Calculating YTM

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CFA考试指定计算器TI BaII-Plus使用方法

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Memory function The calculator can store numbers for you Example: You calculate the answer to 2 + 3.5 = 5.5 and then wish to store it Press D then K (5.5 has now been stored and assigned to button K Having cleared the screen (P), it is now possible to recall the number by pressing J then K
CFA考试指定计算器TI BaII-Plus使用方法
2016年6月CFA考试已不久远，考生们都如火如荼的备考着，浦江财经老师也一刻不停息的为学员们解答着各Level的疑惑。近期不少学员询问TI BaII-Plus的使用方法，众所周知TI BaII-Plus是CFA考试指定计算器，但是还是有许多新老考生出现不会使用情况，这样其实对CFA考试是硬伤，浦江财经觉得有必要整理一篇文档，来和大家来说说如何正确快速的使用TI BaII-Plus计算器。
Example: Present value of an annuity due Compute the present value of a four year $1,000 annuity using a discount rate of 6% where the first payment is received today. T+0 $1,000 T+1 $1,000 T+2 $1,000 T+3 $1,000 T+4

商业银行管理 ROSE 7e 课后答案chapter_10

CHAPTER 10THE INVESTMENT FUNCTION IN BANKING AND FINANCIAL SERVICESMANAGEMENTGoal of This Chapter: The purpose of this chapter is to discover the types of securities that financial institutions acquire for their investment portfolio and to explore the factors that a manager should consider in determining what securities a financial institution should buy or sell.Key Topics in This Chapter•Nature and Functions of Investments•Investment Securities Available: Advantages and Disadvantages•Measuring Expected Returns•Taxes, Credit, and Interest Rate Risks•Liquidity, Prepayment, and Other Risks•Investment Maturity Strategies•Maturity Management ToolsChapter OutlineI. Introduction: The Roles Performed by Investment Securities in Bank PortfoliosII. Investment Instruments Available to Banks and Other Financial FirmsIII. Popular Money-Market InstrumentsA. Treasury BillsB. Short-Term Treasury Notes and BondsC. Federal Agency SecuritiesD. Certificates of DepositE. International Eurocurrency DepositsF. Bankers' AcceptancesG. Commercial PaperH. Short-Term Municipal ObligationsIV. Popular Capital Market InstrumentsA. Treasury Notes and BondsB. Municipal Notes and BondsC. Corporate Notes and BondsIII. Other Investment Instruments Developed More RecentlyA. Structured NotesB. Securitized AssetsC. Stripped SecuritiesIV. Investment Securities Actually Held by Banks128V. Factors Affecting the Choice of Investment SecuritiesA. Expected Rate of ReturnB. Tax Exposure1. The Tax Status of State and Local Government Bonds2. Bank Qualified Bonds3. Tax Swapping Tool4. The Portfolio Shifting ToolC. Interest-Rate RiskD. Credit or Default RiskE. Business RiskF. Liquidity RiskG. Call RiskH. Prepayment RiskI. Inflation RiskJ. Pledging RequirementsVI. Investment Maturity StrategiesA. The Ladder or Spaced-Maturity PolicyB. The Front-End Load Maturity PolicyC. The Back-End Load Maturity PolicyD. The Barbell StrategyE. The Rate Expectations ApproachVII. Maturity Management ToolsA. The Yield CurveB. DurationVIII. Summary of the ChapterConcept Checks10-1. Why do banks and institutions choose to devote a significant portion of their assets to investment securities?Investments perform many different roles that act as a necessary complement to the advantages loans provide. Investments generally have less credit risk than loans, allow the bank or thrift institution to diversify into different localities than most of its loans permit, provide additional liquid reserves in case more cash is needed, provide collateral as called for by law and regulation to back government deposits, help to stabilize bank income over the business cycle, and aid banks in reducing their exposure to taxes.10-2. What key roles do investments play in the management of a bank or other depository institution?See answer to 10-110-3. What are the principal money market and capital market instruments available to institutions today? What are their most important characteristics?129Banks purchase a wide range of investment securities. The principal money market instruments available to banks today are Treasury bills, federal agency securities, CD's issued by other depository institutions, Eurodollar deposits, bankers' acceptances, commercial paper, andshort-term municipal obligations. The common characteristics of most these instruments is their safety and high marketability. Capital market instruments available to banks include Treasury notes and bonds, state and local government notes and bonds, mortgage-backed securities, and corporate notes and bonds. The characteristics of these securities is their long run income potential.10-4. What types of investment securities do banks prefer the most? Can you explain why?Commercial banks clearly prefer these major types of investment securities: United States Treasury securities, federal agency securities, and state and local government (municipal) bonds and notes. They hold small amounts of equities and other debt securities (mainly corporate notes and bonds). They pick these types because they are best suited to meet the objectives of a banks investment portfolio, such as tax sheltering, reducing overall risk exposure, a source of liquidity and naturally generating income as well as diversifying their assets.10-5. What are securitized assets? Why have they grown so rapidly in recent years?Securitized assets are loans that are placed in a pool and, as the loans generate interest and principal income, that income is passed on to the holders of securities representing an interest in the loan pool. These loan-backed securities are attractive to many banks because of their higher yields and frequent federal guarantees (in the case, for example, of most home-mortgage-backed securities) as well as their relatively high liquidity and marketability10-6. What special risks do securitized assets present to institutions investing in them?Securitized assets often carry substantial interest-rate risk and prepayment risk, which arises when certain loans in the securitized-asset pool are paid off early by the borrowers (usually because interest rates have fallen and new loans can be substituted for the old loans at cheaper loan rates) or are defaulted. Prepayment risk can significantly decrease the values of securities backed by loans and change their effective maturities.10-7. What are structured notes and stripped securities? What unusual features do they contain?Structured notes usually are packaged investments assembled by security dealers that offer customers flexible yields in order to protect their customers' investments against losses due to inflation and changing interest rates. Most structured notes are based upon government or federal agency securities.Stripped securities consist of either principal payments or interest payments from a debt security. The expected cash flow from a Treasury bond or mortgage-backed security is separated into a stream of principal payments and a stream of interest payments, each of which may be sold as a separate security maturing on the day the payment is due. Some of these stripped payments are highly sensitive to changes in interest rates.13013113210-8. How is the expected yield on most bonds determined?For most bonds, this requires the calculation of the yield to maturity (YTM) if the bond is to be held to maturity or the planned holding period yield (HPY) between point of purchase and point of sale. YTM is the expected rate of return on a bond held until its maturity date is reached, based on the bond's purchase price, promised interest payments, and redemption value at maturity. HPY is a rate of discount bringing the current price of a bond in line with its stream of expected cash inflows and its expected sale price at the end of the bank's holding period.10-9. If a government bond is expected to mature in two years and has a current price of $950, what is the bond's YTM if it has a par value of $1,000 and a promised coupon rate of 10 percent? Suppose this bond is sold one year after purchase for a price of $970. What would this investor's holding period yield be?The relevant formula is:$950 = 221Y TM) 1(1000$Y TM) (1$100 Y TM) 1(100$+++++Using a financial calculator we get:YTM = 12.99%If the bond is sold after one year, the formula entries change to:$950 = 11Y TM)(1$970 Y TM) 1(100$+++and the YTM is:YTM = 12.63%10-10. What forms of risk affect investments?The following forms of risk affect investments: interest-rate risk, credit risk, business risk, liquidity risk, prepayment risk, call risk, and inflation risk. Interest-rate risk captures thesensitivity of the value of investments to interest-rate movements, while credit risk reflects the risk of default on either interest or principal payments. Business risk refers to the impact of credit conditions and the economy, while liquidity risk focuses on the price stability and marketability of investments. Prepayment risk is specific to certain types of investments and focuses on the fact that some loans which the securities are based on can be paid off early. Call risk refers to the early retirement of securities and inflation risk refers to their possible loss of purchasing power.10-11. How has the tax exposure of various U.S. bank security investments changed in recent years?In recent years, the government has treated interest income and capital gains from most bank investments as ordinary income for tax purposes. In the past, only interest was treated as ordinary income and capital gains were taxed at a lower rate. Tax reform in the United States has also had a major impact on the relative attractiveness of state and local government bonds as bank investments, limiting bankers’ ability to deduct borrowing costs for tax purposes when borrowing money to buy municipal securities.10-12. Suppose a corporate bond an investment officer would like to purchase for her bank has a before-tax yield of 8.98 percent and the bank is in the 35 percent federal income tax bracket. What is the bond's after-tax gross yield? What after tax rate of return must a prospective loan generate to be competitive with the corporate bond? Does a loan have some advantages for a lending institution that a corporate bond would not have?After-tax Gross Yield on Corporate Bond = 8.98 %( 1 - 0.35) = 5.84%.A prospective loan must generate a comparable yield to that of the bond to be competitive. However, granting a loan to a corporation may have the added advantage of bringing in additional service business for the bank that merely purchasing a corporate bond would not do. In this case the bank would accept a somewhat lower yield on the loan compared to the bond in anticipation of getting more total revenue from the loan relationship due to the sale of other bank services.10-13. What is the net after-tax return on a qualified municipal security whose nominal gross return is 6 percent, the cost of borrowed funds is 5 percent, and the bank is in the 35 percent tax bracket? What is the tax-equivalent gross yield (TEY) on this tax-exempt security?Net After-Tax Return = (.06 - .05) + (0.35 x 0.80 x .05) = 0.024 or 2.4%The security's tax-equivalent yield in gross terms is 6 %/( 1-0.35) or 9.23%.10-14. Spiro Savings Bank currently holds a government bond valued on the day of its purchase at $5 million, with a promised interest yield of 6-percent, whose current market value is $3.9 million. Comparable quality bonds are available today for a promised yield of 8 percent. What are the advantages to Spiro Savings from selling the government bond bearing a 6 percent promised yield and buying some 8 percent bonds?In this instance the bank could sell the 6-percent bonds, buy the 8 percent bonds, and experience an extra 2 percent in yield. The bank would experience a capital loss of $1.1 million from the bond's book value, but the after-tax loss would be only $1.1 million * (1-0.35) or $0.715 million.13310-15. What is tax swapping? What is portfolio shifting? Give an example of each?A tax swap involves exchanging one type of investment security for another when it is advantageous to do so in reducing the bank's current or future tax exposure. For example, the bank may sell investment securities at a loss to offset high taxable income on loans or to replace taxable securities with tax-exempt securities. Portfolio switching which involves selling certain securities out of a bank's portfolio, often at a loss, and replacing them with other securities, is usually carried out to gain additional current income, add to future income, or to minimize a bank's current or future tax liability. For example, the bank may shift its holdings of investment securities by selling off selected lower-yielding securities at a loss, and substituting higher-yielding securities in order to offset large amounts of loan income.10-16. Why do depository institutions face pledging requirements when they accept government deposits?Pledging requirements are in place to safeguard the deposit of public funds. The first $100,000 of public deposits is covered by federal deposit insurance; the rest must be backed up by bank holdings of U.S. Treasury and federal agency securities valued at their par values.10-17. What types of securities are used to meet collateralization requirements?When a bank borrows from the discount window of its district Federal Reserve bank, it must pledge either federal government securities or other collateral acceptable to the Fed. Typically, banks will use U.S. Treasury securities to meet these collateral requirements. If the bank raises funds through repurchase agreements (RPs), banks must pledge securities, typically U.S. Treasury and federal agency issues, as collateral in order to borrow at the low RP interest rate.10-18. What factors affect a financial service institution’s decision regarding the different maturities of securities it should hold?In choosing among various maturities of short-term and long-term securities to hold, the financial institution needs to carefully consider the use of two key maturity management tools - the yield curve and duration. These two tools help management understand more fully the consequences and potential impact on earnings and risk of any particular maturity mix of securities they choose.10-19. What maturity strategies do financial firms employ in managing their portfolios?In choosing the maturity distribution of securities to be held in the financial firm’s investment portfolio one of the following strategies typically is chosen by most institutions:A. The Ladder or Spread-Maturity StrategyB. The Front-End Load Maturity StrategyC. The Back-End Load Maturity StrategyD. The Bar Bell StrategyE. The Rate-Expectation Approach134The ladder or spaced-maturity strategy involves equally spacing out a bank's security holdings over its preferred maturity range to stabilize investment earnings. The front-end load maturity strategy implies that a bank will pile up its security holdings into the shortest maturities to have maximum liquidity and minimize the risk of loss due to rising interest rates. The back-end loaded maturity policy calls for placing all security holdings at the long-term end of the maturity spectrum to maximize potential gains if interest rates fall and to earn the highest average yields. In contrast, the bar-bell strategy places a portion of the bank's security holdings at the short-end of the maturity spectrum and the rest at the longest maturities, thus providing both liquidity and maximum income potential. Finally, the rate expectations approach calls for shifting maturities toward the short end if rates are expected to rise and toward the long-end of the maturity scale if interest rates are expected to fall.10-20. Bacone National Bank has structured its investment portfolio, which extends out tofour-year maturities, so that it holds about $11 million each in one-year, two-year, three-year and four-year securities. In contrast, Dunham National Bank and Trust holds $36 million on one- and two-year securities and about $30 million in 8- to 10-year maturities. What investment maturity strategy is each bank following? Why do you believe that each of these banks has adopted the particular strategy it has reflected in the maturity structure of its portfolio?Bacone National Bank has structured its investment portfolio to include $11 million equally in each of four one-year maturity intervals. This is clearly a spaced maturity or ladder policy. In contrast, Dunham National Bank holds $36 million in one and two-year securities and about $30 million in 8 and 10-year maturities, which is clearly a barbell strategy. Dunham National Bank pursues its strategy to provide both liquidity (from the short maturities) and high income (from the long maturities), while Bacone National is a small bank that needs a simple-to-execute strategy. 