $1,200.Thus, the value at t = 5 is $1,200 / 1.13 = $901.58.4.24 P = $3 (1.05) / (0.12 - 0.05) = $45.004.25 P = $1 / (0.1 - 0.04) = $16.674.26 The first cash flow will be generated 2 years from today.The value at the end of 1 year from today = $200,000 / (0.1 - 0.05) = $4,000,000.Thus, PV = $4,000,000 / 1.1 = $3,636,363.64.4.27 A zero NPV-$100,000 + $50,000 / r = 0-r = 0.54.28 Apply the NPV technique. Since the inflows are an annuity you can use the present valueof an annuity factor.NPV = -$6,200 + $1,200 8A1.0= -$6,200 + $1,200 (5.3349)= $201.88Yes, you should buy the asset.4.29 Use an annuity factor to compute the value two years from today of the twenty payments.Remember, the annuity formula gives you the value of the stream one year before the first payment. Hence, the annuity factor will give you the value at the end of year two of the stream of payments. Value at the end of year two = $2,000 20A08.0= $2,000 (9.8181)= $19,636.20The present value is simply that amount discounted back two years.PV = $19,636.20 / 1.082 = $16,834.884.30 The value of annuity at the end of year five= $500 15A = $500 (5.84737) = $2,923.6915.0The present value = $2,923.69 / 1.125 = $1,658.984.31 The easiest way to do this problem is to use the annuity factor. The annuity factor must beequal to $12,800 / $2,000 = 6.4; remember PV =C A t r. The annuity factors are in theappendix to the text. To use the factor table to solve this problem, scan across the rowlabeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%.You can find a more precise answer by interpolating between nine and ten percent.10% ⎤ 6.1446 ⎤a ⎡ r ⎥bc ⎡ 6.4 ⎪ d⎣ 9% ⎦⎣ 6.4177 ⎦By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d.(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)r = 9.0648%The exact value could be obtained by solving the annuity formula for the interest rate.Sophisticated calculators can compute the rate directly as 9.0626%.公司理财习题答案第四章4.32 a. The annuity amount can be computed by first calculating the PV of the $25,000which you need in five years. That amount is $17,824.65 [= $25,000 / 1.075].Next compute the annuity which has the same present value.$17,824.65 = C 5A.007$17,824.65 = C (4.1002)C = $4,347.26Thus, putting $4,347.26 into the 7% account each year will provide $25,000 fiveyears from today.b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 /1.075 = $17,824.65The formula for future value of any annuity can be used to solve the problem (seefootnote 14 of the text).4.33The amount of loan is $120,000 ⨯ 0.85 = $102,000.20C A= $102,000.010The amount of equal installments isC = $102,000 / 20A = $102,000 / 8.513564 = $11,980.8810.04.34 The present value of salary is $5,000 36A = $150,537.53.001The present value of bonus is $10,000 3A = $23,740.42 (EAR = 12.68% is used since.01268bonuses are paid annually.)The present value of the contract = $150,537.53 + $23,740.42 = $174,277.944.35 The amount of loan is $15,000 ⨯ 0.8 = $12,000.C 48A = $12,0000067.0The amount of monthly installments isC = $12,000 / 48A = $12,000 / 40.96191 = $292.960067.04.36 Option one: This cash flow is an annuity due. To value it, you must use the after-taxamounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of$115,200 to obtain the value of this option.Value = $115,200 + $115,200 30A10.0= $115,200 + $115,200 (9.4269)= $1,201,178.88Option two: This option is valued similarly. You are able to have $446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-taxpayment is $72,759.60 [= $101,055 (1 - 0.28)].Value = $446,000 + $72,759.60 30A.010= $446,000 + $72,759.60 (9.4269)= $1,131,897.47Since option one has a higher PV, you should choose it.4.37 The amount of loan is $9,000. The monthly payment C is given by solving the equation: C 60008.0A = $9,000 C = $9,000 / 47.5042 = $189.46In October 2000, Susan Chao has 35 (= 12 ⨯ 5 - 25) monthly payments left, including the one due in October 2000.Therefore, the balance of the loan on November 1, 2000 = $189.46 + $189.46 34008.0A = $189.46 + $189.46 (29.6651) = $5,809.81Thus, the total amount of payoff = 1.01 ($5,809.81) = $5,867.91 4.38 Let r be the rate of interest you must earn. $10,000(1 + r)12 = $80,000 (1 + r)12 = 8 r = 0.18921 = 18.921%4.39 First compute the present value of all the payments you must make for your children’s education. The value as of one year before matriculation of one child’s education is$21,000 415.0A= $21,000 (2.8550) = $59,955. This is the value of the elder child’s education fourteen years from now. It is the value of the younger child’s education sixteen years from today. The present value of these is PV = $59,955 / 1.1514 + $59,955 / 1.1516 = $14,880.44You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,880.44. Payment = $14,880.44 / 1515.0A = $14,880.44 / 5.8474 = $2,544.804.40 The NPV of the policy isNPV = -$750 306.0A - $800306.0A / 1.063 + $250,000 / [(1.066) (1.0759)] = -$2,004.76 - $1,795.45 + $3,254.33= -$545.88 Therefore, you should not buy the policy.4.41 The NPV of the lease offer isNPV = $120,000 - $15,000 - $15,000 908.0A - $25,000 / 1.0810= $105,000 - $93,703.32 - $11,579.84 = -$283.16 Therefore, you should not accept the offer.4.42 This problem applies the growing annuity formula. The first payment is $50,000(1.04)2(0.02) = $1,081.60. PV = $1,081.60 [1 / (0.08 - 0.04) - {1 / (0.08 - 0.04)}{1.04 / 1.08}40]= $21,064.28 This is the present value of the payments, so the value forty years from today is $21,064.28 (1.0840) = $457,611.46公司理财习题答案第四章4.43 Use the discount factors to discount the individual cash flows. Then compute the NPV ofthe project. Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is 2.6198 (= 4.3553 - 1.7355).Year Cash Flow Factor PV 1 $700 0.9091 $636.37 2 900 0.8264 743.76 3 1,000 ⎤ 4 1,000 ⎥ 2.6198 2,619.80 5 1,000 ⎥ 6 1,000 ⎦ 7 1,250 0.5132 641.50 8 1,375 0.4665 641.44 Total $5,282.87NPV = -$5,000 + $5,282.87 = $282.87 Purchase the machine.4.44 Weekly inflation rate = 0.039 / 52 = 0.00075 Weekly interest rate = 0.104 / 52 = 0.002 PV = $5 [1 / (0.002 - 0.00075)] {1 – [(1 + 0.00075) / (1 + 0.002)]52 ⨯ 30} = $3,429.384.45 Engineer:NPV = -$12,000 405.0A + $20,000 / 1.055 + $25,000 / 1.056 - $15,000 / 1.057- $15,000 / 1.058 + $40,000 2505.0A / 1.058= $352,533.35 Accountant:NPV = -$13,000 405.0A + $31,000 3005.0A / 1.054= $345,958.81 Become an engineer.After your brother announces that the appropriate discount rate is 6%, you can recalculate the NPVs. Calculate them the same way as above except using the 6% discount rate. Engineer NPV = $292,419.47 Accountant NPV = $292,947.04Your brother made a poor decision. At a 6% rate, he should study accounting.4.46 Since Goose receives his first payment on July 1 and all payments in one year intervalsfrom July 1, the easiest approach to this problem is to discount the cash flows to July 1 then use the six month discount rate (0.044) to discount them the additional six months. PV = $875,000 / (1.044) + $650,000 / (1.044)(1.09) + $800,000 / (1.044)(1.092) + $1,000,000 / (1.044)(1.093) + $1,000,000/(1.044)(1.094) + $300,000 / (1.044)(1.095)+ $240,000 1709.0A / (1.044)(1.095) + $125,000 1009.0A / (1.044)(1.0922) = $5,051,150Remember that the use of annuity factors to discount the deferred payments yields the value of the annuity stream one period prior to the first payment. Thus, the annuity factor applied to the first set of deferred payments gives the value of those payments on July 1 of 1989. Discounting by 9% for five years brings the value to July 1, 1984. The use of the six month discount rate (4.4%) brings the value of the payments to January 1, 1984. Similarly, the annuity factor applied to the second set of deferred payments yields the value of those payments in 2006. Discounting for 22 years at 9% and for six months at 4.4% provides the value at January 1, 1984.The equivalent five-year, annual salary is the annuity that solves: $5,051,150 = C 509.0A C = $5,051,150/3.8897C = $1,298,596The student must be aware of possible rounding errors in this problem. The differencebetween 4.4% semiannual and 9.0% and for six months at 4.4% provides the value at January 1, 1984. 4.47 PV = $10,000 + ($35,000 + $3,500) [1 / (0.12 - 0.04)] [1 - (1.04 / 1.12) 25 ]= $415,783.604.48 NPV = -$40,000 + $10,000 [1 / (0.10 - 0.07)] [1 - (1.07 / 1.10)5 ] = $3,041.91 Revise the textbook.4.49The amount of the loan is $400,000 (0.8) = $320,000 The monthly payment is C = $320,000 / 3600067.0.0A = $ 2,348.10 Thirty years of payments $ 2,348.10 (360) = $ 845,316.00 Eight years of payments $2,348.10 (96) = $225,417.60 The difference is the balloon payment of $619,898.404.50 The lease payment is an annuity in advanceC + C 2301.0A = $4,000 C (1 + 20.4558) = $4,000 C = $186.424.51 The effective annual interest rate is[ 1 + (0.08 / 4) ] 4 – 1 = 0.0824The present value of the ten-year annuity is PV = 900 100824.0A = $5,974.24 Four remaining discount periodsPV = $5,974.24 / (1.0824) 4 = $4,352.43公司理财习题答案第四章4.52The present value of Ernie’s retirement incomePV = $300,000 20A / (1.07) 30 = $417,511.5407.0The present value of the cabinPV = $350,000 / (1.07) 10 = $177,922.25The present value of his savingsPV = $40,000 10A = $280,943.26.007In present value terms he must save an additional $313,490.53 In future value termsFV = $313,490.53 (1.07) 10 = $616,683.32He must saveC = $616.683.32 / 20A = $58,210.5407.0。
英文版罗斯公司理财习题答案ChapWord版
CHAPTER 8MAKING CAPITAL INVESTMENT DECISIONSAnswers to Concepts Review and Critical Thinking Questions1.In this context, an opportunity cost refers to the value of an asset or other input that will be used in aproject. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire.2. a.Yes, the reduction in the sales of the company’s other products, referred to as erosion, andshould be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product.b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. Theseare costs of the new product line. However, if these expenditures have already occurred, they are sunk costs and are not included as incremental cash flows.c. No, the research and development costs should not be treated as incremental cash flows. Thecosts of research and development undertaken on the product during the past 3 years are sunk costs and should not be included in the evaluation of the project. Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project.d. Yes, the annual depreciation expense should be treated as an incremental cash flow.Depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects cash flow, it decreases a firm’s net income and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation.e.No, dividend payments should not be treated as incremental cash flows. A firm’s decision topay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, it is not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters.f.Yes, the resale value of plant and equipment at the end of a project’s life should be treated as anincremental cash flow. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create gains or lossesthat result in either a tax credit or liability.g.Yes, salary and medical costs for production employees hired for a project should be treated asincremental cash flows. The salaries of all personnel connected to the project must be included as costs of that project.3.Item I is a relevant cost because the opportunity to sell the land is lost if the new golf club is produced. Item II is also relevant because the firm must take into account the erosion of sales of existing products when a new product is introduced. If the firm produces the new club, the earnings from the existing clubs will decrease, effectively creating a cost that must be included in the decision.Item III is not relevant because the costs of Research and Development are sunk costs. Decisions made in the past cannot be changed. They are not relevant to the production of the new clubs.4.For tax purposes, a firm would choose MACRS because it provides for larger depreciationdeductions earlier. These larger deductions reduce taxes, but have no other cash consequences.Notice that the choice between MACRS and straight-line is purely a time value issue; the total depreciation is the same; only the timing differs.5.It’s probably only a mild over-simplification. Current liabilities will all be paid, presumably. Thecash portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold, of course. Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end of the project’s life) acts to increase working capital. These effects tend to offset one another.6.Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since anyone particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure remains unchanged, financing cost s are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone principle.7.The EAC approach is appropriate when comparing mutually exclusive projects with different livesthat will be replaced when they wear out. This type of analysis is necessary so that the projects havea common life span over which they can be compared; in effect, each project is assumed to existover an infinite horizon of N-year repeating projects. Assuming that this type of analysis is valid implies that the project cash flows remain the same forever, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible effects of future technology improvement that could alter the project cash flows.8.Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thusdepreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield, t c D. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental aftertax cash flows.9.There are two particularly important considerations. The first is erosion. Will the “essentialized”book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s perspective) or new books (not good). The concern arises any time there is an active market for used product.10.Definitely. The damage to Porsche’s reputation is definitely a factor the company needed to consider.If the reputation was damaged, the company would have lost sales of its existing car lines.11.One company may be able to produce at lower incremental cost or market better. Also, of course,one of the two may have made a mistake!12.Porsche would recognize that the outsized profits would dwindle as more products come to marketand competition becomes more intense.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basicing the tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = [($5 × 2,000 – ($2 × 2,000)](1 – 0.35) + 0.35($10,000/5)OCF = $4,600So, the NPV of the project is:NPV = –$10,000 + $4,600(PVIFA17%,5)NPV = $4,7172.We will use the bottom-up approach to calculate the operating cash flow for each year. We also mustbe sure to include the net working capital cash flows each year. So, the total cash flow each year will be:Year 1 Year 2 Year 3 Year 4 Sales Rs.7,000 Rs.7,000 Rs.7,000 Rs.7,000Costs 2,000 2,000 2,000 2,000Depreciation 2,500 2,500 2,500 2,500EBT Rs.2,500 Rs.2,500 Rs.2,500 Rs.2,500Tax 850 850 850 850Net income Rs.1,650 Rs.1,650 Rs.1,650 Rs.1,650OCF 0 Rs.4,150 Rs.4,150 Rs.4,150 Rs.4,150Capital spending –Rs.10,000 0 0 0 0NWC –200 –250 –300 –200 950Incremental cashflow –Rs.10,200 Rs.3,900 Rs.3,850 Rs.3,950 Rs.5,100The NPV for the project is:NPV = –Rs.10,200 + Rs.3,900 / 1.10 + Rs.3,850 / 1.102 + Rs.3,950 / 1.103 + Rs.5,100 / 1.104NPV = Rs.2,978.333. Using the tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = (R2,400,000 – 960,000)(1 – 0.30) + 0.30(R2,700,000/3)OCF = R1,278,000So, the NPV of the project is:NPV = –R2,700,000 + R1,278,000(PVIFA15%,3)NPV = R217,961.704.The cash outflow at the beginning of the project will increase because of the spending on NWC. Atthe end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be:Year Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,278,0002 1,278,0003 1,725,000 = R1,278,000 + 300,000 + 210,000 + (0 – 210,000)(.30)And the NPV of the project is:NPV = –R3,000,000 + R1,278,000(PVIFA15%,2) + (R1,725,000 / 1.153)NPV = R211,871.465. First we will calculate the annual depreciation for the equipment necessary for the project. Thedepreciation amount each year will be:Year 1 depreciation = R2.7M(0.3330) = R899,100Year 2 depreciation = R2.7M(0.4440) = R1,198,800Year 3 depreciation = R2.7M(0.1480) = R399,600So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is:Book value in 3 years = R2.7M – (R899,100 + 1,198,800 + 399,600)Book value in 3 years = R202,500The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = R202,500 + (R202,500 – 210,000)(0.30)Aftertax salvage value = R207,750To calculate the OCF, we will use the tax shield approach, so the cash flow each year is:OCF = (Sales – Costs)(1 – t C) + t C DepreciationYear Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,277,730.00 = (R1,440,000)(.70) + 0.30(R899,100)2 1,367,640.00 = (R1,440,000)(.70) + 0.30(R1,198,800)3 1,635,630.00 = (R1,440,000)(.70) + 0.30(R399,600) + R207,750 + 300,000Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project.The NPV of the project with these assumptions is:NPV = – R3.0M + (R1,277,730/1.15) + (R1,367,640/1.152) + (R1,635,630/1.153)NPV = R220,655.206. First, we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation charge = €925,000/5Annual depreciation charge = €185,000The aftertax salvage value of the equipment is:Aftertax salvage value = €90,000(1 – 0.35)Aftertax salvage value = €58,500Using the tax shield approach, the OCF is:OCF = €360,000(1 – 0.35) + 0.35(€185,000)OCF = €298,750Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –€925,000 + 125,000 + €298,750(PVIFA IRR%,5) + [(€58,500 – 125,000) / (1+IRR)5]IRR = 23.85%7.First, we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation = £390,000/5Annual depreciation = £78,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:Aftertax salvage value = £60,000(1 – 0.34)Aftertax salvage value = £39,600Using the tax shield approach, we find the OCF for the project is:OCF = £120,000(1 – 0.34) + 0.34(£78,000)OCF = £105,720Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –£390,000 – 28,000 + £105,720(PVIFA10%,5) + [(£39,600 + 28,000) / 1.15]NPV = £24,736.268.To find the BV at the end of four years, we need to find the accumulated depreciation for the firstfour years. We could calculate a table with the depreciation each year, but an easier way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get:BV4 = $9,300,000 – 9,300,000(0.2000 + 0.3200 + 0.1920 + 0.1150)BV4 = $1,608,900The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = $2,100,000 + ($1,608,900 – 2,100,000)(.40)Aftertax salvage value = $1,903,5609. We will begin by calculating the initial cash outlay, that is, the cash flow at Time 0. To undertake theproject, we will have to purchase the equipment and increase net working capital. So, the cash outlay today for the project will be:Equipment –€2,000,000NWC –100,000Total –€2,100,000Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow each year will be:Sales €1,200,000Costs 300,000Depreciation 500,000EBT €400,000Tax 140,000Net income €260,000The operating cash flow is:OCF = Net income + DepreciationOCF = €260,000 + 500,000OCF = €760,000To find the NPV of the project, we add the present value of the project cash flows. We must be sure to add back the net working capital at the end of the project life, since we are assuming the net working capital will be recovered. So, the project NPV is:NPV = –€2,100,000 + €760,000(PVIFA14%,4) + €100,000 / 1.144NPV = €173,629.3810.We will need the aftertax salvage value of the equipment to compute the EAC. Even though theequipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $20,000(1 – 0.35) = $13,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = – $34,000(1 – 0.35) + 0.35($210,000/3) = $2,400NPV = –$210,000 + $2,400(PVIFA14%,3) + ($13,000/1.143) = –$195,653.45EAC = –$195,653.45 / (PVIFA14%,3) = –$84,274.10And the OCF and NPV for Techron II is:OCF = – $23,000(1 – 0.35) + 0.35($320,000/5) = $7,450NPV = –$320,000 + $7,450(PVIFA14%,5) + ($13,000/1.145) = –$287,671.75EAC = –$287,671.75 / (PVIFA14%,5) = –$83,794.05The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.。
Cha08 罗斯公司理财第九版原版书课后习题
Earlier in the chapter, we saw how bonds were rated based on their credit risk. What you will find if you start looking at bonds of different ratings is that lower-rated bonds have higher yields.We stated earlier in this chapter that a bond’s yield is calculated assuming that all the promised payments will be made. As a result, it is really a promised yield, and it may or may not be what you will earn. In particular, if the issuer defaults, your actual yield will be lower, probably much lower. This fact is particularly important when it comes to junk bonds. Thanks to a clever bit of marketing, such bonds are now commonly called high-yield bonds, which has a much nicer ring to it; but now you recognize that these are really high promised yield bonds.Next, recall that we discussed earlier how municipal bonds are free from most taxes and, as a result, have much lower yields than taxable bonds. Investors demand the extra yield on a taxable bond as compensation for the unfavorable tax treatment. This extra compensation is the taxability premium.Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an enormous number of bond issues, most of which do not trade on a regular basis. As a result, if you wanted to sell quickly, you would probably not get as good a price as you could otherwise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity premium on top of all the other premiums we have discussed. As a result, all else being the same, less liquid bonds will have higher yields than more liquid bonds.ConclusionIf we combine everything we have discussed, we find that bond yields represent the combined effect of no fewer than six factors. The first is the real rate of interest. On top of the real rate are five premiums representing compensation for (1) expected future inflation, (2) interest rate risk, (3) default risk, (4) taxability, and (5) lack of liquidity. As a result, determining the appropriate yield on a bond requires careful analysis of each of these factors.Summary and ConclusionsThis chapter has explored bonds, bond yields, and interest rates. We saw that:1. Determining bond prices and yields is an application of basic discounted cash flow principles.2. Bond values move in the direction opposite that of interest rates, leading to potential gains orlosses for bond investors.3. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no riskof default, whereas so-called junk bonds have substantial default risk.4. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result,bond price and volume information can be difficult to find for some types of bonds.5. Bond yields and interest rates reflect six different factors: the real interest rate and fivepremiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability, and lack of liquidity.In closing, we note that bonds are a vital source of financing to governments and corporations of all types. Bond prices and yields are a rich subject, and our one chapter, necessarily, touches on only the most important concepts and ideas. There is a great deal more we could say, but, instead, we will move on to stocks in our next chapter.Concept Questions1. Treasury Bonds Is it true that a U.S. Treasury security is risk-free?2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year21. Using Bond Quotes Suppose the following bond quote for IOU Corporation appears in thefinancial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is April 15, 2010. What is the yield to maturity of the bond? What is the current yield?22. Finding the Maturity You’ve just found a 10 percent coupon bond on the market that sells forpar value. What is the maturity on this bond?CHALLENGE (Questions 23–30)23. Components of Bond Returns Bond P is a premium bond with a 9 percent coupon. Bond D isa 5 percent coupon bond currently selling at a discount. Both bonds make annual payments, havea YTM of 7 percent, and have five years to maturity. What is the current yield for Bond P? For BondD? If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D? Explain your answers and the interrelationship among the various types of yields.24. Holding Period Yield The YTM on a bond is the interest rate you earn on your investment ifinterest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).1. Suppose that today you buy a 9 percent annual coupon bond for $1,140. The bond has 10years to maturity. What rate of return do you expect to earn on your investment?2. Two years from now, the YTM on your bond has declined by 1 percent, and you decide tosell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?25. Valuing Bonds The Morgan Corporation has two different bonds currently outstanding. Bond Mhas a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of20 years; it makes no coupon payments over the life of the bond. If the required return on boththese bonds is 8 percent compounded semiannually, what is the current price of Bond M? Of Bond N?26. R eal Cash Flows When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place freshflowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $8.Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died.Assume that the EAR is 10.7 percent. Also, assume that the price of the flowers will increase at 3.5 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.27. Real Cash Flows You are planning to save for retirement over the next 30 years. To save forretirement, you will invest $800 a month in a stock account in real dollars and $400 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an 8 percent effective return. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuminga 25-year withdrawal period? What is the nominal dollar amount of your last withdrawal?28. Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges hiscustomers an annual fee of $500 and has an existing customer base of 500. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of3 percent for the next five years. The overall expenses of running the health club are $75,000 ayear and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul2. How many of the coupon bonds must East Coast Yachts issue to raise the $40 million? Howmany of the zeroes must it issue?3. In 20 years, what will be the principal repayment due if East Coast Yachts issues the couponbonds? What if it issues the zeroes?4. What are the company’s considerations in issuing a coupon bond compared to a zero couponbond?5. Suppose East Coast Yachts issues the coupon bonds with a make-whole call provision. Themake-whole call rate is the Treasury rate plus .40 percent. If East Coast calls the bonds in 7 years when the Treasury rate is 5.6 percent, what is the call price of the bond? What if it is 9.1 percent?6. Are investors really made whole with a make-whole call provision?7. After considering all the relevant factors, would you recommend a zero coupon issue or aregular coupon issue? Why? Would you recommend an ordinary call feature or a make-whole call feature? Why?。
罗斯-公司理财-英文练习题-附带答案-第九章
罗斯-公司理财-英文练习题-附带答案-第九章CHAPTER 9Risk Analysis, Real Options, and Capital Budgeting Multiple Choice Questions:I. DEFINITIONSSCENARIO ANALYSISb 1. An analysis of what happens to the estimate of the net present value when you examinea number of different likely situations is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasySENSITIVITY ANALYSISc 2. An analysis of what happens to the estimate of net present value when only onevariable is changed is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasySIMULATION ANALYSISd 3. An analysis which combines scenario analysis with sensitivity analysis is called _____analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasyBREAK-EVEN ANALYSISe 4. An analysis of the relationship between the sales volume and various measures ofprofitability is called _____ analysis.a. forecastingb. scenarioc. sensitivityd. simulatione. break-evenDifficulty level: EasyVARIABLE COSTSa 5. Variable costs:a. change in direct relationship to the quantity of output produced.b. are constant in the short-run regardless of the quantity of output produced.c. reflect the change in a variable when one more unit of output is produced.d. are subtracted from fixed costs to compute the contribution margin.e. form the basis that is used to determine the degree of operating leverage employed by afirm.Difficulty level: EasyFIXED COSTSb 6. Fixed costs:a. change as the quantity of output produced changes.b. are constant over the short-run regardless of the quantity of output produced.c. reflect the change in a variable when one more unit of output is produced.d. are subtracted from sales to compute the contribution margin.e. can be ignored in scenario analysis since they are constant over the life of a project.Difficulty level: EasyACCOUNTING BREAK-EVENc 7. The sales level that results in a project’s net income exactly equaling zero is called the_____ break-even.a. operationalb. leveragedc. accountingd. cashe. present valueDifficulty level: EasyPRESENT VALUE BREAK-EVENe 8. The sales level that results in a project’s net present value exactly equaling zero iscalled the _____ break-even.a. operationalb. leveragedc. accountingd. cashe. present valueDifficulty level: EasyII. CONCEPTSSCENARIO ANALYSISb 9. Conducting scenario analysis helps managers see the:a. impact of an individual variable on the outcome of a project.b. potential range of outcomes from a proposed project.c. changes in long-term debt over the course of a proposed project.d. possible range of market prices for their stock over the life of a project.e. allocation distribution of funds for capital projects under conditions of hard rationing.Difficulty level: EasySENSITIVITY ANALYSISb 10. Sensitivity analysis helps you determine the:a. range of possible outcomes given possible ranges for every variable.b. degree to which the net present value reacts to changes in a single variable.c. net present value given the best and the worst possible situations.d. degree to which a project is reliant upon the fixed costs.e. level of variable costs in relation to the fixed costs of a project.Difficulty level: EasySENSITIVITY ANALYSISc 11. As the degree of sensitivity of a project to a single variable rises, the:a. lower the forecasting risk of the project.b. smaller the range of possible outcomes given a pre-defined range of values for theinput.c. more attention management should place on accurately forecasting the future value ofthat variable.d. lower the maximum potential value of the project.e. lower the maximum potential loss of the project.Difficulty level: MediumSENSITIVITY ANALYSISc 12. Sensitivity analysis is conducted by:a. holding all variables at their base level and changing the required rate of returnassigned to a project.b. changing the value of two variables to determine their interdependency.c. changing the value of a single variable and computing the resulting change in thecurrent value of a project.d. assigning either the best or the worst possible value to each variable and comparing theresults to those achieved by the base case.e. managers after a project has been implemented to determine how each variable relatesto the level of output realized.Difficulty level: MediumSENSITIVITY ANALYSISd 13. To ascertain whether the accuracy of the variable cost estimate for a project will havemuch effect on the final outcome of the project, you should probably conduct _____analysis.a. leverageb. scenarioc. break-evend. sensitivitye. cash flowDifficulty level: EasySIMULATIONd 14. Simulation analysis is based on assigning a _____ and analyzing the results.a. narrow range of values to a single variableb. narrow range of values to multiple variables simultaneouslyc. wide range of values to a single variabled. wide range of values to multiple variables simultaneouslye. single value to each of the variablesDifficulty level: MediumSIMULATIONe 15. The type of analysis that is most dependent upon the use of a computer is _____analysis.a. scenariob. break-evenc. sensitivityd. degree of operating leveragee. simulationDifficulty level: EasyVARIABLE COSTSd 16. Which one of the following is most likely a variable cost?a. office rentb. property taxesc. property insuranced. direct labor costse. management salariesDifficulty level: EasyVARIABLE COSTSa 17. Which of the following statements concerning variable costs is (are) correct?I. Variable costs minus fixed costs equal marginal costs.II. Variable costs are equal to zero when production is equal to zero.III. An increase in variable costs increases the operating cash flow.a. II onlyb. III onlyc. I and III onlyd. II and III onlye. I and II onlyDifficulty level: MediumVARIABLE COSTSa 18. All else constant, as the variable cost per unit increases, the:a. contribution margin decreases.b. sensitivity to fixed costs decreases.c. degree of operating leverage decreases.d. operating cash flow increases.e. net profit increases.Difficulty level: MediumFIXED COSTSc 19. Fixed costs:I. are variable over long periods of time.II. must be paid even if production is halted.III. are generally affected by the amount of fixed assets owned by a firm.IV. per unit remain constant over a given range of production output.a. I and III onlyb. II and IV onlyc. I, II, and III onlyd. I, II, and IV onlye. I, II, III, and IVDifficulty level: MediumCONTRIBUTION MARGINc 20. The contribution margin must increase as:a. both the sales price and variable cost per unit increase.b. the fixed cost per unit declines.c. the gap between the sales price and the variable cost per unit widens.d. sales price per unit declines.e. the sales price minus the fixed cost per unit increases.Difficulty level: MediumACCOUNTING BREAK-EVENa 21. Which of the following statements are correct concerning the accounting break-evenpoint?I. The net income is equal to zero at the accounting break-even point.II. The net present value is equal to zero at the accounting break-even point.III. The quantity sold at the accounting break-even point is equal to the total fixed costs plus depreciation divided by the contribution margin.IV. The quantity sold at the accounting break-even point is equal to the total fixed costs divided by the contribution margin.a. I and III onlyb. I and IV onlyc. II and III onlyd. II and IV onlye. I, II, and IV onlyDifficulty level: MediumACCOUNTING BREAK-EVENb 22. All else constant, the accounting break-even level of sales will decrease when the:a. fixed costs increase.b. depreciation expense decreases.c. contribution margin decreases.d. variable costs per unit increase.e. selling price per unit decreases.Difficulty level: MediumPRESENT VALUE BREAK-EVENd 23. The point where a project produces a rate of return equal to the required return isknown as the:a. point of zero operating leverage.b. internal break-even point.c. accounting break-even point.d. present value break-even point.e. internal break-even point.Difficulty level: EasyPRESENT VALUE BREAK-EVENb 24. Which of the following statements are correct concerning the present value break-evenpoint of a project?I. The present value of the cash inflows equals the amount of the initial investment.II. The payback period of the project is equal to the life of the project.III. The operating cash flow is at a level that produces a net present value of zero.IV. The project never pays back on a discounted basis.a. I and II onlyb. I and III onlyc. II and IV onlyd. III and IV onlye. I, III, and IV onlyDifficulty level: MediumINVESTMENT TIMING DECISIONb 25. The investment timing decision relates to:a. how long the cash flows last once a project is implemented.b. the decision as to when a project should be started.c. how frequently the cash flows of a project occur.d. how frequently the interest on the debt incurred to finance a project is compounded.e. the decision to either finance a project over time or pay out the initial cost in cash.Difficulty level: MediumOPTION TO WAITe 26. The timing option