10-21. How can the yield curve and duration help an investment officer choose which securities to acquire or sell?Yield curves possibly provide a forecast of the future course of short-term rates, telling us what the current average expectation is in the market. The yield curve also provides an indication of equilibrium yields at varying maturities and, therefore, gives an indication if there are any significantly underpriced or overpriced securities. Finally, the yield curve's shape gives the bank's investment officer a measure of the yield trade-off - that is, how much yield will change, on average, if a security portfolio is shortened or lengthened in maturity.Duration tells a bank about the price volatility of its earning assets and liabilities due to changes in interest rates. Higher values of duration imply greater risk to the value of assets and liabilities held by a bank. For example, a loan or security with a duration of 4 years stands to lose twice as much in terms of value for the same change in interest rates as a loan or security with a duration of 2 years.13513610-22. A bond currently selling for $950 based on a par value of $1,000 and promises $100 in interest for three years before being retired. Yields to maturity on comparable-quality securities are 12 percent. What is the bond’s du ration? Suppose interest rates in the market fall to 10 percent. What will be the approximate percent change in the bond’s price?Year Cash Flow Present Value Factor at 12% Present Value of Cash Flow Weight Of Each Cash FlowDuration Components 1 $100 0.893 $89.30 (89.30/950)=0.0940 0.09402 100 0.797 79.70 (79.70/950)=0.0839 0.16783 1100 0.712 783.20 (783.20/950)=0.8244 2.47332.7351 yearsClearly the bond's duration is 2.7351 years. If interest in the market fall to 10 percent, the approximate percentage change in the bond's price will be:Percentage Change in Price =100% x i)(1i x D +∆- percent 4.884 100% x .12)(1.02- x 2.7351- =+= Problems10-1. A 10-year U.S. Treasury bond with a par value of $1000 is currently for $1015 fromvarious security dealers. The bond carries a 7-percent coupon rate. If purchased today and held to maturity is its expected yield to maturity?(Hint - the following relationships can help in solving for the yield:If price < par value, then yield > coupon rate;If price = par value, then yield = coupon rate;If price > par value, then yield < coupon rate.)Since the bond is selling at a premium, that is, price > par value, the yield will be less than the coupon rate, or a yield < 7%.137 The relevant formula is:$1015 = 101021Y TM) (1$1000 Y TM) (1$70 ... Y TM) (1$70 Y TM) (1$70++++++++YTM = 6.79% (using a financial calculator)10-2. A municipal bond is selling today for $1036.80 and has a $1,000 face (par) value. Its yield to maturity is 6 percent, and the bond promises its holders $65 per year in interest for the next 10 years. What is the bond's duration?Year Annual Interest Income PV at 6% PV of Annual Interest Time Period Recorded Time-Weighted PV1 $ 65 0.943 61.32 x 1 = $61.322 $ 65 0.890 57.85 x 2 = $115.703 $ 65 0.840 54.58 x 3 = $163.744 $ 65 0.792 51.49 x 4 = $205.965 $ 65 0.747 48.57 x 5 = $242.856 $ 65 0.705 45.82 x 6 = $274.927 $ 65 0.665 43.23 x 7 = $302.618 $ 65 0.627 40.78 x 8 = $326.249 $ 65 0.592 38.47 x 9 = $346.2310 $ 65 0.558 36.30 x 10 = $363.0010 $1000 0.558 558.39 x 10 = $5583.90$1036.80 $7986.47Then duration = $ 7986.47 / $1036.80 = 7.703years10-3. Calculate the yield to maturity of a 10-year U.S. Government bond that is currently selling for $1050 in today's market and carries an 8-percent coupon rate with interest paid semiannually. $1050 = 202021Y TM/2) (1$1000 Y TM/2) (1$40 ... Y TM/2) (1$40 Y TM/2) (1$40++++++++YTM/2 = 3.64%, YTM = 7.29% (using a financial calculator)10-4. A corporate bond being seriously considered for purchase by First Security Savings Bank will mature 20 years from today and promises a 12 percent interest payment once a year. Recent inflation in the economy has driven the yield to maturity on this bond to 15 percent, and it carries a face value of $1000. Calculate this bond’s d uration.Year AnnualInterestIncomePVat 15%PV ofAnnualInterest XTimePeriodRecorded =Time-WeightedPV1 $120 0.870 $104.40 1 $104.402 120 0.756 90.72 2 181.443 120 0.658 78.96 3 235.884 120 0.572 68.84 4 274.565 120 0.497 59.64 5 298.206 120 0.432 51.84 6 311.047 120 0.376 45.12 7 315.848 120 0.327 39.24 8 313.929 120 0.284 34.08 9 306.7210 120 0.247 29.64 10 296.4011 120 0.215 25.80 11 283.8012 120 0.187 22.44 12 269.2813 120 0.163 19.56 13 254.2814 120 0.141 16.92 14 236.8815 120 0.123 14.76 15 221.4016 120 0.017 12.84 16 205.4417 120 0.093 11.16 17 189.7218 120 0.081 9.72 18 174.9619 120 0.070 8.40 19 159.6020 120 0.061 7.32 20 146.4020 1000 0.061 61.00 20 1220.00$812.2$6001.16Therefore, the bond's duration is: $6001.16/$812.20 = 7.39 years.10-5. Tiger National Bank regularly purchases municipal bonds issued by small rural school districts in its region of the state. At the moment, the bank is considering purchasing an $8 million general obligation issue from the Youngstown school district, the only bond issue that district plans this year. The bonds, which mature in 15 years, carry a nominal annual rate of return of 7.75%. Tiger, which is in the top corporate tax bracket of 35 percent, must pay an average interest rate of 7.38% to borrow the funds needed to purchase the municipals. Would you recommend purchasing these bonds?a) Calculate the net after tax return on this bank qualified municipal security. What isthe tax advantage for being a qualified bond?138Because these bonds were issued by a small governmental unit issuing less than $10 million in securities annually, the interest cost the bank has to pay to acquire the funds needed to buy these bonds is tax deductible. Therefore, their net after-tax return is:Net A.T.R = (7.75% - 7.38%) + (0.80 x 0.35 x 7.38%)= 7.75% -7.38% + 2.066%= 2.436%This net yield figure should be compared with other investments of comparable risk on an after-tax basis. However, the tax-exempt status of the income coupled with thetax-deductibility of the interest expense make these bonds a very attractive alternative. b) What is the tax equivalent yield for this bank qualified municipal security?TEY = 7752066135...+-= 15.10%10-6. Tiger National Bank also purchases municipal bonds issued by the city of Cleveland. Currently the bank is considering a nonqualified general obligation municipal issue. The bonds which mature in 10 years provide a nominal annual rate of return of 8.1 percent. Tiger National Bank has the same cost of funds and tax rate as stated in the previous problem.a. Calculate the net after tax return on this nonqualified municipal securityNet A.T.R. = 8.1 – 7.38 = 0.72 percentb. What is the tax equivalent yield for this nonqualified municipal security?TEY =810135..-= 12.46 percentc. Discuss the pros and cons of purchasing the nonqualified rather than the bankqualified municipal described in the previous problem.Clearly, the net after tax return for the nonqualified bond is lower than for thequalified bond. On the other hand, smaller municipal bonds are less liquid and thus,carry a higher liquidity risk (they also tend to have a higher default risk, but thatshould already be priced into the yield of the bond).10-7. Lakeway Thrift savings and Trust is interested in doing some investment portfolio shifting. This institution has had a good year thus far with strong loan demand; its loan revenue has increased by 16 percent over last year’s level. Lakeway is subject to the 35 percent corporate income tax rate. The investments officer has several options in the form of bonds that have been held for some time in its portfolio:139a. Selling $4 million in 12-year City of Dallas bonds with a coupon rate of 7.5 percentand purchasing $4 million in bonds from Bexar County (also with 12-year maturities) witha coupon rate of 8% and issued at par. The Dallas bonds have a current market value of$3,750,000 but are listed at par on the thrift institution’s booksb. Selling $4 million in 12-year U.S. Treasury bonds that carry a coupon rate of 12%and are recorded at par, which was the price when the bank purchased them. The market value of these bonds has risen to $4,330,000.Which of these two portfolio shifts would you recommend? Is there a good reason for not selling the Treasury bonds? What other information is needed to make the best decision? Please explain. Under Option A Lakeway will take an immediate $4 million - $3.75 million, or $250,000, loss before taxes (or a loss of $162,500 after taxes) which can be used to help offset the high taxable loan income earned this year. Moreover, the thrift will be able to earn 8% on an investment of $4 million, or $320,000, in annual interest income compared to only $300,000 with the bonds currently held or a gain in tax-exempt income of $20,000 per year. (Of course, if the thrift can only afford to buy $3,750,000 in new municipals - the sale price of the old bonds - it will generate about $300,000 in after-tax interest and have no net gain in tax-exempt interest income, but will still have a tax-deductible loss on the sale of the old bonds.)Under Option B the U.S. Treasury bonds must be sold for a gain of $330,000 which is taxable income. Because Lakeway does not need additional taxable income, Option B is less desirable than Option A. Besides, the Treasury bonds are selling at a premium above par which indicates their coupon rate is higher than current interest rates on investments of comparable risk, suggesting the wisdom of retaining these bonds in the bank's portfolio either until loan revenues decline and the bank needs additional taxable income or until interest rates rise well above current levels and new securities appear that promise significantly higher interest yields.10-8. Current market yields on U.S. government securities are distributed by maturity as follows: 3-month T bills = 7.69 percent6-month T bills = 7.49 percent1-year T notes = 7.77 percent2-year T notes = 7.80 percent3-year T notes = 7.80 percent5-year T notes = 7.81 percent7-year T notes = 7.86 percent10-year T notes = 7.87 percent30-year T bonds = 7.90 percent140141Draw a yield curve for the above securities. What shape does the curve have? What significance might this yield curve have for an investing institution with 75 percent of its investment portfolio in 7-year to 30-year Treasury bonds and 25 percent in U.S. government bills and notes under one year? What would you recommend to management?The yield curve for U.S. Treasury bonds clearly slopes upward after the 6-month maturity point and declines for 3- to 6-month maturities. Like most yield curves this curve becomes quite flat at longer maturities, particularly over the 7- to 30-year maturity segment. A financial institution with 75 percent of its portfolio in this 7- to 30-year range gains very little yield advantage over those institutions holding shorter maturities in the form of 3-month bills to 5-year notes. Yet, the longer-term bonds are less liquid so that a bank holding 7+-year maturities faces substantially greater liquidity risk. This bank would probably be better off to do some portfolio shifting into medium-term maturities.10-9. A bond possesses a duration of 5.82 years. Suppose that market interest rates oncomparable bonds were 7 percent this morning but have now shifted upward to 7.5 percent. What percentage change in the bon d’s value occurred when interest rates moved 0.5 percent higher? Percent Change in Value = 5.82 2.72%or 0272.-=-=⎪⎭⎫ ⎝⎛++ 1.072.91.071.00510-10. The investment officer for Sillistine Savings is concerned about interest-rate risk lowering the value of t he institution’s bonds. A check of the bond portfolio reveals an average duration of4.5 years. How could this bond portfolio be altered in order to minimize interest rate risk within the next year?Sillistine’s bond portfolio has an average duration of 4.5 years. This is relatively long, subjecting them to substantial interest-rate risk. Shortening the duration of the portfolio or the use of hedging tools (such as futures and options) is recommended.10-11. A bank’s economic department has just forec ast accelerated growth in the economy with GDP expected to grow at a 4.5 percent annual growth rate for at least the next two years. What are the implications of this economic forecast for an investment officer? What types of securitiesshould the investment officer think most seriously about adding to the investment portfolio? Why? Suppose the bank holds a security portfolio similar to the one described in Table 10-3 for allinsured U.S. banks. Which type of securities might the investments officer want to think seriously about selling if the projected economic expansion takes place? What losses might occur and how could these be minimized?。