that gives the option to wait:I. may be of minimal value if the project relates to a rapidly changing technology.II. is partially dependent upon the discount rate applied to the project being evaluated.III. is defined as the situation where operations are shut down for a period of time.IV. has a value equal to the net present value of the project if it is started today versus the net present value if it is started at some later date.a. I and III onlyb. II and IV onlyc. I and II onlyd. II, III, and IV onlye. I, II, and IV onlyDifficulty level: ChallengeOPTION TO EXPANDb 27. Last month you introduced a new product to the market. Consumer demand has beenoverwhelming and appears that strong demand will exist over the long-term. Given thissituation, management should consider the option to:a. suspend.b. expand.c. abandon.d. contract.e. withdraw.Difficulty level: EasyOPTION TO EXPANDc 28. Including the option to expand in your project analysis will tend to:a. extend the duration of a project but not affect the project’s net present value.b. incre ase the cash flows of a project but decrease the project’s net present value.c. increase the net present value of a project.d. decrease the net present value of a project.e. have no effect on either a project’s c ash flows or its net present value.Difficulty level: MediumSENSITIVITY AND SENARIO ANALYSISd 29. Theoretically, the NPV is the most appropriate method to determine the acceptabilityof a project. A false sense of security can be overwhelm the decision-maker when theprocedure is applied properly and the positive NPV resultsare accepted blindly.Sensitivity and scenario analysis aid in the process bya. changing the underlying assumptions on which the decision is based.b. highlights the areas where more and better data are needed.c. providing a picture of how an event can affect the calculations.d. All of the above.e. None of the above.Difficulty level: MediumDECSION TREEa 30. In order to make a decision with a decision treea. one starts farthest out in time to make the first decision.b. one must begin at time 0.c. any path can be taken to get to the end.d. any path can be taken to get back to the beginning.e. None of the above.Difficulty level: MediumDECISION TREEc 31. In a decision tree, the NPV to make the yes/no decision is dependent ona. only the cash flows from successful path.b. on the path where the probabilities add up to one.c. all cash flows and probabilities.d. only the cash flows and probabilities of the successful path.e. None of the above.Difficulty level: MediumDECISION TREEe 32. In a decision tree, caution should be used in analysis becausea. early stage decisions are probably riskier and should not likely use the same discountrate.b. if a negative NPV is actually occurring, management should opt out of the project andminimize their loss.c. decision trees are only used for planning, not actually daily management.d. Both A and C.e. Both A and B.Difficulty level: MediumSENSITIVITY ANALYSISd 33. Sensitivity analysis evaluates the NPV with respect toa. changes in the underlying assumptions.b. one variable changing while holding the others constant.c. different economic conditions.d. All of the above.e. None of the above.Difficulty level: MediumSENSITIVITY ANALYSISd 34. Sensitivity analysis provides information ona. whether the NPV should be trusted, it may provide a false sense of security if allNPVs are positive.b. the need for additional information as it tests each variablein isolation.c. the degree of difficulty in changing multiple variables together.d. Both A and B.e. Both A and C.Difficulty level: MediumFIXED COSTSb 35. Fixed production costs area. directly related to labor costs.b. measured as cost per unit of time.c. measured as cost per unit of output.d. dependent on the amount of goods or services produced.e. None of the above.Difficulty level: MediumVARIABLE COSTSd 36. Variable costsa. change as the quantity of output changes.b. are zero when production is zero.c. are exemplified by direct labor and raw materials.d. All of the above.e. None of the above.Difficulty level: EasySENSITIVITY ANALYSISb 37. An investigation of the degree to which NPV depends on assumptions made about anysingular critical variable is called a(n)a. operating analysis.b. sensitivity analysis.c. marginal benefit analysis.d. decision tree analysis.e. None of the above.Difficulty level: EasySENSITIVITY AND SCENARIOS ANALYSISb 38. Scenario analysis is different than sensitivity analysisa. as no economic forecasts are changed.b. as several variables are changed together.c. because scenario analysis deals with actual data versus sensitivity analysis which dealswith a forecast.d. because it is short and simple.e. because it is 'by the seat of the pants' technique.Difficulty level: MediumEQUIVALENT ANNUAL COSTc 39. In the present-value break-even the EAC is used toa. determine the opportunity cost of investment.b. allocate depreciation over the life of the project.c. allocate the initial investment at its opportunity cost over the life of the project.d. determine the contribution margin to fixed costs.e. None of the above.Difficulty level: MediumBREAK-EVENb 40. The present value break-even point is superior to the accounting break-even pointbecausea. present value break-even is more complicated to calculate.b. present value break-even covers the economic opportunity costs of the investment.c. present value break-even is the same as sensitivity analysis.d. present value break-even covers the fixed costs of production, which the accountingbreak-even does not.e. present value break-even covers the variable costs of production, which the accountingbreak-even does not.Difficulty level: EasyABANDONMENTd 41. The potential decision to abandon a project has option value becausea. abandonment can occur at any future point in time.b. a project may be worth more dead than alive.c. management is not locked into a negative outcome.d. All of the above.e. None of the above.Difficulty level: EasyTYPES OF BREAK-EVEN ANALYSISd 42. Which of the following are types of break-even analysis?a. present value break-evenb. accounting profit break-evenc. market value break-evend. Both A and B.e. Both A and C.Difficulty level: EasyMONTE CARLO SIMULATIONc 43. The approach that further attempts to model real word uncertainty by analyzingprojects the way one might analyze gambling strategies is calleda. gamblers approach.b. blackjack approach.c. Monte Carlo simulation.d. scenario analysis.e. sensitivity analysis.Difficulty level: MediumMONTE CARLO SIMULATIONc 44. Monte Carlo simulation isa. the most widely used by executives.b. a very simple formula.c. provides a more complete analysis that sensitivity or scenario.d. the oldest capital budgeting technique.e. None of the above.Difficulty level: EasyOPTIONS IN CAPITAL BUDGETINGd 45. Which of the following are hidden options in capital budgeting?a. option to expand.b. timing option.c. option to abandon.d. All of the above.e. None of the above.Difficulty level: EasyIII. PROBLEMSUse this information to answer questions 46 through 50.The Adept Co. is analyzing a proposed project. The company expects to sell 2,500units, give or take 10 percent. The expected variable cost per unit is $8 and the expected fixed costs are $12,500. Cost estimates are considered accurate within a plus or minus 5 percent range. The depreciation expense is $4,000. The sale price is estimated at $16 aunit, give or take 2 percent. The company bases their sensitivity analysis on the expected case scenario.SCENARIO ANALYSISd 46. What is the sales revenue under the optimistic case scenario?a. $40,000b. $43,120c. $44,000d. $44,880e. $48,400Difficulty level: MediumSCENARIO ANALYSISd 47. What is the contribution margin under the expected case scenario?a. $2.67b. $3.00c. $7.92d. $8.00e. $8.72Difficulty level: MediumSCENARIO ANALYSISc 48. What is the amount of the fixed cost per unit under the pessimistic case scenario?a. $4.55b. $5.00c. $5.83d. $6.02e. $6.55Difficulty level: MediumSENSITIVITY ANALYSISb 49. The company is conducting a sensitivity analysis on the sales price using a salesprice estimate of $17. Using this value, the earnings before interest and taxes will be:a. $4,000b. $6,000c. $8,500d. $10,000e. $18,500Difficulty level: MediumSENSITIVITY ANALYSISb 50. The company conducts a sensitivity analysis using a variable cost of $9. The totalvariable cost estimate will be:a. $21,375b. $22,500c. $23,625d. $24,125e. $24,750Difficulty level: MediumUse this information to answer questions 51 through 55.The Can-Do Co. is analyzing a proposed project. The company expects to sell 12,000units, give or take 4 percent. The expected variable cost per unit is $7 and the expectedfixed cost is $36,000. The fixed and variable cost estimates are considered accuratewithin a plus or minus 6 percent range. The depreciation expense is $30,000. The tax rate is 34 percent. The sale price is estimated at $14 a unit, give or take 5 percent. Thecompany bases their sensitivity analysis on the expected case scenario.SCENARIO ANALYSISa 51. What is the earnings before interest and taxes under the expected case scenario?a. $18,000b. $24,000c. $36,000d. $48,000e. $54,000Difficulty level: MediumSCENARIO ANALYSISc 52. What is the earnings before interest and taxes under anoptimistic case scenario?a. $22,694.40b. $24,854.40c. $37,497.60d. $52,694.40e. $67,947.60Difficulty level: ChallengeSCENARIO ANALYSISb 53. What is the earnings before interest and taxes under the pessimistic case scenario?b. -$422.40c. -$278.78d. $3,554.50e. $5,385.60Difficulty level: ChallengeSENSITIVITY ANALYSISd 54. What is the operating cash flow for a sensitivity analysis using total fixed costs of$32,000?a. $14,520b. $16,520c. $22,000d. $44,520e. $52,000Difficulty level: MediumSENSITIVITY ANALYSISd 55. What is the contribution margin for a sensitivity analysis using a variable cost per unitof $8?a. $3b. $4c. $5d. $6e. $7Difficulty level: MediumVARIABLE COSTc 56. A firm is reviewing a project with labor cost of $8.90 per unit, raw materials cost of$21.63 a unit, and fixed costs of $8,000 a month. Sales are projected at 10,000 unitsover the three-month life of the project. What are the total variable costs of the project?a. $216,300b. $297,300c. $305,300d. $313,300e. $329,300Difficulty level: MediumVARIABLE COSTd 57. A project has earnings before interest and taxes of $5,750, fixed costs of $50,000, aselling price of $13 a unit, and a sales quantity of 11,500 units. Depreciation is $7,500.What is the variable cost per unit?a. $6.75c. $7.25d. $7.50e. $7.75Difficulty level: MediumFIXED COSTb 58. At a production level of 5,600 units a project has total costs of $89,000. The variablecost per unit is $11.20. What is the amount of the total fixed costs?a. $24,126b. $26,280c. $27,090d. $27,820e. $28,626Difficulty level: MediumFIXED COSTe 59. At a production level of 6,000 units a project has total costs of $120,000. The variablecost per unit is $14.50. What is the amount of the total fixed costs?a. $25,165b. $28,200c. $30,570d. $32,000e. $33,000Difficulty level: MediumCONTRIBUTION MARGINc 60. Wilson’s Meats has computed their fixed costs to be $.60 for every pound of meatthey sell given an average daily sales level of 500 pounds. They charge $3.89 perpound of top-grade ground beef. The variable cost perpound is $2.99. What is thecontribution margin per pound of ground beef sold?a. $.30b. $.60c. $.90d. $2.99e. $3.89Difficulty level: MediumCONTRIBUTION MARGINe 61. Ralph and Emma’s is considering a project with total sales of $17,500, total variablecosts of $9,800, total fixed costs of $3,500, and estimated production of 400 units. Thedepreciation expense is $2,400 a year. What is the contribution margin per unit?a. $4.50b. $10.50d. $19.09e. $19.25Difficulty level: MediumACCOUNTING BREAK-EVENa 62. You are considering a new project. The project has projected depreciation of $720,fixed costs of $6,000, and total sales of $11,760. The variable cost per unit is$4.20. What is the accounting break-even level of production?a. 1,200 unitsb. 1,334 unitsc. 1,372 unitsd. 1,889 unitse. 1,910 unitsDifficulty level: MediumACCOUNTING BREAK-EVENb 63. The accounting break-even production quantity for a project is 5,425 units. The fixedcosts are $31,600 and the contribution margin is $6. What is the projecteddepreciation expense?a. $700b. $950c. $1,025d. $1,053e. $1,100Difficulty level: MediumACCOUNTING BREAK-EVENd 64. A project has an accounting break-even point of 2,000 units. The fixed costs are$4,200 and the depreciation expense is $400. The projected variable cost per unit is$23.10. What is the projected sales price?a. $20.80b. $21.00c. $21.20d. $25.40e. $25.60Difficulty level: MediumACCOUNTING BREAK-EVENa 65. A proposed project has fixed costs of $3,600,depreciation expense of $1,500, and asales quantity of 1,300 units. What is the contribution margin if the projected level ofsales is the accounting break-even point?a. $3.92c. $4.50d. $4.80e. $5.00Difficulty level: MediumPRESENT VALUE BREAK-EVENc 66. A project has a contribution margin of $5, projected fixed costs of $12,000, projectedvariable cost per unit of $12, and a projected present value break-even point of 5,000units. What is the operating cash flow at this level of output?a. $1,000b. $12,000c. $13,000d. $68,000e. $73,000Difficulty level: MediumPRESENT VALUE BREAK-EVENa 67. Thompson & Son have been busy analyzing a new product. They have determined thatan operating cash flow of $16,700 will result in a zero net present value, which is acompany requirement for project acceptance. The fixed costs are $12,378 and thecontribution margin is $6.20. The company feels that they can realistically capture10 percent of the 50,000 unit market for this product. Should the company develop thenew product? Why or why not?a. yes; because 5,000 units of sales exceeds the quantity required for a zero net presentvalueb. yes; because the internal break-even point is less than 5,000 unitsc. no; because the firm can not generate sufficient sales to obtain at least a zero netpresent valued. no; because the project has an expected internal rate of return of negative 100percente. no; because the project will not pay back on a discounted basisDifficulty level: ChallengePRESENT VALUE BREAK-EVENe 68. Kurt Neal and Son is considering a project with a discounted payback just equal to theproject’s life. The projections include a sales price of $11, variable cost per unit of$8.50, and fixed costs of $4,500. The operating cash flow is $6,200. What is the break-even quantity?a. 1,800 unitsb. 2,480 unitsc. 3,057 unitsd. 3,750 unitse. 4,280 unitsDECISION TREE NET PRESENT VALUEb 69. At stage 2 of the decision tree it shows that if a project is successful, the payoff will be$53,000 with a 2/3 chance of occurrence. There is also the 1/3 chance of a $-24,000payoff. The cost of getting to stage 2 (1 year out) is $44,000. The cost of capital is15%. What is the NPV of the project at stage 1?a. $-13,275b. $-20,232c. $ 2,087d. $ 7,536e. Can not be calculated without the exact timing of future cash flows.Difficulty level: MediumUse the following to answer questions 70-71:The Quick-Start Company has the following pattern of potential cash flows with their planned investment in a new cold weather starting system for fuel injected cars.DECISION TREEa 70. If the company has a discount rate of 17%, what is the value closest to time 1 netpresent value?a. $ 48.6 millionb. $ 80.9 millionc. $108.2 milliond. $181.4 millione. None of the above.DECISION TREEb 71. If the company has a discount rate of 17%, should they decide to invest?a. yes, NPV = $ 2.2 millionb. yes, NPV = $ 21.6 millionc. no, NPV = $-1.9 milliond. yes, NPV = $ 8.6 millione. No, since more than one branch is NPV = 0 or negative you must reject.Difficulty level: ChallengeACCOUNTING BREAK-EVENe 72. The Mini-Max Company has the following cost information on their new prospectiveproject. Calculate the accounting break-even point.Initial investment: $700。
公司理财第九版罗斯课后案例答案 Case Solutions Corporate Finance
公司理财第九版罗斯课后案例答案 Case Solutions CorporateFinance1. 案例一：公司资金需求分析问题：一家公司需要资金支持其新项目。
通过分析现金流量，推断该公司是否需要向外部借款或筹集其他资金。
解答：为了确定公司是否需要外部资金，我们需要分析公司的现金流量状况。
首先，我们需要计算公司的净现金流量（净收入加上非现金项目）。
然后，我们需要将净现金流量与项目的投资现金流量进行对比。
假设公司预计在项目开始时投资100万美元，并在项目运营期为5年。
预计该项目每年将产生50万美元的净现金流量。
现在，我们需要进行以下计算：净现金流量 = 年度现金流量 - 年度投资现金流量年度投资现金流量 = 100万美元年度现金流量 = 50万美元净现金流量 = 50万美元 - 100万美元 = -50万美元根据计算结果，公司的净现金流量为负数（即净现金流出），意味着公司每年都会亏损50万美元。
因此，公司需要从外部筹集资金以支持项目的运营。
2. 案例二：公司股权融资问题：一家公司正在考虑通过股权融资来筹集资金。
根据公司的财务数据和资本结构分析，我们需要确定公司最佳的股权融资方案。
解答：为了确定最佳的股权融资方案，我们需要参考公司的财务数据和资本结构分析。
首先，我们需要计算公司的资本结构比例，即股本占总资本的比例。
然后，我们将不同的股权融资方案与资本结构比例进行对比，选择最佳的方案。
假设公司当前的资本结构比例为60%的股本和40%的债务，在当前的资本结构下，公司的加权平均资本成本（WACC）为10%。
现在，我们需要进行以下计算：•方案一：以新股发行筹集1000万美元，并将其用于项目投资。
在这种方案下，公司的资本结构比例将发生变化。
假设公司的股本增加至80%，债务比例减少至20%。
根据资本结构比例的变化，WACC也将发生变化。
新的WACC可以通过以下公式计算得出：新的WACC = (股本比例 * 股本成本) + (债务比例 * 债务成本)假设公司的股本成本为12%，债务成本为8%：新的WACC = (0.8 * 12%) + (0.2 * 8%) = 9.6%•方案二：以新股发行筹集5000万美元，并将其用于项目投资。
罗斯《公司理财》第9版英文原书课后部分章节答案
罗斯《公司理财》第9版精要版英文原书课后部分章节答案详细»1 / 17 CH5 11，13，18，19，20 11. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $1,000,000 / (1.10) 80 = $488.19 13. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for r, we get: r = (FV / PV) 1 / t –1 r = ($1,260,000 / $150) 1/112 – 1 = .0840 or 8.40% To find the FV of the first prize, we use: FV = PV(1 + r) t FV = $1,260,000(1.0840) 33 = $18,056,409.94 18. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $4,000(1.11) 45 = $438,120.97 FV = $4,000(1.11) 35 = $154,299.40 Better start early! 19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six. FV = PV(1 + r) t FV = $20,000(1.084)6 = $32,449.33 20. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($75,000 / $10,000) / ln(1.11) = 19.31 So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. From now, you’ll wait: 2 years + 19.31 years = 21.31 years CH6 16，24，27，42，58 16. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t 2 / 17 It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $2,100[1 + (.084/2)] 34 = $8,505.93 24. This problem requires us to find the FV A. The equation to find the FV A is: FV A = C{[(1 + r) t – 1] / r} FV A = $300[{[1 + (.10/12) ] 360 – 1} / (.10/12)] = $678,146.38 27. The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get: EAR = [1 + (APR / m)] m – 1 EAR = [1 + (.11/4)] 4 – 1 = .1146 or 11.46% And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.1146 2 + $1,360 / 1.1146 4 = $2,320.36 42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,150 monthly payments is: PV A = $1,150[(1 – {1 / [1 + (.0635/12)]} 360 ) / (.0635/12)] = $184,817.42 The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is: $240,000 – 184,817.42 = $55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = $55,182.58[1 + (.0635/12)] 360 = $368,936.54 58. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $99 + $450{1 –[1 / (1 + .07/12) 12(3) ]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $23,000 / [1 + (.07/12)] 12(3) = $18,654.82 The PV of the decision to purchase is: $32,000 – 18,654.82 = $13,345.18 3 / 17 In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be: $32,000 – PV of resale price = $14,672.91 PV of resale price = $17,327.09 The resale price that would make the PV of the lease versus buy decision is the FV ofthis value, so: Breakeven resale price = $17,327.09[1 + (.07/12)] 12(3) = $21,363.01 CH7 3，18，21，22，31 3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $75({1 – [1/(1 + .0875)] 10 } / .0875) + $1,000[1 / (1 + .0875) 10 ] = $918.89 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PV A equation, it is common to abbreviate the equations as: PVIF R,t = 1 / (1 + r) t which stands for Present V alue Interest Factor PVIFA R,t = ({1 – [1/(1 + r)] t } / r ) which stands for Present V alue Interest Factor of an Annuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key. 18. The bond price equation for this bond is: P 0 = $1,068 = $46(PVIFA R%,18 ) + $1,000(PVIF R%,18 ) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.06% This is thesemiannual interest rate, so the YTM is: YTM = 2 4.06% = 8.12% The current yield is:Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.0406) 2 – 1 = .0829 or 8.29% 20. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $74/2 × 2/6 = $12.33 And we calculate the clean price as: 4 / 17 Clean price = Dirty price –Accrued interest = $968 –12.33 = $955.67 21. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $68/2 × 4/6 = $22.67 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.67 22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P 0 P 0 = $80/.0755 = $1,059.60 Now that we have the price of the bond, the bond price equation is: P = $1,059.60 = $80[(1 – (1/1.072) t ) / .072 ] + $1,000/1.072 t We can solve this equation for t as follows: $1,059.60(1.072) t = $1,111.11(1.072) t –1,111.11 + 1,000 111.11 = 51.51(1.072) t2.1570 = 1.072 t t = log 2.1570 / log 1.072 = 11.06 11 years The bond has 11 years to maturity.31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: P M = $1,100(PVIFA 3.5%,16 )(PVIF 3.5%,12 ) + $1,400(PVIFA3.5%,12 )(PVIF 3.5%,28 ) + $20,000(PVIF 3.5%,40 ) P M = $19,018.78 Notice that for the coupon payments of $1,400, we found the PV A for the coupon payments, and then discounted the lump sum back to today. Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or: P N = $20,000(PVIF3.5%,40 ) = $5,051.45 CH8 4，18，20，22，244. Using the constant growth model, we find the price of the stock today is: P 0 = D 1 / (R – g) = $3.04 / (.11 – .038) = $42.22 5 / 17 18. The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 20, so we can find the price of the stock in Y ear 19, one year before the first dividend payment. Doing so, we get: P 19 = $20.00 / .064 P 19 = $312.50 The price of the stock today is the PV of the stock price in the future, so the price today will be: P 0 = $312.50 / (1.064) 19 P 0 = $96.15 20. We can use the two-stage dividend growth model for this problem, which is: P 0 = [D 0 (1 + g 1 )/(R – g 1 )]{1 – [(1 + g 1 )/(1 + R)] T }+ [(1 + g 1 )/(1 + R)] T [D 0 (1 + g 2 )/(R –g 2 )] P0 = [$1.25(1.28)/(.13 –.28)][1 –(1.28/1.13) 8 ] + [(1.28)/(1.13)] 8 [$1.25(1.06)/(.13 – .06)] P 0 = $69.55 22. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W: P 0 = D 0 (1 + g) / (R – g) = $4.50(1.10)/(.19 – .10) = $55.00 Dividend yield = D 1 /P 0 = $4.50(1.10)/$55.00 = .09 or 9% Capital gains yield = .19 – .09 = .10 or 10% X: P 0 = D 0 (1 + g) / (R – g) = $4.50/(.19 – 0) = $23.68 Dividend yield = D 1 /P 0 = $4.50/$23.68 = .19 or 19% Capital gains yield = .19 – .19 = 0% Y: P 0 = D 0 (1 + g) / (R – g) = $4.50(1 – .05)/(.19 + .05) = $17.81 Dividend yield = D 1 /P 0 = $4.50(0.95)/$17.81 = .24 or 24% Capital gains yield = .19 – .24 = –.05 or –5% Z: P 2 = D 2 (1 + g) / (R – g) = D 0 (1 + g 1 ) 2 (1 +g 2 )/(R – g 2 ) = $4.50(1.20) 2 (1.12)/(.19 – .12) = $103.68 P 0 = $4.50 (1.20) / (1.19) + $4.50(1.20) 2 / (1.19) 2 + $103.68 / (1.19) 2 = $82.33 Dividend yield = D 1 /P 0 = $4.50(1.20)/$82.33 = .066 or 6.6% Capital gains yield = .19 – .066 = .124 or 12.4% In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time. 24. Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Y ear 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Y ear 3 will be the dividend in Y ear 4, divided by the required return minus the constant dividend growth rate. So, the price in Y ear 3 will be: 6 / 17 P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08 The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Y ear 3, so: P 0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.11 2 + $2.45(1.20)(1.15)(1.10)/1.11 3 + $65.08/1.11 3 P 0 = $55.70 CH9 3，4，6，9，15 3. Project A has cash flows of $19,000 in Y ear 1, so the cash flows are short by $21,000 of recapturing the initial investment, so the payback for Project A is: Payback = 1 + ($21,000 / $25,000) = 1.84 years Project B has cash flows of: Cash flows = $14,000 + 17,000 + 24,000 = $55,000 during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: B: Payback = 3 + ($5,000 / $270,000) = 3.019 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 4. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: V alue today of Y ear 1 cash flow = $4,200/1.14 = $3,684.21 V alue today of Y ear 2 cash flow = $5,300/1.14 2 = $4,078.18 V alue today of Y ear 3 cash flow = $6,100/1.14 3 = $4,117.33 V alue today of Y ear 4 cash flow = $7,400/1.14 4 = $4,381.39 To findthe discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is: Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years For an initial cost of $10,000, the discounted payback is: Discounted payback = 2 + ($10,000 –3,684.21 –4,078.18)/$4,117.33 = 2.54 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Y ear 1 and Y ear 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Y ear 3 to get the fractional portion of the discounted payback. If the initial cost is $13,000, the discounted payback is: Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years 7 / 17 6. Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: A verage net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325 And the average book value is: A verage book value = ($15,000,000 + 0) / 2 = $7,500,000 So, the AAR for this project is: AAR = A verage net income / A verage book value = $1,836,325 / $7,500,000 = .2448 or 24.48% 9. The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA 8%, 9 ) = $40,036.31 At an 8 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 20 percent required return is: NPV = –$138,000 + $28,500(PVIFA 20%, 9 ) = –$23,117.45 At a 20 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = –$138,000 + $28,500(PVIFA IRR, 9 ) IRR = 14.59% 15. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 10 percent is: PI = [$7,300/1.1 + $6,900/1.1 2 + $5,700/1.1 3 ] / $14,000 = 1.187 The equation for the profitability index at a required return of 15 percent is: PI = [$7,300/1.15 + $6,900/1.15 2 + $5,700/1.15 3 ] / $14,000 = 1.094 The equation for the profitability index at a required return of 22 percent is: PI = [$7,300/1.22 + $6,900/1.22 2 + $5,700/1.22 3 ] / $14,000 = 0.983 8 / 17 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI。
英文版罗斯公司理财习题答案Chap009.doc
CHAPTER 9RISK ANALYSIS, REAL OPTIONS, AND CAPITAL BUDGETINGAnswers to Concepts Review and Critical Thinking Questions1.Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows.The danger is greatest with a new product because the cash flows are probably harder to predict.2.With a sensitivity analysis, one variable is examined over a broad range of values. With a scenarioanalysis, all variables are examined for a limited range of values.3.It is true that if average revenue is less than average cost, the firm is losing money. This much of thestatement is therefore correct. At the margin, however, accepting a project with marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow.4.From the shareholder perspective, the financial break-even point is the most important. A project canexceed the accounting and cash break-even points but still be below the financial break-even point.This causes a reduction in shareholder (your) wealth.5.The project will reach the cash break-even first, the accounting break-even next and finally thefinancial break-even. For a project with an initial investment and sales after, this ordering will always apply. The cash break-even is achieved first since it excludes depreciation. The accounting break-even is next since it includes depreciation. Finally, the financial break-even, which includes the time value of money, is achieved.6.Traditional NPV analysis is often too conservative because it ignores profitable options such as theability to expand the project if it is profitable, or abandon the project if it is unprofitable. The option to alter a project when it has already been accepted has a value, which increases the NPV of the project.7.The type of option most likely to affect the decision is the option to expand. If the country justliberalized its markets, there is likely the potential for growth. First entry into a market, whether an entirely new market, or with a new product, can give a company name recognition and market share.This may make it more difficult for competitors entering the market.8.Sensitivity analysis can determine how the financial break-even point changes when some factors(such as fixed costs, variable costs, or revenue) change.9.There are two sources of value with this decision to wait. Potentially, the price of the timber canpotentially increase, and the amount of timber will almost definitely increase, barring a natural catastrophe or forest fire. The option to wait for a logging company is quite valuable, and companies in the industry have models to estimate the future growth of a forest depending on its age.10.When the additional analysis has a negative NPV. Since the additional analysis is likely to occuralmost immediately, this means when the benefits of the additional analysis outweigh the costs. The benefits of the additional analysis are the reduction in the possibility of making a bad decision. Of course, the additional benefits are often difficult, if not impossible, to measure, so much of this decision is based on experience.Solutions to Questions and ProblemsNOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.a. To calculate the accounting breakeven, we first need to find the depreciation for each year. Thedepreciation is:Depreciation = $896,000/8Depreciation = $112,000 per yearAnd the accounting breakeven is:Q A = ($900,000 + 112,000)/($38 – 25)Q A = 77,846 unitsb.We will use the tax shield approach to calculate the OCF. The OCF is:OCF base = [(P – v)Q – FC](1 – t c) + t c DOCF base = [($38 – 25)(100,000) – $900,000](0.65) + 0.35($112,000)OCF base = $299,200Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:NPV base = –$896,000 + $299,200(PVIFA15%,8)NPV base = $446,606.60To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 105,000 units. The NPV at this sales level is:OCF new = [($38 – 25)(105,000) – $900,000](0.65) + 0.35($112,000)OCF new = $341,450And the NPV is:NPV new = –$896,000 + $341,450(PVIFA15%,8)NPV new = $636,195.93So, the change in NPV for every unit change in sales is:∆NPV/∆S = ($636,195.93 – 446,606.60)/(105,000 – 100,000)∆NPV/∆S = +$37.918If sales were to drop by 100 units, then NPV would drop by:NPV drop = $37.918(100) = $3,791.80You may wonder why we chose 105,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.c.To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at avariable cost of $24. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use.So, using the tax shield approach, the OCF at a variable cost of $24 is:OCF new = [($38 – 24)(100,000) – 900,000](0.65) + 0.35($112,000)OCF new = $364,200So, the change in OCF for a $1 change in variable costs is:∆OCF/∆v = ($299,200 – 364,200)/($25 – 24)∆OCF/∆v = –$65,000If variable costs decrease by $5 then, OCF would increase byOCF increase = $65,000*5 = $325,0002.We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. Forthe best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get:OCF best = {[($38)(1.1) – ($25)(0.9)](100K)(1.1) – $900K(0.9)}(0.65) + 0.35($112K)OCF best = $892,650The best-case NPV is:NPV best = –$896,000 + $892,650(PVIFA15%,8)NPV best = $3,109,607.54For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: OCF worst = {[($38)(0.9) – ($25)(1.1)](100K)(0.9) – $900K(1.1)}(0.65) + 0.35($112K)OCF worst = –212,350The worst-case NPV is:NPV worst = –$896,000 – $212,350(PVIFA15%,8)NPV worst = –$1,848,882.723.We can use the accounting breakeven equation:Q A = (FC + D)/(P – v)to solve for the unknown variable in each case. Doing so, we find:(1): Q A = 130,200 = (€850,000 + D)/(€41 – 30)D = €582,200(2): Q A = 135,000 = (€3.2M + 1.15M)/(P –€56)P = €88.22(3): Q A = 5,478 = (€160,000 + 105,000)/(€105 – v)v = €56.624.When calculating the financial breakeven point, we express the initial investment as an equivalentannual cost (EAC). Dividing the in initial investment by the seven-year annuity factor, discounted at12 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA12%,5EAC = £200,000 / 3.60478EAC = £55,481.95Note, this calculation solves for the annuity payment with the initial investment as the present value of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)£200,000 = C{[1 – (1/1.12)5 ] / .12}C = £55,481.95The annual depreciation is the cost of the equipment divided by the economic life, or:Annual depreciation = £200,000 / 5Annual depreciation = £40,000Now we can calculate the financial breakeven point. The financial breakeven point for this project is: Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [£55,481.95 + £350,000(.75) – £40,000(0.25)] / [(£25 – 5) (.25)]Q F = 20,532.13 or about 20,532 units5.If we purchase the machine today, the NPV is the cost plus the present value of the increased cashflows, so:NPV0 = –฿1,500,000 + ฿280,000(PVIFA12%,10)NPV0 = ฿82,062.45We should not purchase the machine today. We would want to purchase the machine when the NPV is the highest. So, we need to calculate the NPV each year. The NPV each year will be the cost plus the present value of the increased cash savings. We must be careful however. In order to make the correct decision, the NPV for each year must be taken to a common date. We will discount all of the NPVs to today. Doing so, we get:Year 1: NPV1 = [–฿1,375,000 + ฿280,000(PVIFA12%,9)] / 1.12NPV1 = ฿104,383.88Year 2: NPV2 = [–฿1,250,000 + ฿280,000(PVIFA12%,8)] / 1.122NPV2 = ฿112,355.82Year 3: NPV3 = [–฿1,125,000 + ฿280,000(PVIFA12%,7)] / 1.123NPV3 = ฿108,796.91Year 4: NPV4 = [–฿1,000,000 + ฿280,000(PVIFA12%,6)] / 1.124NPV4 = ฿96,086.55Year 5: NPV5 = [–฿1,000,000 + ฿280,000(PVIFA12%,5)] / 1.125NPV5 = ฿5,298.26Year 6: NPV6 = [–฿1,000,000 + ฿280,000(PVIFA12%,4)] / 1.126NPV6 = –฿75,762.72The company should purchase the machine two years from now when the NPV is the highest.6.We need to calculate the NPV of the two options, go directly to market now, or utilize test marketingfirst. The NPV of going directly to market now is:NPV = C Success (Prob. of Success) + C Failure (Prob. of Failure)NPV = $20,000,000(0.45) + $5,000,000(0.55)NPV = $11,750,000Now we can calculate the NPV of test marketing first. Test marketing requires a $2 million cashoutlay. Choosing the test marketing option will also delay the launch of the product by one year.Thus, the expected payoff is delayed by one year and must be discounted back to year 0.NPV= C0 + {[C Success (Prob. of Success)] + [C Failure (Prob. of Failure)]} / (1 + R)tNPV = –$2,000,000 + {[$20,000,000 (0.75)] + [$5,000,000 (0.25)]} / 1.15NPV = $12,130,434.78The company should not go directly to market with the product since that option has lower expected payoff.7.We need to calculate the NPV of each option, and choose the option with the highest NPV. So, theNPV of going directly to market is:NPV = C Success (Prob. of Success)NPV = Rs.1,200,000 (0.55)NPV = Rs.660,000The NPV of the focus group is:NPV = C0 + C Success (Prob. of Success)NPV = –Rs.120,000 + Rs.1,200,000 (0.70)NPV = Rs.720,000And the NPV of using the consulting firm is:NPV = C0 + C Success (Prob. of Success)NPV = –Rs.400,000 + Rs.1,200,000 (0.90)NPV = Rs.680,000The firm should conduct a focus group since that option has the highest NPV.8.The company should analyze both options, and choose the option with the greatest NPV. So, if thecompany goes to market immediately, the NPV is:NPV = C Success (Prob. of Success) + C Failure (Prob. of Failure)NPV = ₦30,000,000(.55) + ₦3,000,000(.45)NPV = ₦17,850,000.00Customer segment research requires a ₦1 million cash outlay. Choosing the research option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. So, the NPV of the customer segment research is:NPV= C0 + {[C Success (Prob. of Success)] + [C Failure (Prob. of Failure)]} / (1 + R)tNPV = –₦1,000,000 + {[₦30,000,000 (0.70)] + [₦3,000,000 (0.30)]} / 1.15NPV = ₦18,043,478.26Graphically, the decision tree for the