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?。

天然气发热量计算标准差异性分析

天然气贸易计量方式有体积、质量和能量计量三种方式，北美、欧洲等国家实施能量计量计价，我国以体积计量方式为主，目前正在逐步向能量计量计价的方式转变。

在能量计量过程中，不同产地、不同气源的天然气因其组分不同，单位体积蕴含的发热量差异较大[1]。

天然气发热量的测定方法分为直接法和间接法。

直接法是将天然气在热量计中燃烧，直接测量其释放的热量的方法。

直接法能够直观地反映出天然气的实际发热量，但是对测量设备要求较高。

我国发热量直接测量技术测量不确定度为0.17%（k =2），达到ISO 15971规定的1级水平，可以满足现场发热量测量结果核查和争议仲裁要求；但未建立ISO 15971标准定义的0级发热量装置，与欧美发热量直接测定不确定度优于0.10%相比还有一定差距[2]。

中国计量科学研究院保存的水流式热量计测量不确定度小于1.0%，不能满足GB/T 18603《天然气计量系统技术要求》中Ａ级站的发热量测天然气发热量计算标准差异性分析李天琦1，2（1.大庆油田设计院有限公司；2.国家石油天然气大流量计量站）摘要：国际上天然气发热量计算标准主要为ISO 6976、GPA 2172以及ASTM D 3588，不同国家计算天然气的发热量选用的计算标准也有所不同。

针对发热量计算标准，分别从标准的适用范围、参比条件、计算方法、计算结果和基础数据引用等方面开展了分析比较。

最后根据不同地域的天然气气质组分数据，对发热量计算结果的差异性开展了的统计分析。

结果显示，不同标准发热量计算值的相对偏差不超过0.0043%，标准偏差为0.0003%。

通过差异性分析为天然气贸易双方对天然气发热量计算标准的选择提供参考。

关键词：天然气；发热量；参比压力；参比温度；ISO 6976；GPA 2172；ASTM D 3588DOI :10.3969/j.issn.2095-1493.2023.10.015Differential analysis of calorific value calculation standards for natural gas LI Tianqi 1,21Daqing Oilfield Design Institute Co ．，Ltd．2Nature Gas Large Flow Measurement Station，CNPCAbstract：The international standards for natural gas calorific value calculation are mainly ISO 6976，GPA 2172and ASTM D 3588．The calculation standards used to calculate the calorific value of natural gas vary in different countries．In view of the calorific value calculation standard，the application scope，reference conditions，calculation methods，calculation results and basic data quotation of the standard are analyzed and compared．Finally，according to the data of natural gas composition in dif-ferent regions，statistical analysis is carried out on the difference of calorific value calculation results ．The results show that the relative deviation of the calculated calorific value does not exceed 0.0043%，and the standard deviation is 0.0003%.The difference analysis is provided a reference for the selection of natural gas calorific value calculation standards by both sides of natural gas trade ．Keywords ：natural gas ；calorific value ；reference pressure ；reference temperature ；ISO 6976；GPA 2172；ASTM D 3588作者简介：李天琦，工程师，2014年毕业于东北石油大学（测控技术仪器专业），从事原油、天然气流量仪表检定与技术研究工作，182****6665，***************************.cn，黑龙江省大庆市让胡路区西苑街42号，163000。