project is:₦3 million at t = 0The company should undertake the market segment research since it has the largest NPV.9. a.The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge dividedby the aftertax contribution margin (selling price minus variable cost). So, the accounting breakeven level of sales is:Q A = [(FC + Depreciation)(1 – t C)] / [(P – VC)(1 – t C)]Q A = [($340,000 + $20,000) (1 – 0.35)] / [($2.00 – 0.72) (1 – 0.35)]Q A = 281,250.00b.When calculating the financial breakeven point, we express the initial investment as anequivalent annual cost (EAC). Dividing the in initial investment by the seven-year annuity factor, discounted at 15 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA15%,7EAC = $140,000 / 4.1604EAC = $33,650.45Note, this calculation solves for the annuity payment with the initial investment as the presentvalue of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)$140,000 = C{[1 – (1/1.15)7 ] / .15}C = $33,650.45Now we can calculate the financial breakeven point. The financial breakeven point for this project is:Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [$33,650.45 + $340,000(.65) – $20,000(.35)] / [($2 – 0.72) (.65)]Q F = 297,656.79 or about 297,657 units10.When calculating the financial breakeven point, we express the initial investment as an equivalentannual cost (EAC). Dividing the in initial investment by the five-year annuity factor, discounted at 8 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA8%,5EAC = ¥300,000 / 3.60478EAC = ¥75,136.94Note, this calculation solves for the annuity payment with the initial investment as the present value of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)¥300,000 = C{[1 – (1/1.08)5 ] / .08}C = ¥75,136.94The annual depreciation is the cost of the equipment divided by the economic life, or:Annual depreciation = ¥300,000 / 5Annual depreciation = ¥60,000Now we can calculate the financial breakeven point. The financial breakeven point for this project is: Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [¥75,136.94 + ¥100,000(.66) – ¥60,000(0.34)] / [(¥60 – 8) (.34)]Q F = 3,517.98 or about 3,518 unitsIntermediate11.a. At the accounting breakeven, the IRR is zero percent since the project recovers the initialinvestment. The payback period is N years, the length of the project since the initial investmentis exactly recovered over the project life. The NPV at the accounting breakeven is:NPV = I [(1/N)(PVIFA R%,N) – 1]b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and theNPV is negative and equal to the initial cash outlay.c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true,then the IRR of the project is equal to the required return. It is impossible to state the paybackperiod, except to say that the payback period must be less than the length of the project. Sincethe discounted cash flows are equal to the initial investment, the undiscounted cash flows aregreater than the initial investment, so the payback must be less than the project life.ing the tax shield approach, the OCF at 110,000 units will be:OCF = [(P – v)Q – FC](1 – t C) + t C(D)OCF = [($28 – 19)(110,000) – 150,000](0.66) + 0.34($420,000/4)OCF = $590,100We will calculate the OCF at 111,000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is:OCF = [($28 – 19)(111,000) – 150,000](0.66) + 0.34($420,000/4)OCF = $596,040The sensitivity of the OCF to changes in the quantity sold is:Sensitivity = ∆OCF/∆Q = ($596,040 – 590,100)/(111,000 – 110,000)∆OCF/∆Q = +$5.94OCF will increase by $5.94 for every additional unit sold.13.a. The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease,and costs increase.Scenario Unit sales Variable cost Fixed costsBase 190 元15,000 元225,000Best 209 元13,500 元202,500Worst 171 元16,500 元247,500Using the tax shield approach, the OCF and NPV for the base case estimate is:OCF base = [(元21,000 – 15,000)(190) –元225,000](0.65) + 0.35(元720,000/4)OCF base = 元657,750NPV base = –元720,000 + 元657,750(PVIFA15%,4)NPV base = 元1,157,862.02The OCF and NPV for the worst case estimate are:OCF worst = [(元21,000 – 16,500)(171) –元247,500](0.65) + 0.35(元720,000/4)OCF worst = 元402,300NPV worst = –元720,000 + 元402,300(PVIFA15%,4)NPV worst = +元428,557.80And the OCF and NPV for the best case estimate are:OCF best = [(元21,000 – 13,500)(209) –元202,500](0.65) + 0.35(元720,000/4)OCF best = 元950,250NPV best = –元720,000 + 元950,250(PVIFA15%,4)NPV best = 元1,992,943.19b. To calculate the sensitivity of the NPV to changes in fixed costs we choose another level offixed costs. We will use fixed costs of 元230,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get:OCF = [(元21,000 – 15,000)(190) –元230,000](0.65) + 0.35(元720,000/4)OCF = 元654,500And the NPV is:NPV = –元720,000 + 元654,500(PVIFA15%,4)NPV = 元1,148,583.34The sensitivity of NPV to changes in fixed costs is:∆NPV/∆FC = (元1,157,862.02 – 1,148,583.34)/(元225,000 – 230,000)∆NPV/∆FC = –元1.856For every dollar FC increase, NPV falls by 元1.86.c. The accounting breakeven is:Q A= (FC + D)/(P – v)Q A = [元225,000 + (元720,000/4)]/(元21,000 – 15,000)Q A = 68At the accounting breakeven, the DOL is:DOL = 1 + FC/OCFDOL = 1 + (元225,000/元180,000) = 2.25For each 1% increase in unit sales, OCF will increase by 2.25%.14.The marketing study and the research and development are both sunk costs and should be ignored.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €700 ⨯ 55,000 = €38,500,000Exp. clubs €1,100 ⨯ (–13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€28,200,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs –€320 ⨯ 55,000 = –€17,600,000Exp. clubs –€600 ⨯ (–13,000) = 7,800,000Cheap clubs –€180 ⨯ 10,000 = –1,800,000–€11,600,000The pro forma income statement will be:Sales €28,200,000Variable costs 11,600,000Costs 7,500,000Depreciation 2,600,000EBT 6,500,000Taxes 2,600,000Net income € 3,900,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €3,900,000 + 2,600,000OCF = €6,500,000So, the payback period is:Payback period = 2 + €6.15M/€6.5MPayback period = 2.946 yearsThe NPV is:NPV = –€18.2M – .95M + €6.5M(PVIFA14%,7) + €0.95M/1.147NPV = €9,103,636.91And the IRR is:IRR = –€18.2M – .95M + €6.5M(PVIFA IRR%,7) + €0.95M/IRR7IRR = 28.24%15.The upper and lower bounds for the variables are:Base Case Lower Bound Upper Bound Unit sales (new) 55,000 49,500 60,500Price (new) €700 €630 €770VC (new) €320 €288 €352Fixed costs €7,500,000 €6,750,000 €8,250,000Sales lost (expensive) 13,000 11,700 14,300Sales gained (cheap) 10,000 9,000 11,000 Best-caseWe will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €770 ⨯ 60,500 = €46,585,000Exp. clubs €1,100 ⨯ (–11,700) = – 12,870,000Cheap clubs €400 ⨯ 11,000 = 4,400,000€38,115,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €288 ⨯ 60,500 = €17,424,000Exp. clubs €600 ⨯ (–11,700) = – 7,020,000Cheap clubs €180 ⨯ 11,000 = 1,980,000€12,384,000Sales €38,115,000Variable costs 12,384,000Costs 6,750,000Depreciation 2,600,000EBT 16,381,000Taxes 6,552,400Net income €9,828,600Using the bottom up OCF calculation, we get:OCF = Net income + Depreciation = €9,828,600 + 2,600,000OCF = €12,428,600And the best-case NPV is:NPV = –€18.2M – .95M + €12,428,600(PVIFA14%,7) + .95M/1.147NPV = €34,527,280.98Worst-caseWe will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €630 ⨯ 49,500 = €31,185,000Exp. clubs €1,100 ⨯ (– 14,300) = – 15,730,000Cheap clubs €400 ⨯ 9,000 = 3,600,000€19,055,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €352 ⨯ 49,500 = €17,424,000Exp. clubs €600 ⨯ (– 14,300) = – 8,580,000Cheap clubs €180 ⨯ 9,000 = 1,620,000€10,464,000Sales €19,055,000Variable costs 10,464,000Costs 8,250,000Depreciation 2,600,000EBT – 2,259,000Taxes 903,600 *assumes a tax creditNet income –€1,355,400Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = –€1,355,400 + 2,600,000OCF = €1,244,600And the worst-case NPV is:NPV = –€18.2M – .95M + €1,244,600(PVIFA14%,7) + .95M/1.147NPV = –€13,433,120.3416.To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need tochange the price of the new club. We will choose €750, but the choice is irrelevant as the sensitivity will be the same no matter what price we choose.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €750 ⨯ 55,000 = €41,250,000Exp. clubs €1,100 ⨯ (– 13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€30,950,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €320 ⨯ 55,000 = €17,600,000Exp. clubs €600 ⨯ (–13,000) = –7,800,000Cheap clubs €180 ⨯ 10,000 = 1,800,000€11,600,000Sales €30,950,000Variable costs 11,600,000Costs 7,500,000Depreciation 2,600,000EBT 9,250,000Taxes 3,700,000Net income € 5,550,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €5,550,000 + 2,600,000OCF = €8,150,000And the NPV is:NPV = –€18.2M – 0.95M + €8.15M(PVIFA14%,7) + .95M/1.147NPV = €16,179,339.89So, the sensitivity of the NPV to changes in the price of the new club is:∆NPV/∆P = (€16,179,339.89 – 9,103,636.91)/(€750 – 700)∆NPV/∆P = €141,514.06For every euro increase (decrease) in the price of the clubs, the NPV increases (decreases) by €141,514.06.To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply need to change the quantity sold. We will choose 60,000 units, but the choice is irrelevant as the sensitivity will be the same no matter what quantity we choose.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €700 ⨯ 60,000 = €42,000,000Exp. clubs €1,100 ⨯ (– 13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€31,700,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €320 ⨯ 60,000 = €19,200,000Exp. clubs €600 ⨯ (–13,000) = –7,800,000Cheap clubs €180 ⨯ 10,000 = 1,800,000€13,200,000The pro forma income statement will be:Sales €31,700,000Variable costs 13,200,000Costs 7,500,000Depreciation 2,600,000EBT 8,400,000Taxes 3,360,000Net income € 5,040,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €5,040,000 + 2,600,000OCF = €7,640,000The NPV at this quantity is:NPV = –€18.2M –€0.95M + €7.64(PVIFA14%,7) + €0.95M/1.147NPV = €13,992,304.43So, the sensitivity of the NPV to changes in the quantity sold is:∆NPV/∆Q = (€13,992,304.43 – 9,103,636.91)/(60,000 – 55,000)∆NPV/∆Q = €977.73For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by€977.73.17.a. The base-case NPV is:NPV = –£1,750,000 + £420,000(PVIFA16%,10)NPV = £279,955.54b.We would abandon the project if the cash flow from selling the equipment is greater than thepresent value of the future cash flows. We need to find the sale quantity where the two are equal, so:£1,500,000 = (£60)Q(PVIFA16%,9)Q = £1,500,000/[£60(4.6065)]Q = 5,427.11Abandon the project if Q < 5,428 units, because the NPV of abandoning the project is greater than the NPV of the future cash flows.c.The £1,500,000 is the market value of the project. If you continue with the project in one year,you forego the £1,500,000 that could have been used for something else.18. a.If the project is a success, present value of the future cash flows will be:PV future CFs = £60(9,000)(PVIFA16%,9)PV future CFs = £2,487,533.69From the previous question, if the quantity sold is 4,000, we would abandon the project, and the cash flow would be £1,500,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so:Expected value of project at year 1 = [(£2,487,533.69 + £1,500,000)/2] + £420,000Expected value of project at year 1 = £2,413,766.85The NPV is the present value of the expected value in one year plus the cost of the equipment, so:NPV = –£1,750,000 + (£2,413,766.85)/1.16NPV = £330,833.49b. If we couldn’t abandon the project, the present value of the fut ure cash flows when the quantityis 4,000 will be:PV future CFs = £60(4,000)(PVIFA16%,9)PV future CFs = £1,105,570.53The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project, so:Gain from option to abandon = £1,500,000 – 1,105,570.53Gain from option to abandon = £394,429.47We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is:Option value = (.50)(£394,429.47)/1.16Option value = £170,012.70。
罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】
![罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】](https://img.taocdn.com/s3/m/e1dcbc711fb91a37f111f18583d049649b660eea.png)
罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第9章股票估值9.1复习笔记1．不同类型股票的估值（1）零增长股利股利不变时，一股股票的价格由下式给出：在这里假定Div1=Div2=…=Div。
（2）固定增长率股利如果股利以恒定的速率增长，那么一股股票的价格就为：式中，g是增长率；Div是第一期期末的股利。
（3）变动增长率股利2．股利折现模型中的参数估计（1）对增长率g的估计有效估计增长率的方法是：g=留存收益比率×留存收益收益率（ROE）只要公司保持其股利支付率不变，g就可以表示公司的股利增长率以及盈利增长率。
（2）对折现率R的估计对于折现率R的估计为：R=Div/P0+g该式表明总收益率R由两部分组成。
其中，第一部分被称为股利收益率，是预期的现金股利与当前的价格之比。
3．增长机会每股股价可以写做：该式表明，每股股价可以看做两部分的加和。
第一部分（EPS/R）是当公司满足于现状，而将其盈利全部发放给投资者时的价值；第二部分是当公司将盈利留存并用于投资新项目时的新增价值。
当公司投资于正NPVGO的增长机会时，公司价值增加。
反之，当公司选择负NPVGO 的投资机会时，公司价值降低。
但是，不管项目的NPV是正的还是负的，盈利和股利都是增长的。
不应该折现利润来获得每股价格，因为有部分盈利被用于再投资了。
只有股利被分到股东手中，也只有股利可以加以折现以获得股票价格。
4．市盈率即股票的市盈率是三个因素的函数：（1）增长机会。
拥有强劲增长机会的公司具有高市盈率。
（2）风险。
低风险股票具有高市盈率。
（3）会计方法。
采用保守会计方法的公司具有高市盈率。
5．股票市场交易商：持有一项存货，然后准备在任何时点进行买卖。
经纪人：将买者和卖者撮合在一起，但并不持有存货。
9.2课后习题详解一、概念题1．股利支付率（payout ratio）答：股利支付率一般指公司发放给普通股股东的现金股利占总利润的比例。
公司理财 罗斯 第9 版Chap005
Advantages:
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IRR: Example
Consider the following project:
$50 $100 $150
0 -$200
1
2
3
The internal rate of return for this project is 19.44%
$50 $100 $150 NPV 0 200 2 (1 IRR ) (1 IRR ) (1 IRR ) 3
You first enter your range of cash flows, beginning with the initial cash flow. You can enter a guess, but it is not necessary. The default format is a whole percent – you will normally want to increase the decimal places to at least two.
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5.2 The Payback Period Method
How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria:
$150.00 $100.00 NPV $50.00 $0.00 -1% ($50.00) ($100.00) Discount rate
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Cha10 罗斯公司理财第九版原版书课后习题
Company Stock One option in the 401(k) plan is stock in East Coast Yachts. The company is currently privately held. However, when you interviewed with the owner, Larissa Warren, she informed you the company was expected to go public in the next three to four years. Until then, a company stock price is simply set each year by the board of directors.Bledsoe S&P 500 Index Fund This mutual fund tracks the S&P 500. Stocks in the fund are weighted exactly the same as the S&P 500. This means the fund return is approximately the return on the S&P 500, minus expenses. Because an index fund purchases assets based on the composition of the index it is following, the fund manager is not required to research stocks and make investment decisions. The result is that the fund expenses are usually low. The Bledsoe S&P 500 Index Fund charges expenses of .15 percent of assets per year.Bledsoe Small-Cap Fund This fund primarily invests in small-capitalization stocks. As such, the returns of the fund are more volatile. The fund can also invest 10 percent of its assets in companies based outside the United States. This fund charges 1.70 percent in expenses.Bledsoe Large-Company Stock Fund This fund invests primarily in large-capitalization stocks of companies based in the United States. The fund is managed by Evan Bledsoe and has outperformed the market in six of the last eight years. The fund charges 1.50 percent in expenses.Bledsoe Bond Fund This fund invests in long-term corporate bonds issued by U.S.–domiciled companies. The fund is restricted to investments in bonds with an investment-grade credit rating. This fund charges 1.40 percent in expenses.Bledsoe Money Market Fund This fund invests in short-term, high–credit quality debt instruments, which include Treasury bills. As such, the return on the money market fund is only slightly higher than the return on Treasury bills. Because of the credit quality and short-term nature of the investments, there is only a very slight risk of negative return. The fund charges .60 percent in expenses.1. What advantages do the mutual funds offer compared to the company stock?2. Assume that you invest 5 percent of your salary and receive the full 5 percent match from EastCoast Yachts. What EAR do you earn from the match? What conclusions do you draw about matching plans?3. Assume you decide you should invest at least part of your money in large-capitalization stocksof companies based in the United States. What are the advantages and disadvantages of choosing the Bledsoe Large-Company Stock Fund compared to the Bledsoe S&P 500 Index Fund?4. The returns on the Bledsoe Small-Cap Fund are the most volatile of all the mutual funds offeredin the 401(k) plan. Why would you ever want to invest in this fund? When you examine the expenses of the mutual funds, you will notice that this fund also has the highest expenses. Does this affect your decision to invest in this fund?5. A measure of risk-adjusted performance that is often used is the Sharpe ratio. The Sharpe ratiois calculated as the risk premium of an asset divided by its standard deviation. The standard deviations and returns of the funds over the past 10 years are listed here. Calculate the Sharpe ratio for each of these funds. Assume that the expected return and standard deviation of the company stock will be 16 percent and 70 percent, respectively. Calculate the Sharpe ratio for the company stock. How appropriate is the Sharpe ratio for these assets? When would you use the Sharpe ratio?6. What portfolio allocation would you choose? Why? Explain your thinking carefully.。
Chap022公司理财罗斯英文原书第九版底2章
Option Premium
=
Intrinsic Value
+ Speculative Value
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Call Option Payoffs
60
Option payoffs ($)
40
20
20 –20
40
50
60
80
100
120 Stock price ($)
–40
Exercise price = $50
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Put Option Pricing at Expiry
At expiry, an American put option is worth the same as a European option with the same characteristics. If the put is in-the-money, it is worth E – ST. If the put is out-of-the-money, it is worthless. P = Max[E – ST, 0]
Option Quotes
In-the-Money
At-the-Money
Exercising the option would result in a zero payoff (i.e., exercise price equal to spot price). Exercising the option would result in a negative payoff.
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Option Quotes
This option has a strike price of $135;
公司理财Corporate_Finance_第九版_CASE答案(完整资料).doc
【最新整理，下载后即可编辑】Case SolutionsFundamentals of Corporate FinanceRoss, Westerfield, and Jordan9th editionCHAPTER 1THE McGEE CAKE COMPANY1.The advantages to a LLC are: 1) Reduction of personal liability. A soleproprietor has unlimited liability, which can include the potential loss of all personal assets. 2) Taxes. Forming an LLC may mean that more expenses can be considered business expenses and be deducted from the company’s income. 3) Improved credibility. The business may have increased credibility in the business world compared to a sole proprietorship. 4) Ability to attract investment. Corporations, even LLCs, can raise capital through the sale of equity. 5) Continuous life. Sole proprietorships have a limited life, while corporations have a potentially perpetual life. 6) Transfer of ownership. It is easier to transfer ownership in a corporation through the sale of stock.The biggest disadvantage is the potential cost, although the cost of forminga LLC can be relatively small. There are also other potential costs, includingmore expansive record-keeping.2.Forming a corporation has the same advantages as forming a LLC, but thecosts are likely to be higher.3.As a small company, changing to a LLC is probably the most advantageousdecision at the current time. If the company grows, and Doc and Lyn are willing to sell more equity ownership, the company can reorganize as a corporation at a later date. Additionally, forming a LLC is likely to be less expensive than forming a corporation.CHAPTER 2CASH FLOWS AND FINANCIAL STATEMENTS AT SUNSET BOARDS Below are the financial statements that you are asked to prepare.1.The income statement for each year will look like this:Income statement2008 2009Sales $247,259 $301,392Cost of goods sold 126,038 159,143Selling & administrative 24,787 32,352Depreciation 35,581 40,217EBIT $60,853 $69,680Interest 7,735 8,866EBT $53,118 $60,814Taxes 10,624 12,163Net income $42,494 $48,651Dividends $21,247 $24,326Addition to retainedearnings 21,247 24,3262.The balance sheet for each year will be:Balance sheet as of Dec. 31, 2008C-26 CASE SOLUTIONSCash $18,187 Accounts payable $32,143 Accountsreceivable 12,887 Notes payable 14,651 Inventory 27,119 Current liabilities $46,794 Current assets $58,193Long-term debt $79,235 Net fixed assets $156,975 Owners' equity 89,139Total assets $215,168 Total liab. &equity $215,168In the first year, equity is not given. Therefore, we must calculate equity as a plug variable. Since total liabilities & equity is equal to total assets, equity can be calculated as:Equity = $215,168 – 46,794 – 79,235Equity = $89,139CHAPTER 2 C-5Balance sheet as of Dec. 31, 2009Cash $27,478 Accounts payable $36,404 Accountsreceivable 16,717 Notes payable 15,997 Inventory 37,216 Current liabilities $52,401 Current assets $81,411Long-term debt $91,195 Net fixed assets $191,250 Owners' equity 129,065Total assets $272,661 Total liab. &equity $272,661The owner’s equity for 2009 is the beginning of year owner’s equity, plus the addition to retained earnings, plus the new equity, so:Equity = $89,139 + 24,326 + 15,600Equity = $129,065ing the OCF equation:OCF = EBIT + Depreciation – TaxesThe OCF for each year is:OCF2008 = $60,853 + 35,581 – 10,624OCF2008 = $85,180OCF2009 = $69,680 + 40,217 – 12,163OCF2009 = $97,734C-26 CASE SOLUTIONS4.To calculate the cash flow from assets, we need to find the capital spendingand change in net working capital. The capital spending for the year was: Capital spendingEnding net fixed assets $191,250– Beginning net fixedassets 156,975+ Depreciation 40,217Net capital spending $74,492And the change in net working capital was:Change in net working capitalEnding NWC $29,010– Beginning NWC 11,399Change in NWC $17,611CHAPTER 2 C-5 So, the cash flow from assets was:Cash flow from assetsOperating cash flow $97,734– Net capital spending 74,492– Change in NWC 17,611Cash flow from assets $ 5,6315.The cash flow to creditors was:Cash flow to creditorsInterest paid $8,866– Net new borrowing 11,960Cash flow to creditors –$3,0946.The cash flow to stockholders was:Cash flow tostockholdersDividends paid $24,326– Net new equityraised 15,600Cash flow tostockholders $8,726Answers to questions1.The firm had positive earnings in an accounting sense (NI > 0) and hadpositive cash flow from operations. The firm invested $17,611 in new netC-26 CASE SOLUTIONSworking capital and $74,492 in new fixed assets. The firm gave $5,631 to its stakeholders. It raised $3,094 from bondholders, and paid $8,726 to stockholders.2.The expansion plans may be a little risky. The company does have a positivecash flow, but a large portion of the operating cash flow is already going to capital spending. The company has had to raise capital from creditors and stockholders for its current operations. So, the expansion plans may be too aggressive at this time. On the other hand, companies do need capital to grow. Before investing or loaning the company money, you would want to know where the current capital spending is going, and why the company is spending so much in this area already.CHAPTER 3RATIOS ANALYSIS AT S&S AIR1.The calculations for the ratios listed are:Current ratio = $2,186,520 / $2,919,000Current ratio = 0.75 timesQuick ratio = ($2,186,250 – 1,037,120) / $2,919,000Quick ratio = 0.39 timesCash ratio = $441,000 / $2,919,000Cash ratio = 0.15 timesTotal asset turnover = $30,499,420 / $18,308,920Total asset turnover = 1.67 timesInventory turnover = $22,224,580 / $1,037,120Inventory turnover = 21.43 timesReceivables turnover = $30,499,420 / $708,400Receivables turnover = 43.05 timesTotal debt ratio = ($18,308,920 – 10,069,920) / $18,308,920 Total debt ratio = 0.45 timesDebt-equity ratio = ($2,919,000 + 5,320,000) / $10,069,920C-26 CASE SOLUTIONSDebt-equity ratio = 0.82 timesEquity multiplier = $18,308,920 / $10,069,920Equity multiplier = 1.82 timesTimes interest earned = $3,040,660 / $478,240Times interest earned = 6.36 timesCash coverage = ($3,040,660 + 1,366,680) / $478,420 Cash coverage = 9.22 timesProfit margin = $1,537,452 / $30,499,420Profit margin = 5.04%Return on assets = $1,537,452 / $18,308,920Return on assets = 8.40%Return on equity = $1,537,452 / $10,069,920Return on equity = 15.27%CHAPTER 3 C-11 2. Boeing is probably not a good aspirant company. Even though bothcompanies manufacture airplanes, S&S Air manufactures small airplanes, while Boeing manufactures large, commercial aircraft. These are two different markets. Additionally, Boeing is heavily involved in the defense industry, as well as Boeing Capital, which finances airplanes.Bombardier is a Canadian company that builds business jets, short-range airliners and fire-fighting amphibious aircraft and also provides defense-related services. It is the third largest commercial aircraft manufacturer in the world. Embraer is a Brazilian manufacturer than manufactures commercial, military, and corporate airplanes. Additionally, the Brazilian government is a part owner of the company. Bombardier and Embraer are probably not good aspirant companies because of the diverse range of products and manufacture of larger aircraft.Cirrus is the world's second largest manufacturer of single-engine, piston-powered aircraft. Its SR22 is the world's best selling plane in its class. The company is noted for its innovative small aircraft and is a good aspirant company.Cessna is a well known manufacturer of small airplanes. The company produces business jets, freight- and passenger-hauling utility Caravans, personal and small-business single engine pistons. It may be a good aspirant company, however, its products could be considered too broad and diversified since S&S Air produces only small personal airplanes.3. S&S is below the median industry ratios for the current and cash ratios.This implies the company has less liquidity than the industry in general.However, both ratios are above the lower quartile, so there are companiesC-26 CASE SOLUTIONSin the industry with lower liquidity ratios than S&S Air. The company may have more predictable cash flows, or more access to short-term borrowing.If you created an Inventory to Current liabilities ratio, S&S Air would havea ratio that is lower than the industry median. The current ratio is below theindustry median, while the quick ratio is above the industry median. This implies that S&S Air has less inventory to current liabilities than the industry median. S&S Air has less inventory than the industry median, but more accounts receivable than the industry since the cash ratio is lower than the industry median.The turnover ratios are all higher than the industry median; in fact, all three turnover ratios are above the upper quartile. This may mean that S&S Air is more efficient than the industry.The financial leverage ratios are all below the industry median, but above the lower quartile. S&S Air generally has less debt than comparable companies, but still within the normal range.The profit margin, ROA, and ROE are all slightly below the industry median, however, not dramatically lower. The company may want to examine its costs structure to determine if costs can be reduced, or price can be increased.Overall, S&S Air’s performance seems good, although the liquidity ratios indicate that a closer look may be needed in this area.CHAPTER 3 C-11 Below is a list of possible reasons it may be good or bad that each ratio is higher or lower than the industry. Note that the list is not exhaustive, but merely one possible explanation for each ratio.Ratio Good BadCurrent ratio Better at managingcurrent accounts. May be having liquidity problems.Quick ratio Better at managingcurrent accounts. May be having liquidity problems.Cash ratio Better at managingcurrent accounts. May be having liquidity problems.Total asset turnover Better at utilizing assets. Assets may be older anddepreciated, requiringextensive investmentsoon.Inventory turnover Better at inventorymanagement, possibly dueto better procedures.Could be experiencinginventory shortages.Receivables turnover Better at collectingreceivables.May have credit termsthat are too strict.Decreasing receivablesturnover may increasesales.Total debt ratio Less debt than industrymedian means thecompany is less likely toexperience creditproblems. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE.Debt-equity Less debt than industry Increasing the amount ofC-26 CASE SOLUTIONSratio median means thecompany is less likely toexperience creditproblems. debt can increase shareholder returns. Especially notice that it will increase ROE.Equity multiplier Less debt than industrymedian means thecompany is less likely toexperience creditproblems.Increasing the amount ofdebt can increaseshareholder returns.Especially notice that itwill increase ROE.TIE Higher quality materialscould be increasing costs. The company may have more difficulty meeting interest payments in a downturn.Cash coverage Less debt than industrymedian means thecompany is less likely toexperience creditproblems. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE.Profit margin The PM is slightly belowthe industry median. Itcould be a result of higherquality materials or bettermanufacturing. Company may be having trouble controlling costs.ROA Company may have newerassets than the industry. Company may have newer assets than the industry.ROE Lower profit margin maybe a result of higherquality. Profit margin and EM are lower than industry, which results in the lower ROE.CHAPTER 4PLANNING FOR GROWTH AT S&S AIR1.To calculate the internal growth rate, we first need to find the ROA and theretention ratio, so:ROA = NI / TAROA = $1,537,452 / $18,309,920ROA = .0840 or 8.40%b = Addition to RE / NIb = $977,452 / $1,537,452b = 0.64Now we can use the internal growth rate equation to get:Internal growth rate = (ROA × b) / [1 – (ROA × b)]Internal growth rate = [0.0840(.64)] / [1 – 0.0840(.64)]Internal growth rate = .0564 or 5.64%To find the sustainable growth rate, we need the ROE, which is:ROE = NI / TEROE = $1,537,452 / $10,069,920ROE = .1527 or 15.27%C-26 CASE SOLUTIONSUsing the retention ratio we previously calculated, the sustainable growth rate is:Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]Sustainable growth rate = [0.1527(.64)] / [1 – 0.1527(.64)]Sustainable growth rate = .1075 or 10.75%The internal growth rate is the growth rate the company can achieve with no outside financing of any sort. The sustainable growth rate is the growth rate the company can achieve by raising outside debt based on its retained earnings and current capital structure.CHAPTER 4 C-21 2.Pro forma financial statements for next year at a 12 percent growth rate are:Income statementSales $ 34,159,35COGS 24,891,530 Other expenses 4,331,600 Depreciation 1,366,680EBIT $ 3,569,541Interest 478,240Taxable income $ 3,091,301Taxes (40%) 1,236,520Net income $ 1,854,78Dividends $ 675,583C-26 CASE SOLUTIONSAdd to RE 1,179,197Balance sheetAssets Liabilities & EquityCurrent Assets Current LiabilitiesCash $ 493,92AccountsPayable $ 995,680Accounts rec. 793,408 Notes Payable 2,030,000 Inventory 1,161,574 Total CL $ 3,025,680 Total CA $ 2,448,902Long-term debt $ 5,320,000ShareholderEquityCommon stock $ 350,000Fixed assets Retainedearnings 10,899,117Net PP&E $ 18,057,088 Total Equity $ 11,249,117Total Assets $ 20,505,990 Total L&E $ 19,594,787CHAPTER 4 C-21 So, the EFN is:EFN = Total assets – Total liabilities and equityEFN = $20,505,990 – 19,594,797EFN = $911,193The company can grow at this rate by changing the way it operates. For example, if profit margin increases, say by reducing costs, the ROE increases, it will increase the sustainable growth rate. In general, as long as the company increases the profit margin, total asset turnover, or equity multiplier, the higher growth rate is possible. Note however, that changing any one of these will have the effect of changing the pro forma financial statements.C-26 CASE SOLUTIONS3.Now we are assuming the company can only build in amounts of $5 million.We will assume that the company will go ahead with the fixed asset acquisition. To estimate the new depreciation charge, we will find the current depreciation as a percentage of fixed assets, then, apply this percentage to the new fixed assets. The depreciation as a percentage of assets this year was:Depreciation percentage = $1,366,680 / $16,122,400Depreciation percentage = .0848 or 8.48%The new level of fixed assets with the $5 million purchase will be:New fixed assets = $16,122,400 + 5,000,000 = $21,122,400So, the pro forma depreciation will be:Pro forma depreciation = .0848($21,122,400)Pro forma depreciation = $1,790,525We will use this amount in the pro forma income statement. So, the pro forma income statement will be:Income statementSales $ 34,159,35COGS 24,891,530 Other expensesCHAPTER 4 C-214,331,600Depreciation 1,790,525EBIT $ 3,145,696Interest 478,240Taxable income $ 2,667,456Taxes (40%) 1,066,982Net income $ 1,600,473Dividends $ 582,955Add to RE 1,017,519C-26 CASE SOLUTIONSThe pro forma balance sheet will remain the same except for the fixed asset and equity accounts. The fixed asset account will increase by $5 million, rather than the growth rate of sales.Balance sheetAssets Liabilities & EquityCurrent Assets Current LiabilitiesCash $ 493,92AccountsPayable $ 995,680Accounts rec. 793,408 Notes Payable 2,030,000 Inventory 1,161,574 Total CL $ 3,025,680 Total CA $ 2,448,902Long-term debt $ 5,320,000ShareholderEquityCommon stock $ 350,000Fixed assets Retainedearnings 10,737,439Net PP&E $ 21,122,400 Total Equity $ 11,087,439Total Assets $ 23,571,302 Total L&E $ 19,433,119CHAPTER 4 C-21 So, the EFN is:EFN = Total assets – Total liabilities and equityEFN = $23,581,302 – 19,433,119EFN = $4,138,184Since the fixed assets have increased at a faster percentage than sales, the capacity utilization for next year will decrease.CHAPTER 6THE MBA DECISION1. Age is obviously an important factor. The younger an individual is, the moretime there is for the (hopefully) increased salary to offset the cost of the decision to return to school for an MBA. The cost includes both the explicit costs such as tuition, as well as the opportunity cost of the lost salary.2. Perhaps the most important nonquantifiable factors would be whether ornot he is married and if he has any children. With a spouse and/or children, he may be less inclined to return for an MBA since his family may be less amenable to the time and money constraints imposed by classes. Other factors would include his willingness and desire to pursue an MBA, job satisfaction, and how important the prestige of a job is to him, regardless of the salary.3.He has three choices: remain at his current job, pursue a Wilton MBA, orpursue a Mt. Perry MBA. In this analysis, room and board costs are irrelevant since presumably they will be the same whether he attends college or keeps his current job. We need to find the aftertax value of each, so:Remain at current job:Aftertax salary = $55,000(1 – .26) = $40,700CHAPTER 6 C-27 His salary will grow at 3 percent per year, so the present value of his aftertax salary is:PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $40,700{[1 – [(1 +.065)/(1 + .03)]38} / (.065 – .03)PV = $836,227.34Wilton MBA:Costs:Total direct costs = $63,000 + 2,500 + 3,000 = $68,500PV of direct costs = $68,500 + 68,500 / (1.065) = $132,819.25PV of indirect costs (lost salary) = $40,700 / (1.065) + $40,700(1 + .03) / (1 + .065)2 = $75,176.00Salary:PV of aftertax bonus paid in 2 years = $15,000(1 –.31) / 1.0652= $9,125.17Aftertax salary = $98,000(1 – .31) = $67,620C-26 CASE SOLUTIONSHis salary will grow at 4 percent per year. We must also remember that he will now only work for 36 years, so the present value of his aftertax salary is: PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $67,620{[1 – [(1 +.065)/(1 + .04)]36} / (.065 – .04)PV = $1,554,663.22Since the first salary payment will be received three years from today, so we need to discount this for two years to find the value today, which will be: PV = $1,544,663.22 / 1.0652PV = $1,370,683.26So, the total value of a Wilton MBA is:Value = –$75,160 – 132,819.25 + 9,125.17 + 1,370,683.26 =$1,171,813.18Mount Perry MBA:Costs:Total direct costs = $78,000 + 3,500 + 3,000 = $86,500. Note, this is also the PV of the direct costs since they are all paid today.PV of indirect costs (lost salary) = $40,700 / (1.065) = $38,215.96Salary:CHAPTER 6 C-27 PV of aftertax bonus paid in 1 year = $10,000(1 – .29) / 1.065 = $6,666.67 Aftertax salary = $81,000(1 – .29) = $57,510His salary will grow at 3.5 percent per year. We must also remember that he will now only work for 37 years, so the present value of his aftertax salary is: PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $57,510{[1 – [(1 +.065)/(1 + .035)]37} / (.065 – .035)PV = $1,250,991.81Since the first salary payment will be received two years from today, so we need to discount this for one year to find the value today, which will be:PV = $1,250,991.81 / 1.065PV = $1,174,640.20So, the total value of a Mount Perry MBA is:Value = –$86,500 – 38,215.96 + 6,666.67 + 1,174,640.20 = $1,056,590.90C-26 CASE SOLUTIONS4.He is somewhat correct. Calculating the future value of each decision willresult in the option with the highest present value having the highest future value. Thus, a future value analysis will result in the same decision. However, his statement that a future value analysis is the correct method is wrong since a present value analysis will give the correct answer as well.5. To find the salary offer he would need to make the Wilton MBA asfinancially attractive as the as the current job, we need to take the PV of his current job, add the costs of attending Wilton, and the PV of the bonus on an aftertax basis. So, the necessary PV to make the Wilton MBA the same as his current job will be:PV = $836,227.34 + 132,819.25 + 75,176.00 – 9,125.17 = $1,035,097.42This PV will make his current job exactly equal to the Wilton MBA on a financial basis. Since his salary will still be a growing annuity, the aftertax salary needed is:PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]$1,035,097.42 = C {[1 – [(1 +.065)/(1 + .04)]36} / (.065 – .04)C = $45,021.51This is the aftertax salary. So, the pretax salary must be:Pretax salary = $45,021.51 / (1 – .31) = $65,248.576.The cost (interest rate) of the decision depends on the riskiness of the use offunds, not the source of the funds. Therefore, whether he can pay cash orCHAPTER 6 C-27 must borrow is irrelevant. This is an important concept which will be discussed further in capital budgeting and the cost of capital in later chapters.CHAPTER 7FINANCING S&S AIR’S EXPANSION PLANS WITH A BOND ISSUEA rule of thumb with bond provisions is to determine who benefits by theprovision. If the company benefits, the bond will have a higher coupon rate.If the bondholders benefit, the bond will have a lower coupon rate.1. A bond with collateral will have a lower coupon rate. Bondholders have theclaim on the collateral, even in bankruptcy. Collateral provides an asset that bondholders can claim, which lowers their risk in default. The downside of collateral is that the company generally cannot sell the asset used as collateral, and they will generally have to keep the asset in good working order.2.The more senior the bond is, the lower the coupon rate. Senior bonds getfull payment in bankruptcy proceedings before subordinated bonds receive any payment. A potential problem may arise in that the bond covenant may restrict the company from issuing any future bonds senior to the current bonds.3. A sinking fund will reduce the coupon rate because it is a partial guaranteeto bondholders. The problem with a sinking fund is that the company must make the interim payments into a sinking fund or face default. This means the company must be able to generate these cash flows.4. A provision with a specific call date and prices would increase the couponrate. The call provision would only be used when it is to the company’s advantage, thus the bondholder’s disadvantage. The downside is theCHAPTER 7 C-29 higher coupon rate. The company benefits by being able to refinance at a lower rate if interest rates fall significantly, that is, enough to offset the call provision cost.5. A deferred call would reduce the coupon rate relative to a call provision witha deferred call. The bond will still have a higher rate relative to a plain vanillabond. The deferred call means that the company cannot call the bond for a specified period. This offers the bondholders protection for this period. The disadvantage of a deferred call is that the company cannot call the bond during the call protection period. Interest rates could potentially fall to the point where it would be beneficial for the company to call the bond, yet the company is unable to do so.6. A make-whole call provision should lower the coupon rate in comparison toa call provision with specific dates since the make-whole call repays thebondholder the present value of the future cash flows. However, a make-whole call provision should not affect the coupon rate in comparison to a plain vanilla bond. Since the bondholders are made whole, they should be indifferent between a plain vanilla bond and a make-whole bond. If a bond with a make-whole provision is called, bondholders receive the market value of the bond, which they can reinvest in another bond with similar characteristics. If we compare this to a bond with a specific call price, investors rarely receive the full market value of the future cash flows.CASE 3 C-30 7. A positive covenant would reduce the coupon rate. The presence of positivecovenants protects bondholders by forcing the company to undertake actions that benefit bondholders. Examples of positive covenants would be: the company must maintain audited financial statements; the company must maintain a minimum specified level of working capital or a minimum specified current ratio; the company must maintain any collateral in good working order. The negative side of positive covenants is that the company is restricted in its actions. The positive covenant may force the company into actions in the future that it would rather not undertake.8. A negative covenant would reduce the coupon rate. The presence ofnegative covenants protects bondholders from actions by the company that would harm the bondholders. Remember, the goal of a corporation is to maximize shareholder wealth. This says nothing about bondholders.Examples of negative covenants would be: the company cannot increase dividends, or at least increase beyond a specified level; the company cannot issue new bonds senior to the current bond issue; the company cannot sell any collateral. The downside of negative covenants is the restriction of the company’s actions.9.Even though the company is not public, a conversion feature would likelylower the coupon rate. The conversion feature would permit bondholders to benefit if the company does well and also goes public. The downside is that the company may be selling equity at a discounted price.10. The downside of a floating-rate coupon is that if interest rates rise, thecompany has to pay a higher interest rate. However, if interest rates fall, the company pays a lower interest rate.CHAPTER 8STOCK VALUATION AT RAGAN, INC.1.The total dividends paid by the company were $126,000. Since there are100,000 shares outstanding, the total earnings for the company were: Total earnings = 100,000($4.54) = $454,000This means the payout ratio was:Payout ratio = $126,000/$454,000 = 0.28So, the retention ratio was:Retention ratio = 1 – .28 = 0.72Using the retention ratio, the company’s growth rate is:g = ROE × b = 0.25*(.72) = .1806 or 18.06%The dividend per share paid this year was:= $63,000 / 50,000D= $1.26DNow we can find the stock price, which is:C-84 CASE SOLUTIONSP 0 = D 1 / (R – g )P 0 = $1.26(1.1806) / (.20 – .1806)P 0 = $76.752.Since Expert HVAC had a write off which affected its earnings per share, we need to recalculate the industry EPS. So, the industry EPS is:Industry EPS = ($0.79 + 1.38 + 1.06) / 3 = $1.08Using this industry EPS, the industry payout ratio is:Industry payout ratio = $0.40/$1.08 = .3715 or 37.15%So, the industry retention ratio isIndustry retention ratio = 1 – .3715 = .6285 or 62.85%。
公司理财第九版英文答案
Solutions ManualCorporate FinanceRoss, Westerfield, and Jaffe9th editionCHAPTER 1INTRODUCTION TO CORPORATE FINANCEAnswers to Concept Questions1. In the corporate form of ownership, the shareholders are the owners of the firm.The shareholders elect the directors of the corporation, who in turn appoint the firm’s management. This separation of ownership from control in the corporate form of organization is what causes agency problems to exist. Management may actin its own or someone else’s best interests, rather than those of the shareholders. If such events occur, they may contradict the goal of maximizing the share price of the equity of the firm.2.Such organizations frequently pursue social or political missions, so manydifferent goals are conceivable. One goal that is often cited is revenue minimization; i.e., provide whatever goods and services are offered at the lowest possible cost to society. A better approach might be to observe that even a not-for-profit business has equity. Thus, one answer is that the appropriate goal is to maximize the value of the equity.3.Presumably, the current stock value reflects the risk, timing, and magnitude ofall future cash flows, both short-term and long-term. If this is correct, then the statement is false.4.An argument can be made either way. At the one extreme, we could argue that in amarket economy, all of these things are priced. There is thus an optimal level of, for example, ethical and/or illegal behavior, and the framework of stock valuation explicitly includes these. At the other extreme, we could argue that these are non-economic phenomena and are best handled through the political process. A classic (and highly relevant) thought question that illustrates this debate goes something like this: “A firm has estimated that the cost of improving the safety of one of its products is $30 million. However, the firm believes that improving the safety of the product will only save $20 million in product liability claims. What s hould the firm do?”5.The goal will be the same, but the best course of action toward that goal may bedifferent because of differing social, political, and economic institutions.6.The goal of management should be to maximize the share price for the currentshareholders. If management believes that it can improve the profitability of the firm so that the share price will exceed $35, then they should fight the offer from the outside company. If management believes that this bidder or other unidentified bidders will actually pay more than $35 per share to acquire the company, then they should still fight the offer. However, if the current management cannot increase the value of the firm beyond the bid price, and no other higher bids come in, then management is not acting in the interests of the shareholders by fighting the offer. Since current managers often lose their jobs when the corporation is acquired, poorly monitored managers have an incentive to fight corporate takeovers in situations such as this.7.We would expect agency problems to be less severe in other countries, primarilydue to the relatively small percentage of individual ownership. Fewer individual owners should reduce the number of diverse opinions concerning corporate goals.The high percentage of institutional ownership might lead to a higher degree of agreement between owners and managers on decisions concerning risky projects. In addition, institutions may be better able to implement effective monitoring mechanisms on managers than can individual owners, based on the institutions’ deeper resources and experiences with their own management.8. The increase in institutional ownership of stock in the United States and thegrowing activism of these large shareholder groups may lead to a reduction in agency problems for U.S. corporations and a more efficient market for corporate control. However, this may not always be the case. If the managers of the mutual fund or pension plan are not concerned with the interests of the investors, the agency problem could potentially remain the same, or even increase since there is the possibility of agency problems between the fund and its investors.9. How much is too much? Who is worth more, Ray Irani or Tiger Woods? The simplestanswer is that there is a market for executives just as there is for all types of labor. Executive compensation is the price that clears the market. The same is true for athletes and performers. Having said that, one aspect of executive compensation deserves comment. A primary reason executive compensation has grown so dramatically is that companies have increasingly moved to stock-based compensation. Such movement is obviously consistent with the attempt to better align stockholder and management interests. In recent years, stock prices have soared, so management has cleaned up. It is sometimes argued that much of this reward is simply due to rising stock prices in general, not managerial performance. Perhaps in the future, executive compensation will be designed to reward only differential performance, i.e., stock price increases in excess of general market increases.10. Maximizing the current share price is the same as maximizing the future shareprice at any future period. The value of a share of stock depends on all of the future cash flows of company. Another way to look at this is that, barring large cash payments to shareholders, the expected price of the stock must be higher in the future than it is today. Who would buy a stock for $100 today when the share price in one year is expected to be $80?CHAPTER 2FINANCIAL STATEMENTS AND CASH FLOWAnswers to Concepts Review and Critical Thinking Questions1.True. Every asset can be converted to cash at some price. However, when we arereferring to a liquid asset, the added assumption that the asset can be quickly converted to cash at or near market value is important.2. The recognition and matching principles in financial accounting call for revenues,and the costs associated with producing those revenues, to be “booked” when the revenue process is essentially complete, not necessarily when the cash is collected or bills are paid. Note that this way is not necessarily correct; it’s the way accountants have chosen to do it.3.The bottom line number shows the change in the cash balance on the balance sheet.As such, it is not a useful number for analyzing a company.4. The major difference is the treatment of interest expense. The accountingstatement of cash flows treats interest as an operating cash flow, while the financial cash flows treat interest as a financing cash flow. The logic of the accounting statement of cash flows is that since interest appears on the income statement, which shows the operations for the period, it is an operating cash flow. In reality, interest is a financing expense, which results from the company’s choice of debt and equity. We will have more to say about this in a later chapter. When comparing the two cash flow statements, the financial statement of cash flows is a more appropriate measure of the company’s performance because of its treatment of interest.5.Market values can never be negative. Imagine a share of stock selling for –$20.This would mean that if you placed an order for 100 shares, you would get the stock along with a check for $2,000. How many shares do you want to buy? More generally, because of corporate and individual bankruptcy laws, net worth for a person or a corporation cannot be negative, implying that liabilities cannot exceed assets in market value.6.For a successful company that is rapidly expanding, for example, capital outlayswill be large, possibly leading to negative cash flow from assets. In general, what matters is whether the money is spent wisely, not whether cash flow from assets is positive or negative.7.It’s probably not a good sign for an established company to have negative cashflow from operations, but it would be fairly ordinary for a start-up, so it depends.8. For example, if a company were to become more efficient in inventory management,the amount of inventory needed would decline. The same might be true if the company becomes better at collecting its receivables. In general, anything that leads to a decline in ending NWC relative to beginning would have this effect.Negative net capital spending would mean more long-lived assets were liquidated than purchased.9.If a company raises more money from selling stock than it pays in dividends in aparticular period, its cash flow to stockholders will be negative. If a company borrows more than it pays in interest and principal, its cash flow to creditors will be negative.10. The adjustments discussed were purely accounting changes; they had no cash flowor market value consequences unless the new accounting information caused stockholders to revalue the derivatives.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.To find owners’ equity, we must construct a balance sheet as follows:Balance SheetCA $ 5,300 CL $ 3,900NFA 26,000 LTD 14,200OE ??TA $31,300 TL & OE $31,300We know that total liabilities and owners’ equity (TL & OE) must equal total assets of $31,300. We also know that TL & OE is equal to current liabilities plus long-term debt plus owner’s equity, so owner’s equity is:O E = $31,300 –14,200 – 3,900 = $13,200N WC = CA – CL = $5,300 – 3,900 = $1,4002. The income statement for the company is:Income StatementSales $493,000Costs 210,000Depreciation 35,000EBIT $248,000Interest 19,000EBT $229,000Taxes 80,150Net income $148,850One equation for net income is:Net income = Dividends + Addition to retained earningsRearranging, we get:Addition to retained earnings = Net income – DividendsAddition to retained earnings = $148,850 – 50,000Addition to retained earnings = $98,8503.To find the book value of current assets, we use: NWC = CA – CL. Rearranging tosolve for current assets, we get:CA = NWC + CL = $800,000 + 2,100,000 = $2,900,000The market value of current assets and net fixed assets is given, so:Book value CA = $2,900,000 Market value CA = $2,800,000Book value NFA = $5,000,000 Market value NFA = $6,300,000Book value assets = $7,900,000 Market value assets = $9,100,0004.Taxes = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($246K – 100K)Taxes = $79,190The average tax rate is the total tax paid divided by net income, so:Average tax rate = $79,190 / $246,000Average tax rate = 32.19%The marginal tax rate is the tax rate on the next $1 of earnings, so the marginal tax rate = 39%.5.To calculate OCF, we first need the income statement:Income StatementSales $14,900Costs 5,800Depreciation 1,300EBIT $7,800Interest 780Taxable income $7,020Taxes 2,808Net income $4,212OCF = EBIT + Depreciation – TaxesOCF = $7,800 + 1,300 – 2,808OCF = $6,292 capital spending = NFA end– NFA beg + DepreciationNet capital spending = $1,730,000 – 1,650,000 + 284,000 Net capital spending = $364,0007.The long-term debt account will increase by $10 million, the amount of the newlong-term debt issue. Since the company sold 10 million new shares of stock witha $1 par value, the common stock account will increase by $10 million. Thecapital surplus account will increase by $33 million, the value of the new stock sold above its par value. Since the company had a net income of $9 million, and paid $2 million in dividends, the addition to retained earnings was $7 million, which will increase the accumulated retained earnings account. So, the new long-term debt and stockholders’ equity portion of the balance sheet will be:Long-term debt $ 82,000,000Total long-term debt $ 82,000,000Shareholders equityPreferred stock $ 9,000,000Common stock ($1 par value) 30,000,000Accumulated retained earnings 104,000,000Capital surplus 76,000,000Total equity $ 219,000,000Total Liabilities & Equity $ 301,000,0008.Cash flow to creditors = Interest paid – Net new borrowingCash flow to creditors = $118,000 – (LTD end– LTD beg)Cash flow