Nike--Cost-of-Capital-资本成本分析案例

1. What is the WACC and why is it important to estimate a firm’s cost of capital? Do you agree with Joanna Cohen’s WACC calculation? Why or why not?1.1 The definition of WACCWeighted average cost of capital(WACC), is a weighted-computational method of analyzing the cost of capital based on the whole capital structure of a firm. The result of WACC is the rate a firm use to monitor the application of the current assets because it represents the return the firm MUST get. For example this rate could be used as the discount rate of evaluating an investment, and maintaining the price of firm’s stock.1.2 Analysis of Johanna Cohen’s calculationWe analyzed the process of Johanna Cohen’s calculation, and found some flaws we believe caused computational mistakes.i. When using the WACC method, the book value of bond is available as themarket value since bonds are not quite active in the market, but the book value of equity isn’t. Instead of Johanna’s using equity’s book value, we should multiply the current price of Nike’s stock price by the numbers of shares outstanding.ii. When calculating the YTM of the firm’s bond, Johanna only used the interest expense of the year divided by the average debt balance, which fully ignored the discounted cash flow of the cost of debt.2. If you do not agree with Cohen’s analysis, calculate your own WACC for Nike and be prepared to justify your assumptions. Combining the analysis above, we now give our own WACC calculation as following: 2.1 The value of debt(based on EXIHIBIT 3).Since the book value of debt may represent the market value, we merely need to sum up the values of Long-term debt, Notes payable, and the Current portion of long-term debt:435.9+855.3+5.4=$1,296.6 m2.2 The cost of debt (based on EXIHIBIT 4):PV: -95.6FV: 100n: 40Pmt: 6.75/2= 3.375 (as it pays semiannually)So, we get the YTM is i*2=3.58*2=7.16%2.3 The value of equity (based on EXIHIBIT 1&4):Price of stock * numbers of shares outstanding= 42.09*273.3=$11,503.2m2.4 The cost of equity (based on EXIHIBIT 4):E(R i) = R f +【E(R m) - R f】* βiBecause the government bond yield is 5.74%, Geometrical historical risk premium is 5.90%, and the average historical βof Nike is 0.80, then we get:E(R i)= 5.74%+5.90%* 0.8=10.46%2.5 Weights of each security (based on 2.1&2.3)Weight of debt=1,296.6/(1,296.6+11,503.2)=10.13%Weight of equity=11427.44/(1,296.6+11,503.2)=89.87%2.6 Cost of capital by WACC method (based above):Cost of capital = Weight of debt * Cost of debt * (1 – Tax rate) + Weight of equity * Cost of equity = 10.13% * 7.16%* (1-0.38) + 89.87% * 10.46% = 9.85%3. Calculate the costs of equity using CAPM, the dividend discount model, and the earnings capitalization ratio. What are the advantages and disadvantages of each method?3.1 Calculating the costs of equity by CAPM, and its advantages & disadvantagesi. Calculation:According to 2.4, we have already got the result of CAPM, which is 10.46%.ii. AdvantagesFirst, because CAPM is a theory based on the whole market, it obviously includes the effects between the market as the integrity and each individual stock. Second, with the counterbalance among each stock in the entire market, CAPM only needs the consideration of systematic risk, which much simplifies the calculation. Third, CAPM also bypasses the specific values of future cash flow because the equation is actually the relation between systematic risk and return rate, which is also another simplification of calculating. Fourth, merely depending on the systematic risk, CAPM could offer the investors a reliable discounting rate to assess the value of a certain investment.iii. Disadvantages:First, involving the counterbalance among the entire market, CAPM acquiesces an effective, active and healthy market environment. Second, comparing the consideration of market risk, CAPM may omit the subtle risk differences among each single firm. Third, the crucial systematic risk, the beta coefficient, is obviously hard to calculate.3.2 Calculating the costs of equity by DDM, and its advantages & disadvantagesi. Calculation (based on EXIHIBIT 4)::Based on the dividend discount model, P0 = D0 * (1+g) / (k – g), then we get the return rate (the cost of equity) k = D0 * (1+g) / P0 + g = 0.48 * (1 + 0.055) /42.09 + 0.055 = 6.7%ii. AdvantagesFirst, DDM fully considers the time value of consistent cash flow of an investment. Second, it is pretty easy to get the necessary historical data. Third DDM is flexible enough for the adjustment of any future situation. Fourth, once the growth pattern is confirmed, it is very straightforward to get the discount rate of assessing an investment.iii. DisadvantagesFirst, without enough consideration of risk cost, DDM may underestimate theequity cost. Second, all of the data is based on historical record, so the resultis not reliable considering of the future situations. Third, with thepredetermined growth rate, it is obviously practical for the stock investors toestimate the possible profit, but may mislead the stock issuing firm from abetter budgeting decision to a comparatively unsubstantial investment.3.3 Calculating the costs of equity by the earnings capitalization ratio, and itsadvantages & disadvantagesi. Calculation (based on EXIHIBIT 1&4)According to the earnings capitalization model, we have cost of equity = E1 / P0 = 2.16 / 42.09 = 5.13%ii. AdvantagesFirst, it’s very e asy to calculate and understand. Second, it’s easy to get the necessary accounting dataiii. DisadvantagesWithout any consideration of the risk and the growth of the firm, it doesn’t reflect the true value of an investment or the cost of the budgeting at all.4. What should Kimi Ford recommend regarding an investment inNike?According to EXIHIBIT 2, the market’s forecasting sensitivity of equi ty value of Nike is 11.17%. But based on our own analysis by WACC, we believe the discount rate of Nike is around 9.85%. That means the market underestimated the value of Nike. So we recommend the Northpoint to purchase the stock of Nike.。

Calculating the Cost of Capital

If a company financed itself with 40% debt, 10% preferred stock and 50% equity, the weighted average CC (WACC) would be:
WEIGHT COST DEBT .40 x 10% = 4.0 PS .10 x 12% = 1.2 EQ. .50 x 20% = 10.0 Weighted average CC = 15.2%
13
• Overall we should expect that the CAPM method for estimating iE will apply more accurately in most cases • If the constant growth model applies it is a good idea to use both methods
THE HIGHEST RETURN THAT WILL NOT BE EARNED IF FUNDS ARE INVESTED IN A PARTICULAR PROJECT
What sources of long-term capital do firms use?
Long-Term Capital Long-Term Debt Preferred Stock Common Stock New Common Stock
– Some type of simple or weighted average of the two methods might be appropriate
14
Example
• Calculate the cost of equity for ADK Industries given the following information:

[资本市场和金融机构].2

6. Predictive Power of the Yield Curve 6.1 Future interest rates 6.2 Economic growth
7. Conclusions
1
1. Interest Rate (i)
i = Cost of borrowing or lending money
4. Analysis of Bond Valuation
It sheds light on the concept of interest rate.
Bond. Contract in which a borrower agrees to pay a bondholder (the lender) a specific amount of money in a period of time.
b) Increases in real personal income make people more willing to make loans (e.g. deposits in banks accounts)
c) Increase in tax exempt financial instruments.
2
3
i = 5%
9
10
If i = 5% i = 10%
i = 15%
P = $100/(1+0.05) + $100/(1+0.05)2 +…+ $100/(1+0.05)10 + $1,000/(1+0.05)10 = $1,386 P = $100/(1+0.10) + $100/(1+0.10)2 +…+ $100/(1+010)10 + $1,000/(1+0.010)10 = $1,000

Duration model

The integrated formula
N
Σ t×CFt×DFt
D= t=1
=
N
Σ CFt×DFt
t=1
N
Σt=1PVt × t
N
Σ PVt
t=1
N
= Σt=1PVt × t P
N
= Σ (PVt / P)× t
t=1
Computing duration
Consider a 2-year, 8% coupon bond, with a face value of $1,000 and yield-to-maturity of 12%. Coupons are paid semi-annually.
2.4 Duration model
Introduction Calculating duration Interpreting duration Understanding more features of duration Using duration for interest rate risk immunization Limitations of duration immunization
Exploring the ambiguity of maturity
What does maturity of a bond exactly mean in a coupon bond case? An ambiguous term!
In the case of coupon bonds, the maturity of a bond is not the maturity of all the cash flows generated in the bond, only that of the last payment, the last coupon plus face value, while other cash flows have shorter “maturities”.

CHAPTER7 Bonds and Their Valuation (《财务管理基础》PPT课件)

Warrant – long-term option to buy a stated number of shares of common stock at a specified price.
Putable bond – allows holder to sell the bond back to the company prior to maturity.
Issue date – when the bond was issued. Yield to maturity - rate of return earned on
a bond held until maturity (also called the “promised yield”).
7-4
Similar to amortization on a term loan. Reduces risk to investor, shortens
average maturity. But not good for investors if rates decline
after issuance.
The discount rate (ki ) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk.
ki = k* + IP + MRP + DRP + LP
VB = ?
100
2
...
100
n 100 + 1,000
7-11
USING A FINANCIAL CALCULATOR TO VALUE A BOND

A non-radial Malmquist productivity index with an illustrative application to Chinese major industri

Int.J.Production Economics 83(2003)27–35A non-radial Malmquist productivity index with an illustrativeapplication to Chinese major industriesYao ChenCollege of Management,University of Massachusetts at Lowell,Lowell,MA 01854,USAReceived 1November 2001;accepted 1May 2002AbstractData envelopment analysis (DEA)measures the relative efﬁciency of peer units when multiple outputs and inputs are present.DEA-based Malmquist productivity index measures the technical and productivity changes over time.The current study extends the Malmquist productivity index into a non-radial index where the decision maker’s preference over performance improvement can be incorporated.The non-radial Malmquist productivity index eliminates possible inefﬁciency represented by the non-zero slacks.The method is applied to measure the productivity change of three Chinese major industries:Textiles,Chemicals and Metallurgicals during four ﬁve-year-plan periods.The paper shows how DEA-based Malmquist productivity index can be employed to evaluate the technology and productivity changes resulted from the economic development plans.The paper also shows the importance of using the non-radial Malmquist productivity index.r 2002Elsevier Science B.V.All rights reserved.Keywords:Data envelopment analysis (DEA);Empirical production frontier (EPF);Technical change;Malmquist productivity index1.IntroductionData envelopment analysis (DEA)has been recognized as an excellent method for analyzing performance and modeling organizations and operational processes,particularly when market prices are unavailable.Unlike the statistical regression method that tries to ﬁt a regression plane through the center of the data,DEA ﬂoats a piecewise linear surface to rest on top of the data by linear programming techniques (Seiford and Thrall,1990).In other words,the statistical regression method estimates the parameters in the assumed functional form by a single optimiza-tion over all decision making units (DMUs)whereas DEA uses different optimizations (linear programming problems)for different DMUs with-out a priori assumptions on the underlying functional forms.Because of this unique feature,DEA has been applied to various areas of efﬁciency evaluation,for example,individual physician practice,program evaluation,macro-economics performance of countries or cities,pollution prevention,reorganization of forest districts and pupil transportation,and others.Most of the DEA applications use cross-sectiondata,however,by the recent result of (F .are et al.,1994a,b),DEA can be applied to panel data to measure the productivity changes between two periods of activities fulﬁlled by a speciﬁc set ofE-mail address:Yao _Chen@ (Y.Chen).0925-5273/02/$-see front matter r 2002Elsevier Science B.V.All rights reserved.PII:S 0925-5273(02)00267-0DMUs.For example,F.a re et al.(1994a,b)studied the productivity change in Swedish individual hospitals operating in a non-market environment. The speciﬁc approach used is called(radial) Malmquist productivity index in which radial DEA efﬁciency scores are used.The DEA models used in the radial Malmquist productivity index can either be input-or output-oriented.Conse-quently,the radial Malmquist productivity index can be input-oriented when the outputs areﬁxed at their current levels or output-oriented when the inputs areﬁxed at their current levels.Note that the DEA efﬁciency is characterized by a radial efﬁciency score and possible non-zero input(output)slacks.However,the radial Malm-quist productivity index is only based upon the radial DEA scores.Ignoring non-zero input slacks in input-oriented index(or non-zero output slacks in output-oriented index)obviously cannot fully characterize the productivity change.Note also that the radial Malmquist productiv-ity index fails to consider the decision-maker’s preference over the performance improvement of individual inputs and outputs.In fact,incorpora-tion of value judgment into DEA analysis is very important in applications to avoid false results and implications.A number of DEA methods have been developed to deal with the incorporation of value judgment(see,e.g.,Charnes et al.,1989). Since the Malmquist productivity index is based upon DEA,incorporation of value judgment is also essential in measuring productivity changes. The current study extends the radial Malmquist productivity index into a non-radial index where non-zero input slacks are not allowed in the input-oriented productivity index and non-zero output slacks are not allowed in the output-oriented productivity index.Furthermore,preferences over individual input and output improvement can be incorporated.The approach is applied to measure the impact of economic development plans on productivity changes of three Chinese major industries—Textiles,Chemicals and Metallurgi-cals.As demonstrated,the use of non-radial Malmquist productivity index correctly charac-terizes the productivity changes while the radial index may provide distorted information.The rest of the paper is organized as follows.The next section presents the input-oriented radial Malm-quist productivity index.The non-radial Malmquist productivity index is then developed.An illustrative application is then presented and discussed.Conclud-ing remarks are made at the last section.2.Malmquist productivity indexSuppose we have n DMUs,each DMU jðj¼1;2;y;nÞproduces a vector of outputs y tj¼ðy t1j;y;y tsjÞby using a vector of inputs x tj¼ðx t1j;y;x tmjÞat each time period t;t¼1;y;T: The CCR DEA model can be expressed as (Charnes et al.,1978):y t0ðx t;y tÞ¼min y;l jy0s:t:P nj¼1l j x t j p y0x t0;P nj¼1l j y tjX y t;l j X0;j¼1;y;n;ð1Þwhere x t¼ðx t10;y;x tm0Þand y t¼ðy t10;y;y ts0Þare the input and output vectors of DMU0among others.Model(1)is input-oriented,because it considers the possible radial reductions of all inputs when the outputs areﬁxed at their current levels.If y tðx t;y tÞ¼1;then DMU0is(radially) efﬁcient in time period t;otherwise,ify tðx t;y tÞo1;then DMU0is(radially)inefﬁcient.It can be seen that(i)if y t0ðx t;y tÞ¼1;then DMU0 is unable to proportionally reduce its inputs and therefore DMU0is on the empirical productionfrontier(EPF);(ii)if y tðx t;y tÞo1;then DMU0can reduce its inputs and therefore DMU0is operating below the EPF.Note that possible non-zero input and output slacks are likely to present at the optimal solutions.By replacing x t j and y t j with x tþ1jand y tþ1j; respectively,we have the technical efﬁciency ofy tþ1ðx tþ1;y tþ1Þfor DMU0at the time period tþ1: From t to tþ1;DMU0’s technical efﬁciency may change or(and)the EPF may shift.Based upon model(1),the radial Malmquist productivity index can be calculated via(F.a re et al.,1994a,b)(i)Comparing x tto EPF at time t;namely,calculating y tðx t;y tÞ;Y.Chen/Int.J.Production Economics83(2003)27–35 28(ii)Comparing x tþ10to EPF at time tþ1;namely,calculating y tþ10ðx tþ1;y tþ1Þ;(iii)Comparing x t0to EPF at time tþ1;that is,calculating y tþ10ðx t;y tÞthrough the followinglinear program:y tþ1 0ðx t;y tÞ¼min y;l jy0s:t:P nj¼1l j x tþ1jp y0x t0;ÁP nj¼1l j y tþ1jX y t;l j X0;j¼1;y;n:ð2Þ(iv)Comparing x tþ10to EPF at time t;namely,calculating y t0ðx tþ1;y tþ1Þthrough the follow-ing linear programy t 0ðx tþ1;y tþ1Þ¼min y;l jy0s:t:P nj¼1l j x tjp y0x tþ10;ÁP nj¼1l j y tjX y tþ1;l j X0;j¼1;y;n:The Malmquist productivity index is deﬁned asPI0¼y t0ðx t;y tÞy tðx;yÞy tþ1ðx t;y tÞyðx;yÞ"#1=2:PI0measures the productivity change betweenperiods t and tþ1:Productivity declines if PI0>1;remains unchanged if PI0¼1and improves ifPI0o1:Note that PI0is expressed by the radial efﬁciency scores obtained from several input-oriented DEA models.Therefore,this PI0is calledinput-oriented radial Malmquist productivityindex.The following modiﬁcation of PI0makes itpossible to measure the change of technicalefﬁciency and the movement of EPF in terms ofa speciﬁc DMU0:PI0¼y tðx t;y tÞyðx tþ1;y tþ1Þy tþ1ðx tþ1;y tþ1Þy tðx;yÞy tþ1ðx t;y tÞy tðx;yÞ"#1=2:ð3ÞTheﬁrst term on the right-hand side measures the magnitude of technical efﬁciency change between periods t and tþ1:Obviously,y t0ðx t0;y tÞy tþ1 0ðx tþ1;y tþ1Þb1accordingly as technical efﬁciency improves,re-mains or declines.The second term measures theshift in the EPF between periods t and tþ1:3.Non-radial Malmquist productivity indexNote that PI0is developed by the input-orientedradial efﬁciency scores.Thus,input slacks in DEAmodels are not considered in the radial Malmquistproductivity index(3).Note also that PI0does notconsider decision-maker’s preference over perfor-mance improvement of individual inputs.It isnecessary to consider such a preference when theradial characterization on efﬁciency and EPF isnot realistic in DMU’s view.Let a i;i¼1;y;m,be user-speciﬁed weightsreﬂecting preferences over the input improve-ments.Zhu(1996)establishes the following DEAmodel,*y tðx t;y tÞ¼1P mi¼1a iminy i;l jP mi¼1a i y is:t:P nj¼1l j x tijp y i0x t i0;i¼1;y;m;ÁP nj¼1l j y trjX y tr0;r¼1;y;s;y0ifree;l j X0;j¼1;y;n:ð4ÞModel(4)measures the relative efﬁciency ofDMU0under weights a i during time period t:Ifsome a i¼0;then set the corresponding y i¼1:The bigger the weight a i;the higher the priorityDMU0gives to reduce its i th input.Model(4)determines a preferred EPF.Consider theﬁve DMUs in Fig.1used in Zhu(2002).DMUs1–3are efﬁcient,DMU4is weaklyefﬁcient with non-zero slack on theﬁrst input,andDMU5is inefﬁcient.To obtain the efﬁciencyscore for DMU5,the radial DEA model(1)selectsa convex combination of DMUs2and3as theefﬁcient target which has x1¼2:4and x2¼1:8based upon lÃ2¼0:8and lÃ3¼0:2:On the otherhand,the non-radial DEA model(4)selects DMU2as the efﬁcient target when a1¼a2¼1:Notethat the efﬁciency score of model(1)does notconsider the slack in DMU4whereas that ofmodel(4)does.Y.Chen/Int.J.Production Economics83(2003)27–3529The dual to (4)can be written as max P s r ¼1u r y t r 0s :t :P s r ¼1u r y t rj ÀP mi ¼1v i x tij p 0;j ¼1;y ;n ;v i x t i 0¼a iP m i ¼1i;i ¼1;y ;m ;u r ;v i X 0;ð5ÞBy the complementary slackness theorem inlinear programming,we haveTheorem 1.Any optimal solution in (4)will always have all input slacks and at least one output slack equal to zero.Theorem 1indicates that model (4)does not allow non-zero input slacks.Furthermore,note that X m i ¼1v i x t i 0¼X m i ¼1a i P m i ¼1a i ¼1in ð5Þ;thereforeX s r ¼1u r y t r 0p 1:Note also that all y i 0in (4)are non-negative inoptimality.Thus we obtain the following theorem.Theorem 2.The optimal value to (4)is less than orequal to one,i.e.,0o *y t 0ðx t 0;y t 0Þp 1:Theorem 2indicates that although some in-dividual y i 0may be bigger than one at optimality,0o *y t 0ðx t 0;y t 0Þp 1:Consequently,the current levels of some inputs may be increased rather than decreased in order to improve the efﬁciency.Similarly,by replacing the data in t by the data in t þ1in (4),we have the relative efﬁciency,0o *y t þ10ðx t þ10;y t þ10Þp 1;and the corresponding pre-ferred EPF,for DMU 0in time period t þ1:We next modify (2)into the following linear program:*y t þ10ðx t 0;y t 0Þ¼1P m i ¼1a imin y i 0;l j P m i ¼1a i y i 0s :t :P n j ¼1l j x t þ1ij p y i 0x t i 0;i ¼1;y ;m ;ÁP n j ¼1l j y t þ1rj X y tr 0;r ¼1;y ;s ;y 0i free ;l j X 0;j ¼1;y ;n :ð6ÞThe value of *y t þ10ðx t 0;y t 0Þmay be either greater or less than or equal to one.By switching the t andt þ1in (6),we obtain *y t 0ðx t þ10;y t þ10Þ:That is,*y t 0ðx t þ10;y t þ10Þ¼1P m i ¼1a imin y i 0;l jP mi ¼1a i y i 0s :t :P nj ¼1l j x tij p y i 0x t þ1i 0;i ¼1;y ;m ;ÁP nj ¼1l j y trj X y t þ1r 0;r ¼1;y ;s ;y 0i free ;l j X 0;j ¼1;y ;n :Now,we deﬁne the following (input-oriented)non-radial Malmquist productivity index by thenon-radial efﬁciency scores of *y t 0ðx t 0;y t 0Þ;*y t þ10ðx t þ10;y t þ10Þ;*y t þ10ðx t 0;y t 0Þ;and *y t 0ðx t þ10;y t þ10Þ:P *I0¼*y t 0ðx t 0;y t 0Þ*y t þ10ðx t þ10;y t þ10Þ*y t þ10ðx t þ10;y t þ10Þ*y t 0ðx t þ10;y t þ10Þ*y t þ10ðx t 0;y t 0Þ*y t 0ðx t 0;y t 0Þ"#1=2:ð7ÞIt is clear that this newly deﬁned productivityindex (7)is incorporated with the preference over the individual input improvements and does not allow the existence of non-zero input slacks.The ﬁrst term on the right-hand side of (7)measures the weighted non-radial input efﬁciencychange,1234560 12 3 4 56 7Input1I n p u t 2Fig.1.Radial and non-radial models.Y.Chen /Int.J.Production Economics 83(2003)27–3530and the second term measures the movement of preferred EPF.We should note the possibility that two different time period EPFs may have intersections.The facets of EPF may not shift in a same direction.Some facets may shift forwards,and some back-wards.In this situation,the movement of EPF is DMU-speciﬁc.I.e.,Malmquist productivity index measures the performance of a speciﬁc DMU in terms of the change of referent DMUs.The selection of a i is independent of the corresponding input units.Some possible choices of a i can be,e.g.,a i ¼1=x i 0;and a i ¼x i 0=P n j ¼1x ij :However,if additional information,say,cone ratios are available,then the lower bounds on multipliers can be used as weights a i :Furthermore,ifv i ¼a ix t i 0P m i ¼1a i ;i ¼1;y ;m ;in ð5Þ;then X s r ¼1u r y t rj p A j ;j ¼1;y ;n ;where A j ¼X m i ¼1v i x tij ¼Xm i ¼1a it ijP mi ¼1iwhich can be interpreted as weighted output for DMU j at time period t :Thus,we may use P mi ¼1#ai x t ij ¼A j to estimate unnormalized #a i given the information on A j :A j can be obtained from addition information,say,the total expenditure for each DMU in a particular time period,or the prices on outputs.4.An application4.1.Data and DMU selectionIn the current study,we employ (3)and (7)to evaluate the productivity changes in three Chinese major industry sectors:Textiles,Chemicals and Metallurgy during the time period from 1966to 1985(see Table 1).Since managers in China were rewarded primarily based on their success in meeting physical targets set by the government,the input-oriented DEA method is more suitable in this study.In order to keep the research consis-tency,we select the same single output and two inputs used in Cooper et al.(1995),although DEA allows more outputs and inputs in empirical studies.The single output of annual gross indus-trial output value (AGIOV)and the input of Capital are measured in 10,000RMB 1by the 1980ofﬁcial prices.The other input,labor,stands for the number of workers and staffs in each industry.DEA is known to be quite sensitive to variable selection.Thus,it is important to establish a priori the existence of an association between the inputs and outputs.The two inputs and one output selected here are key measures used by the Chinese government in evaluating the industrial perfor-mance.They are published in the Yearbook of China’s 40Years issued by the Chinese Statistical Bureau.Based upon Cooper et al.(1995),the relationship between the two inputs and the output is valid.However,this does not exclude the possibility that a more general model can be developed based upon additional data.The textile industry is selected to represent an industry which is labor intensive,the chemical industry is selected to represent an industry which is capital intensive,and metallurgical industry is selected to represent an industry to be in between.Such a selection allows to demonstrate the use of newly developed Malmquist productivity index (7).Note that the time period 1966–1985covers four 5-year-plan periods during which the third 5-year-plan period came on stream during 1966–1970.Chinese government has launched a series 5-year plans since the year 1953.In each 5-year plan,some economic development plans and targets were set up.Therefore,it is meaningful to study the productivity change between two successive 5-year-plan time periods so that we can measure the impact of economic development plans.In the current paper,we study the productivity changes over the third,fourth,ﬁfth and sixth 5-year plan periods.Each year and the year after 5years are considered as the same DMU.For example,the ﬁrst years in all 5-year-plan periods are regarded as1RMB is the Chinese monetary unit of ‘‘Renmingbi’’.Y.Chen /Int.J.Production Economics 83(2003)27–3531the same DMU but in different time periods (see Table 2).4.2.ResultsTable 3reports the results obtained from (3).The average productivity change along with average technical efﬁciency change and average EPF movement are presented.For example,from the third to fourth 5-year-plan period in the textile industry,the scores of efﬁciency change,EPF movement and productivity change are 0.92961,0.82452,and 0.76648,respectively,indicating an efﬁciency and productivity improvement and positive (inward)EPF shift.2On average,the textile industry’s productivity declined 3%from the ﬁfth to the sixth 5-year-plan period.3In particular,from the third to the fourth 5-year-plan period,the productivity improved 30.5%with an improvement of technical efﬁciency and an inward shift of EPF.From the fourth to the ﬁfth 5-year plan period,slight improvement of the productivity occurred with a decline of technical efﬁciency.In overall,technical progress happened after each 5-year-plan period in the textile industry.In the chemical industry,the technical efﬁciency,EPF and productivity improved very little from the third to the fourth 5-year plan period.During all the remaining periods,the chemical industry’sTable 1Data for 1966–1985textiles,chemicals and metallurgicals YearTextiles Chemicals Metallurgicals AGIOVCapital Labor AGIOV Capital Labor AGIOV Capital Labor 196614516348002106910116884577856880051060265042497419671210573813510704710035447570689595008727400256031968135572405841114281023074656571665462592994027430196917784950454115222160948647687778859358383742917419701836304921812242817177467488856126495931720375801971160291436041273931954287746894896704463677727152197216185344677131991197665792251007758959230634307541973181968509581335552098388455710333611258839781351511974188066534191344562192568782010559112101339988321701975206317594301356422326769277711063613209349216319331976196584579141391952090578359311466110939342909338491977187317564101453032141058781812439211941147857365061978229308705581256272729351074631253281712286853836183197925852973542134303278142117348126285185703787463536319803137348718014953328649912564414481819699886504374031981361155105123166794309717143419153201199055890033941219823472291223851948013389891603091596912088979414940005198336963114309820217135451517378816023822618710392545650198446523527661521893737322118801317742622810910808341094198549205331197721496141072022223616931023598112526941146Table 2DMU selectionFive-year plan period Third (t ¼1)Fourth (t ¼2)Fifth (t ¼3)Sixth (t ¼4)DMU 11966197119761981DMU 21967197219771982DMU 31968197319781983DMU 41969197419791984DMU519701975198019852Inward movement of EPF means technical progress and outward movement of EPF means technical decline.3The improvement of productivity is calculated by 1=PI 0À1;since PI 0o 1:The decline of productivity is calculated by 1À1=PI 0;since PI 0>1:Y.Chen /Int.J.Production Economics 83(2003)27–3532productivity,on average,declined.It is clear from Table3that the technical efﬁciency experienced a drop from the fourth to theﬁfth5-year plan period and the EPF slightly moved outward from theﬁfth to the sixth5-year-plan period.From the third to the fourth5-year plan period, the metallurgical industry’s productivity improved dramatically by55.7%even the technical efﬁ-ciency declined by4%.It can be seen that this improvement was accompanied by a large tech-nology progress.However,after the fourth5-year-plan period,the technical decline prevailed in the metallurgical industry.Recall that the textile,chemical and metallurgi-cal industries are labor-intensive,capital-intensive and in-between,respectively.In order to improve the performance given the current output level,the two inputs of labor and capital should be treated differently.I.e.,the preference of decision makers to reduce each input towards the EPF should be incorporated.Unfortunately,the current study does not have access to such preference informa-tion.Therefore,the use of the newly deﬁned productivity index(7)is considered as only illustrative.The current study speciﬁes the following weight combinations on the two inputs to reﬂect the different preferences over the two inputs:for the textile industry;a Capital¼0:3;a Labor¼0:7;for the chemical industry;a Capital¼0:7;a Labor¼0:3;for the metallurgical industry;a Capital¼0:5;a Labor¼0:5:By specifying the above weight combinations,we assume that(i)it is more important to reduce the amount of labor in the textile industry when we improve the performance of the textile industry, because the textile industry is labor intensive,and (ii)it is more important to reduce the amount of capital in the chemical industry when we improve the performance of the chemical industry,because the chemical industry is capital intensive.No preference over the two inputs is given in the metallurgical industry,because the metallurgical industry is in between these two extremes of textile and chemical ing equal weights in measuring the metallurgical industry’s performance indicates that the two inputs are equally important. As indicated in Cooper et al.(1995),large amount of labor slacks are found in each industry. By using(7),inefﬁciency represented by non-zero input slacks can be considered.Table4reports the results in averages obtained from(7).In the textile industry,the productivity improved14.3%and13.7%(versus30.5% and4%with respect to(3))from the third to fourth5-year-plan period and from the fourth to ﬁfth5-year-plan period,respectively.This is partly due to that fact that the radial productivity index (3)only considers the proportional changes of all inputs and ignores the non-zero slacks.When a larger weight is put on the capital input in the chemical industry,the result indicates that from the third to fourth5-year-plan period,(7)reveals more technical efﬁciency improvement than(3) does.However,the characterization of EPF shift almost remains the same,except for the time period from theﬁfth to sixth5-year-plan period.In the metallurgical industry,a serious efﬁciency decline is detected by(7)from the third to fourth 5-year-plan period.In fact,large amount of labor slacks were found before1970using the radialTable3Radial Malmquist productivity indexFive-year-plan period3rd–4th4th–5th5th–6thTextilesEfﬁciency0.92961 1.04979 1.03502EPF0.824520.915560.99742Productivity0.766480.96114 1.03235ChemicalsEfﬁciency0.90850 1.025280.97804EPF0.996860.98265 1.07973Productivity0.90565 1.00749 1.05602MetallurgyEfﬁciency 1.043800.94178 1.00133EPF0.61539 1.00787 1.04102Productivity0.642350.94919 1.04241Y.Chen/Int.J.Production Economics83(2003)27–3533DEA models.Thus,this result indicates that it is important to consider the possible non-zero slacks in measuring the productivity changes.Note that the newly deﬁned Malmquist produc-tivity index (7)shows that productivity improve-ment happened in each industry from the ﬁfth to the sixth 5-year-plan period,while (3)shows the opposite result.In fact,the Chinese industrial growth was especially rapid in the early 1960s,and except for a dip early in the 1966–1976Cultural Revolution period it returned thereafter to a rate slightly under the long-term 11.2%average growth rate (Lippit,1987).However from 1978to 1983,industrial growth averaged 7.9%yearly and in 1984,industrial output rose by 14%.This indicates that the non-radial Malmquist productivity index (7)provides results in consistent with the changes during the 1978–1983economic reform period.5.ConclusionsThe DEA-based Malmquist productivity indexcan be found in F .are et al.(1994a,b)where only radial DEA efﬁciency scores are used.The current paper develops a non-radial Malmquist produc-tivity index that incorporates the preference over the performance improvement and integrates the inefﬁciency represented by slacks.As shown in the current paper,DEA can be used as a tool for measuring the productivity change of the three Chinese major industries whose industrial activities constitute important components of China’s 5-year economic develop-ment planning efforts.The current study indicates that the EPF does not always shift in a desirable direction (production improvement direction).This implies that the intertemporal changes in efﬁciency and technology are not steady during the four 5-year-plan periods studied.This study provides information on the result of Chinese economic developing plans and in turn can improve the economic planning at different administrative levels in China.Furthermore,note that the shift of EPF can be either endogenous or exogenous,i.e.,we should consider the changes in the regulatory environment.Thus,our DEA productivity analysis raises a question as to whether the Cultural Revolution and Economic Reforms have generated some impacts on the Chinese industry.Study of this issue,however,is beyond the scope of the current paper,and should be left for further treatment.The non-radial Malmquist productivity index developed in the current study is input-oriented.Similarly,we can develop an output-oriented non-radial Malmquist productivity index when inputs are ﬁxed at their current levels.The input-oriented non-radial Malmquist productivity index only con-siders the non-zero input slacks and preferences over input changes.If we are interested in the possible output non-zero slacks,we can develop a slack-based Malmquist productivity index.AcknowledgementsThe author is grateful to the comments and suggestions made by an anonymous referee.The author is also grateful to the North American Region Editor,Dr.Peter Kelle for ensuring a timely review process.ReferencesCharnes,A.,Cooper,W.W.,Rhodes,E.,1978.Measuring theefﬁciency of decision making units.European Journal of Operational Research 2,429–444.Table 4Non-radial Malmquist productivity indexFive-year-plan period 3rd–4th4th–5th 5th–6th Textiles Efﬁciency 0.96248 1.101400.99011EPF0.909010.798570.99066Productivity 0.874910.879540.98086Chemicals Efﬁciency 0.89228 1.053040.96158EPF0.996600.981040.91693Productivity 0.88925 1.033080.88169Metallurgy Efﬁciency 1.247880.949820.94930EPF0.551280.96617 1.03133Productivity0.687930.917690.97904Y.Chen /Int.J.Production Economics 83(2003)27–3534。

第06章资本成本

– 收入的周期性（Cyclicity of Revenues）
• 经营风险（Business Risk）
– 经营杠杆（Operating Leverage）
• 财务风险（Financial Risk）
– 财务杠杆（Financial Leverage）
17
收入的周期性
• 有些企业的收入具有明显的周期性，即这些企业在商业周期的扩张阶段经营得很好，而在商业周期的紧缩阶段经营得很差。
7
权益成本的估计方法
Source: Graham and Harvey (2001), The theory and practice of corporate finance: evidence from the field, Journal of Financial Economics 60, 187-243.
• 按贝塔的定义计算如下：
β Cov(Ri , RM ) σi,M
Var (RM )
σ
2 M
15
利用GLS模型计算权益成本
• Gebhardt、Lee和Swaminathan于2003年提出了“剩余收益折现模型(Discounted Residual Income Model 以下简称GLS模型)”，该模型也是基于市场价格和公司财务数据的折现模型。
Bt

FROEt2 re (1 re )2
Bt 1

FROEt3 (1 re )3
re
Bt 2
TV
TV

11 i4
FROEti (1 re )i
re
Bt
i
1

FROEt12 re r(1 re )r1

Calculating initial margin (IM) and variation margin (VM)

Note1: These are estimates and the actual values could differ widely based on: • Level of offsets between positions in a portfolio • Type of Margin Model • Pro-cyclicality considerations Note2: Derive liquidity demands on un-cleared swaps based on information from cleared swaps
Day 1 2 3 Price 78 85 90 Shock -0.02532 0.085942 0.057158 Forecasted Price 97.4682192 108.594243 105.715841 PnL -2.53178 8.594243 5.715841
Filtered Historical Simulation • We would like to give more weight to recent shocks. • Scale returns by ratio of current volatility/volatility at the time of shock
Normal Model Ex: Current Price = $100 1 day volatility (based on historical data) = 1% 10 day volatility = 1%*sqrt(10) = 3.16% 99th percentile price change = 2.33*3.16%*100 = $7.37
Example (from attached Excel) EWMA volatility scaling One of the big advantages of historical simulation is that we need not make any Assumption regarding the parametric distribution of risk factors. Correlation between risk factors is implicit. Easy to implement Shocks are confined to past history IM generated from filtered HS may exhibit pro-cyclicality

债券及股票的定价策略(英文版)

债券及股票的定价策略(英文版)In finance, pricing strategies for bonds and stocks are crucial for investors and financial institutions to determine the fair value of these financial securities. This helps in making informed investment decisions and managing investment portfolios effectively. Let's explore the pricing strategies for bonds and stocks.Bond Pricing Strategy:1. Discounted Cash Flow (DCF) Analysis: This strategy involves calculating the present value of future cash flows generated by the bond. The cash flows include periodic interest payments and the bond's face value at maturity. The present value is determined by discounting these cash flows using an appropriate discount rate, usually the bond's yield to maturity (YTM).2. Comparable Bond Analysis: This strategy relies on comparing the bond in question with similar bonds in the market. By analyzing similar bonds' yields and prices, investors can assess whether the bond is overvalued or undervalued. Factors considered in this analysis include credit rating, coupon rate, maturity, and market conditions.3. Yield Spread Analysis: This strategy involves analyzing the yield spread between a particular bond and a benchmark bond with similar characteristics but different credit ratings. If the yield spread is wider than historical levels, indicating higher risk, the bond may be priced at a discount. Conversely, a narrower yield spread implies a premium.Stock Pricing Strategy:1. Dividend Discount Model (DDM): This strategy focuses on estimating the intrinsic value of a stock based on its future dividends. The DDM involves discounting expected future dividends to the present value using an appropriate discount rate, such as the stock's required rate of return or the dividend growth rate.2. Price-to-Earnings (P/E) Ratio Analysis: This strategy evaluates a stock's value by comparing its market price to its earnings per share (EPS). A low P/E ratio may suggest an undervalued stock, while a high P/E ratio could indicate an overvalued stock. This analysis considers industry P/E ratios, earnings growth prospects, and other relevant factors.3. Comparable Company Analysis: This strategy involves comparing the valuation metrics of a company with its industry peers or similar companies. Parameters such as price-to-sales ratio, price-to-book ratio, or enterprise value-to-EBITDA ratio are compared to identify relative valuation. If a company's valuation is significantly lower than its peers with similar fundamentals, it may be considered undervalued.Both bond and stock pricing strategies require careful analysis of various quantitative and qualitative factors. It is crucial for investors to consider the fundamental characteristics of the security, market conditions, economic indicators, interest rates, and other relevant factors. Additionally, incorporating risk assessment and future market expectations into these pricing strategies enhances their accuracy.Bond Pricing Strategy (Continued):4. Term Structure of Interest Rates Analysis: This strategy takes into account the term structure of interest rates, which shows the relationship between the yields and maturity dates of bonds. By comparing the yields of bonds with different maturities, investors can assess the expectations of future interest rate movements. If the current bond's yield is higher than the expected future rates, it may be undervalued, and vice versa.5. Credit Rating Analysis: Credit ratings assigned by rating agencies provide an indication of a bond's creditworthiness. Higher-rated bonds typically have lower yields due to lower perceived risk. Investors can analyze the bond's credit rating and compare it to similar rated bonds to determine whether the bond is priced appropriately.Stock Pricing Strategy (Continued):4. Discounted Free Cash Flow (DCF) Analysis: This strategy estimates the intrinsic value of a stock by forecasting its future cash flows. The future cash flows are projected based on expected revenue, expenses, and capital expenditures. These cash flows are discounted to their present value using an appropriate discount rate, such as the company's cost of capital. The resulting value represents the fair value of the stock.5. Price-to-Book (P/B) Ratio Analysis: This strategy compares a company's market price per share to its book value per share. The book value represents the net assets of the company, calculated by subtracting liabilities from assets. A low P/B ratio may indicate anundervalued stock, suggesting that the market is not fully recognizing the company's tangible assets.6. Earnings Growth Analysis: This strategy looks at the growth potential of a company's earnings. Investors analyze historical earnings growth rates and projected future growth rates to assess the stock's value. A higher expected earnings growth rate may justify a higher valuation for the stock.7. Technical Analysis: This pricing strategy focuses on analyzing historical price and volume patterns of a stock to predict future price movements. Technical analysts use various tools and techniques such as charts, moving averages, and oscillators to identify trends, support and resistance levels, and other patterns that can guide investment decisions.It is important to note that these pricing strategies serve as a guide and should not be considered definitive methods of valuation. Market conditions, investor sentiment, and unforeseen events can impact the fair value of bonds and stocks. It is recommended to use a combination of these strategies and exercise caution while interpreting the results. Regular monitoring and reassessment of pricing strategies are necessary to adapt to changing market dynamics. Ultimately, investors should conduct thorough research and seek professional advice before making investment decisions.。

ytm fv pv coupon rate 公式

YTM和FV PV Coupon Rate公式1. YTM是什么？YTM是债券的预期收益率，全称为年度收益率。

它衡量了投资者持有债券到期日所能获得的收益率。

在计算YTM时，需要考虑债券的到期日、票面价值、债券的市场价格以及债券的利息支付频率等因素。

2. FV PV Coupon Rate公式在计算债券的YTM时，需要用到FV（未来的价值）、PV（现值）和Coupon Rate（利息率）这三个重要的概念。

FV（未来的价值）是指债券到期时所能获得的总收益，也就是债券的面值。

PV（现值）是指当前时点，投资者愿意支付的价格以购物该债券。

Coupon Rate（利息率）是指债券上所标注的固定利率。

3. YTM的计算公式YTM的计算公式可以表示为：YTM = (C + (FV - PV) / n) / ((FV + PV) / 2)其中，C表示债券每年所支付的利息，FV表示债券的面值，PV表示债券的当前市场价格，n表示债券的剩余期限（年数）。

4. FV PV Coupon Rate公式的实际应用举个例子来说明FV PV Coupon Rate公式的实际应用。

假设有一张面值1000元的债券，每年支付50元的利息，剩余期限为5年，当前市场价格为950元。

根据FV PV Coupon Rate公式，可以先计算出PV、FV和Coupon Rate，然后代入YTM的计算公式中。

PV = 950FV = 1000Coupon Rate = (50 / 1000) = 5代入YTM的计算公式，可以得出该债券的YTM，进而评估该债券的投资价值。

5. 总结YTM是债券的年度预期收益率，计算YTM需要用到FV、PV和Coupon Rate这三个概念，并通过相关的计算公式来求解。

对于投资者来说，了解和计算债券的YTM是评估债券投资价值的重要方法，可以帮助投资者做出更加明智的投资决策。

6. YTM在债券投资中的重要性YTM是债券投资中的重要指标之一，它能够帮助投资者评估债券的真实收益率，从而更好地进行投资决策。

经济学财务报表与证券定价佩因曼英文

• Predictability: dividends are usually fairly stable in the short run so dividends are easy to forecast (in the short run)
Disadvantages
• Relevance: dividends payout is not related to value, at least in the short run; dividend forecasts ignore the capital gain component of payoffs.
• Forecast horizons: typically requires forecasts for long periods; terminal values for shorter periods are hard to calculate with any reliability
When It Works Best
Dividends
•
DDM:
V0E
d1 E
d2
2 E
d3
3 E
Problems: How far does one project?
• Does
V0E
d1
E
d2
2 E
d3
3 E
dT
T E
provide a good estimate of VE0?
(i) Dividend policy can be arbitrary and not linked to value added. (ii) The firm can borrow to pay dividends; this does not create value (iii) Think of a firm that “pays no dividends”

海尔净化器-水分净化器文件-海尔电器-海尔电器中国有限公司说明书

IN-GROUND WATER DIVERTER KITIn-Ground First Flush Water Diverter Kit includes:1. End Caps #5 & #92. Ball Seat #63. Sealing Ball #74. Socket & Screw Cap with O-Ring Seal #125. Flow Control Valves (set of 4) #136. Secondary Filter Screen #107. Hose Connec ti on #148. Filter screen spacer (0.3” long) 9.Primary Filter Screen #11Addi ti onal Materials required:1. Length of 12” pipe for the diverterchamber2. Length of 3” pipe1 x 1.1” length if using 4” pipe for inlet (ball seat keeper ring)1 x 4.5” (minimum) length (chamber outlet)3. 4” T-jun cti on or 3” T-junc ti on4. PVC Cement GlueThe length of 12” PVC pipe required for the diverter chamber varies depending on the amount of water you wish to divert.Calcula ti ng the amount of water to divert Industry experience and ﬁel d tes ti ng suggests the amount of water diverted should be determined based on:• Th e surface area of the roof, and• Th e amount of pollutants on the roof.The following factors can be used as a guide in determining the volume of water to be diverted.Distributed in the US by:Installation GuideThe below image illustrates a typical installation for the In-Ground First Flush Water Diverter.Installation Instruction1. Determine the length of 12” pipe requi red for the diverter chamber using the Pipe Length Calculations table on page 1.2. Cut the pipe to length and then smooth off the sharp edges to allow easy assembly.3. Inlet End: The ball seat #6 is inserted into the top of the end cap as shown below.For 3” Schedule 40 PVC pipe in -feed – insert the ball seat #6 and attach the in-feed pipe hard down on top of the ball seat #6 with the glue.For 4” Schedule 40 PVC pipe in -feed – insert the ball seat #6 and glue a 3” keeper ring (1.1” length 3” Schedule 40 PVC Pipe ) hard down on top of the ball seat #6 to keep it firmly in place with the glue.A coupling is required to attach 4” pipe to the end cap.4. Outlet End : The outlet requires only 3” pipe. Assembly i s shown in the attached “Water Divert Discharge Valve Assembly” drawing on page 4, making sure to insert ball #7 before attaching cap #12. Select one of the four control valves #13 provided and fit into hose connection #14 – the word “TOP” should be visible when the valve has been inserted the correct way up into the hose connection. Save the remaining valves for possible later use. Note: Before gluing the end caps into place be sure they are in line at 12 O’clock and 6 O’clock.Default InstallationAlternative Installation12 o’clock6 o’clock12 o’clock9 o’clockWATER DIVERTER DISCHARGE VALVE ASSEMBLYMaintenanceEnsure the outlet of the diverter is clear of