to creditors = $118,000 – ($1,390,000 – 1,340,000)Cash flow to creditors = $118,000 – 50,000Cash flow to creditors = $68,0009. Cash flow to stockholders = Dividends paid – Net new equityCash flow to stockholders = $385,000 – [(Common end + APIS end) – (Common beg + APIS beg)] Cash flow to stockholders = $385,000 – [($450,000 + 3,050,000) – ($430,000 +2,600,000)]Cash flow to stockholders = $385,000 – ($3,500,000 – 3,030,000)Cash flow to stockholders = –$85,000Note, APIS is the additional paid-in surplus.10. Cash flow from assets = Cash flow to creditors + Cash flow to stockholders= $68,000 – 85,000= –$17,000Cash flow from assets =–$17,000 = OCF – Change in NWC – Net capital spending–$17,000 = OCF – (–$69,000) – 875,000Operating cash flow = –$17,000 – 69,000 + 875,000 Operating cash flow = $789,000Intermediate11.a.The accounting statement of cash flows explains the change in cash duringthe year. The accounting statement of cash flows will be:Statement of cash flowsOperationsNet income $105Depreciation 90Changes in other current assets (55)Accounts payable (10)Total cash flow from operations $170Investing activitiesAcquisition of fixed assets $(140)Total cash flow from investingactivities $(140)Financing activitiesProceeds of long-term debt $30Dividends (45)Total cash flow from financingactivities ($15)Change in cash (on balance sheet) $15b.Change in NWC = NWC end– NWC beg= (CA end– CL end) – (CA beg– CL beg)= [($50 + 155) – 85] – [($35 + 140) – 95)= $120 – 80= $40c.To find the cash flow generated by the firm’s assets, we need the operatingcash flow, and the capital spending. So, calculating each of these, we find:Operating cash flowNet income $105Depreciation 90Operating cashflow $195Note that we can calculate OCF in this manner since there are no taxes.Capital spendingEnding fixed assets $340Beginning fixedassets (290)Depreciation 90Capital spending $140Now we can calculate the cash flow generated by the firm’s assets, which is:Cash flow fromassetsOperating cash flow $195Capital spending (140)Change in NWC (40)Cash flow fromassets $ 1512. With the information provided, the cash flows from the firm are the capitalspending and the change in net working capital, so:Cash flows from the firmCapital spending $(15,000)Additions to NWC (1,500)Cash flows from the firm $(16,500)And the cash flows to the investors of the firm are:Cash flows to investors of thefirmSale of long-term debt (19,000)Sale of common stock (3,000)Dividends paid 19,500Cash flows to investors ofthe firm $(2,500)13.a. The interest expense for the company is the amount of debt times theinterest rate on the debt. So, the income statement for the company is:Income StatementSales $1,200,000Cost of goods sold 450,000Selling costs 225,000Depreciation 110,000EBIT $415,000Interest 81,000Taxable income $334,000Taxes 116,900Net income $217,100b. And the operating cash flow is:OCF = EBIT + Depreciation – TaxesOCF = $415,000 + 110,000 – 116,900OCF = $408,10014. To find the OCF, we first calculate net income.Income StatementSales $167,000Costs 91,000Depreciation 8,000Other expenses 5,400EBIT $62,600Interest 11,000Taxable income $51,600Taxes 18,060Net income $33,540Dividends $9,500Additions to RE $24,040a. OCF = EBIT + Depreciation – TaxesOCF = $62,600 + 8,000 – 18,060OCF = $52,540b. CFC = Interest – Net new LTDCFC = $11,000 – (–$7,100)CFC = $18,100Note that the net new long-term debt is negative because the company repaidpart of its long-term debt.c. CFS = Dividends – Net new equityCFS = $9,500 – 7,250CFS = $2,250d. We know that CFA = CFC + CFS, so:CFA = $18,100 + 2,250 = $20,350CFA is also equal to OCF – Net capital spending – Change in NWC. Wealready know OCF. Net capital spending is equal to:Net capital spending = Increase in NFA + DepreciationNet capital spending = $22,400 + 8,000Net capital spending = $30,400Now we can use:CFA = OCF – Net capital spending – Change in NWC$20,350 = $52,540 – 30,400 – Change in NWC.Solving for the change in NWC gives $1,790, meaning the company increasedits NWC by $1,790.15. The solution to this question works the income statement backwards. Starting at the bottom:Net income = Dividends + Addition to ret. earningsNet income = $1,530 + 5,300Net income = $6,830Now, looking at the income statement:EBT –(EBT × Ta x rate) = Net incomeRecognize that EBT × tax rate is simply the calculation for taxes. Solving this for EBT yields:EBT = NI / (1– Tax rate)EBT = $6,830 / (1 – 0.65)EBT = $10,507.69Now we can calculate:EBIT = EBT + InterestEBIT = $10,507.69 + 1,900EBIT = $12,407.69The last step is to use:EBIT = Sales – Costs – Depreciation$12,407.69 = $43,000 – 27,500 – DepreciationDepreciation = $3,092.31Solving for depreciation, we find that depreciation = $3,092.3116. The balance sheet for the company looks like this:Balance SheetCash $183,000 Accounts payable $465,000 Accounts receivable 138,000 Notes payable 145,000 Inventory 297,000 Current liabilities $610,000 Current assets $618,000 Long-term debt 1,550,000Total liabilities $2,160,000 Tangible net fixed assets3,200,000Intangible net fixed assets 695,000 Common stock ??Accumulated ret. earnings 1,960,000 Total assets $4,513,000 Total liab. & owners’ equity$4,513,000Total liabiliti es and owners’ equity is:TL & OE = Total debt + Common stock + Accumulated retained earningsSolving for this equation for equity gives us:Common stock = $4,513,000 – 1,960,000 – 2,160,000Common stock = $393,00017. The market value of sharehol ders’ equity cannot be negative. A negative marketvalue in this case would imply that the company would pay you to own the stock.The market value of shareholders’ equity can be stated as: Shareholders’ equity = Max [(TA – TL), 0]. So, if TA is $9,700, equity is equal to $800, and if TA is $6,800, equity is equal to $0. We should note here that while the market value of equity cannot be negative, the book value of shareholders’ equity can be negative.18.a. Taxes Growth = 0.15($50K) + 0.25($25K) + 0.34($3K) = $14,770Taxes Income = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($235K) +0.34($7.465M)= $2,652,000b. Each firm has a marginal tax rate of 34% on the next $10,000 of taxableincome, despite their different average tax rates, so both firms will pay an additional $3,400 in taxes.19.Income StatementSales $740,000COGS 610,000A&S expenses 100,000Depreciation 140,000EBIT ($115,000)Interest 70,000Taxable income ($185,000)Taxes (35%) 0 income ($185,000)b.OCF = EBIT + Depreciation – TaxesOCF = ($115,000) + 140,000 – 0OCF = $25,000 income was negative because of the tax deductibility of depreciation andinterest expense. However, the actual cash flow from operations was positive because depreciation is a non-cash expense and interest is a financing expense, not an operating expense.20. A firm can still pay out dividends if net income is negative; it just has to besure there is sufficient cash flow to make the dividend payments.Change in NWC = Net capital spending = Net new equity = 0. (Given)Cash flow from assets = OCF – Change in NWC – Net capital spendingCash flow from assets = $25,000 – 0 – 0 = $25,000Cash flow to stockholders = Dividends – Net new equityCash flow to stockholders = $30,000 – 0 = $30,000Cash flow to creditors = Cash flow from assets – Cash flow to stockholdersCash flow to creditors = $25,000 – 30,000Cash flow to creditors = –$5,000Cash flow to creditors is also:Cash flow to creditors = Interest – Net new LTDSo:Net new LTD = Interest – Cash flow to creditorsNet new LTD = $70,000 – (–5,000)Net new LTD = $75,00021.a.The income statement is:Income StatementSales $15,300Cost of good sold 10,900Depreciation 2,100EBIT $ 2,300Interest 520Taxable income $ 1,780Taxes 712Net income $1,068b.OCF = EBIT + Depreciation – TaxesOCF = $2,300 + 2,100 – 712OCF = $3,688c.Change in NWC = NWC end– NWC beg= (CA end– CL end) – (CA beg– CL beg)= ($3,950 – 1,950) – ($3,400 – 1,900)= $2,000 – 1,500 = $500Net capital spending = NFA end– NFA beg + Depreciation= $12,900 – 11,800 + 2,100= $3,200CFA = OCF – Change in NWC – Net capital spending= $3,688 – 500 – 3,200= –$12The cash flow from assets can be positive or negative, since it represents whether the firm raised funds or distributed funds on a net basis. In this problem, even though net income and OCF are positive, the firm invested heavily in both fixed assets and net working capital; it had to raise a net $12 in funds from its stockholders and creditors to make these investments.d.Cash flow to creditors = Interest – Net new LTD= $520 – 0= $520Cash flow to stockholders = Cash flow from assets –Cash flow to creditors= –$12 – 520= –$532We can also calculate the cash flow to stockholders as:Cash flow to stockholders = Dividends – Net new equitySolving for net new equity, we get:Net new equity = $500 – (–532)= $1,032The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow from operations. The firm invested $500 in new net working capital and $3,200 in new fixed assets. The firm had to raise $12 from its stakeholders to support this new investment. It accomplished this by raising $1,032 in the form of new equity. After paying out $500 of this in the form of dividends to shareholders and $520 in the form of interest to creditors, $12 was left to meet the firm’s cash flow needs for investment.22.a.Total assets 2009 = $780 + 3,480 = $4,260Total liabilities 2009 = $318 + 1,800 = $2,118 Owners’ equity 2009= $4,260 – 2,118 = $2,142Total assets 2010 = $846 + 4,080 = $4,926 Total liabilities 2010 = $348 + 2,064 = $2,412 Owners’ equity 2010 = $4,926 – 2,412 = $2,514b.NWC 2009 = CA09 – CL09 = $780 – 318 = $462NWC 2010 = CA10 – CL10 = $846 – 348 = $498Change in NWC = NWC10 – NWC09 = $498 – 462 = $36c.We can calculate net capital spending as:Net capital spending = Net fixed assets 2010 –Net fixed assets 2009 + DepreciationNet capital spending = $4,080 – 3,480 + 960Net capital spending = $1,560So, the company had a net capital spending cash flow of $1,560. We also know that net capital spending is:Net capital spending = Fixed assets bought – Fixed assets sold$1,560 = $1,800 – Fixed assets soldFixed assets sold = $1,800 – 1,560 = $240To calculate the cash flow from assets, we must first calculate the operating cash flow. The operating cash flow is calculated as follows (you can also prepare a traditional income statement):EBIT = Sales – Costs – DepreciationEBIT = $10,320 – 4,980 – 960EBIT = $4,380EBT = EBIT – InterestEBT = $4,380 – 259EBT = $4,121Taxes = EBT .35Taxes = $4,121 .35Taxes = $1,442OCF = EBIT + Depreciation – TaxesOCF = $4,380 + 960 – 1,442OCF = $3,898Cash flow from assets = OCF – Change in NWC – Net capital spending.Cash flow from assets = $3,898 – 36 – 1,560Cash flow from assets = $2,302 new borrowing = LTD10 – LTD09Net new borrowing = $2,064 – 1,800Net new borrowing = $264Cash flow to creditors = Interest – Net new LTDCash flow to creditors = $259 – 264Cash flow to creditors = –$5Net new borrowing = $264 = Debt issued – Debt retired Debt retired = $360 – 264 = $9623.Balance sheet as of Dec. 31, 2009Cash $2,739 Accounts payable $2,877 Accountsreceivable 3,626 Notes payable 529Inventory 6,447 Currentliabilities $3,406Current assets $12,812Long-term debt $9,173 Net fixed assets $22,970 Owners' equity $23,203Total assets $35,782 Total liab. &equity $35,782Balance sheet as of Dec. 31, 2010Cash $2,802 Accounts payable $2,790 Accountsreceivable 4,085 Notes payable 497Inventory 6,625 Currentliabilities $3,287Current assets $13,512Long-term debt $10,702 Net fixed assets $23,518 Owners' equity $23,041Total assets $37,030 Total liab. &equity $37,0302009 Income Statement 2010 Income Statement Sales $5,223.00Sales $5,606.00 COGS 1,797.00COGS 2,040.00 Other expenses 426.00Other expenses 356.00Depreciation750.00Depreciation751.00EBIT $2,250.00EBIT $2,459.00Interest350.00Interest402.00EBT $1,900.00EBT $2,057.00Taxes646.00Taxes699.38Net income $1,254.00Net income $1,357.62 Dividends $637.00Dividends $701.00Additions toRE 617.00Additions to RE656.6224. OCF = EBIT + Depreciation – TaxesOCF = $2,459 + 751 – 699.38OCF = $2,510.62Change in NWC = NWC end– NWC beg = (CA – CL) end– (CA – CL) beg Change in NWC = ($13,512 – 3,287) – ($12,812 – 3,406) Change in NWC = $819Net capital spending = NFA end– NFA beg+ DepreciationNet capital spending = $23,518 – 22,970 + 751Net capital spending = $1,299Cash flow from assets = OCF – Change in NWC – Net capital spendingCash flow from assets = $2,510.62 – 819 – 1,299Cash flow from assets = $396.62Cash flow to creditors = Interest – Net new LTDNet new LTD = LTD end– LTD begCash flow to creditors = $402 – ($10,702 – 9,173)Cash flow to creditors = –$1,127Net new equity = Common stock end– Common stock begCommon stock + Retained earnings = Total owners’ equityNet new equity = (OE – RE) end– (OE – RE) begNet new equity = OE end– OE beg + RE beg– RE endRE end= RE beg+ Additions to RENet new equity = OE end– OE beg+ RE beg– (RE beg + Additions to RE)= OE end– OE beg– Additions to RENet new equity = $23,041 – 23,203 – 656.62 = –$818.62Cash flow to stockholders = Dividends – Net new equityCash flow to stockholders = $701 – (–$818.62)Cash flow to stockholders = $1,519.62As a check, cash flow from assets is $396.62.Cash flow from assets = Cash flow from creditors + Cash flow to stockholders Cash flow from assets = –$1,127 + 1,519.62Cash flow from assets = $392.62Challenge25. We will begin by calculating the operating cash flow. First, we need the EBIT,which can be calculated as:EBIT = Net income + Current taxes + Deferred taxes + InterestEBIT = $144 + 82 + 16 + 43EBIT = $380Now we can calculate the operating cash flow as:Operating cash flowEarnings before interest and taxes $285Depreciation 78Current taxes (82)Operating cash flow $281The cash flow from assets is found in the investing activities portion of the accounting statement of cash flows, so:Cash flow from assetsAcquisition of fixed assets $148Sale of fixed assets (19)Capital spending $129The net working capital cash flows are all found in the operations cash flow section of the accounting statement of cash flows. However, instead of calculating the net working capital cash flows as the change in net working capital, we must calculate each item individually. Doing so, we find:Net working capital cash flowCash $42Accounts receivable 15Inventories (18)Accounts payable (14)Accrued expenses 7Notes payable (5)Other (2)NWC cash flow $25Except for the interest expense and notes payable, the cash flow to creditors is found in the financing activities of the accounting statement of cash flows. The interest expense from the income statement is given, so:Cash flow to creditorsInterest $43Retirement of debt 135Debt service $178Proceeds from sale of long-term debt (97)Total $81And we can find the cash flow to stockholders in the financing section of the accounting statement of cash flows. The cash flow to stockholders was:Cash flow to stockholdersDividends $ 72Repurchase of stock 11Cash to stockholders $ 83Proceeds from new stock issue (37)Total $ 46。
公司理财(罗斯)第5章(英文)
1 C F PV = 1 + T r (1+ r) (1+ r)T
To value bonds and stocks we need to:
Estimate future cash flows:
Size (how much) and Timing (when)
Discount future cash flows at an appropriate rate:
The rate should be appropriate to the risk presented by the security.
$31.875 $31.875
$31.875
$1,031.875
12 / 31/ 09
1/1/ 05 6 / 30 / 05
McGraw-Hill/Irwin Corporate Finance, 7/e
12 / 31/ 05
6 / 30 / 09
2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
5-6
5.2 How to Value Bonds
We now consider how to value following different types of bonds: Pure discount bonds Level-coupon bonds Consols
2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
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5-8
5.4 The Internal Rate of Return
IRR: the discount rate that sets NPV to zero Minimum Acceptance Criteria:
Ranking Criteria:
Accept if the IRR exceeds the required return Select alternative with the highest IRR
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria
5-2
5.1 Why Use Net Present Value?
Accepting positive NPV projects benefits shareholders.
NPV
uses cash flows NPV uses all the cash flows of the project NPV discounts the cash flows properly
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system.
RANK all alternatives, and select the best one.
Advantages:
Easy to understand Biased toward liquidity
5-7
5.3 The Discounted Payback Period
How long does it take the project to “pay back” its initial investment, taking the time value of money into account? Decision rule: Accept the project if it pays back on a discounted basis within the specified time. By the time you have discounted the cash flows, you might as well calculate the NPV.
Reinvestment assumption:
All future cash flows are assumed to be reinvested at the IRR
Байду номын сангаас
5-9
Internal Rate of Return (IRR)
Disadvantages:
Does not distinguish between investing and borrowing IRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments
$50 $100 $150 NPV 0 200 2 (1 IRR ) (1 IRR ) (1 IRR )3
5-11
NPV Payoff Profile
If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept.
5-13
5.5 Problems with IRR
Multiple IRRs Are We Borrowing or Lending The Scale Problem The Timing Problem
5-14
Mutually Exclusive vs. Independent
5-5
5.2 The Payback Period Method
How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria:
Chapter 5
Net Present Value and Other Investment Rules
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
NPV
$50.00 $0.00 -1% ($50.00) ($100.00) Discount rate
IRR = 19.44%
9% 19% 29% 39%
5-12
Calculating IRR with Spreadsheets
You start with the same cash flows as you did for the NPV. You use the IRR function:
You first enter your range of cash flows, beginning with the initial cash flow. You can enter a guess, but it is not necessary. The default format is a whole percent – you will normally want to increase the decimal places to at least two.
5-3
The Net Present Value (NPV) Rule
Net Present Value (NPV) = Total PV of future CF’s + Initial Investment Estimating NPV:
1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs
5-1
Chapter Outline
5.1 Why Use Net Present Value? 5.2 The Payback Period Method 5.3 The Discounted Payback Period Method 5.4 The Internal Rate of Return 5.5 Problems with the IRR Approach 5.6 The Profitability Index 5.7 The Practice of Capital Budgeting
5-17
The Scale Problem
Would you rather make 100% or 50% on your investments? What if the 100% return is on a $1 investment, while the 50% return is on a $1,000 investment?
0% 4% 8% 12% 16% 20% 24% 28% 32% 36% 40% 44% $100.00 $73.88 $51.11 $31.13 $13.52 ($2.08) ($15.97) ($28.38) ($39.51) ($49.54) ($58.60) ($66.82)
$150.00 $100.00
100% = IRR2
200%
Discount rate
0% = IRR1
5-16
Modified IRR
Calculate the net present value of all cash outflows using the borrowing rate. Calculate the net future value of all cash inflows using the investing rate. Find the rate of return that equates these values. Benefits: single answer and specific rates for borrowing and reinvestment
Be able to compute payback and discounted payback and understand their shortcomings Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches Be able to compute net present value and understand why it is the best decision criterion
Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV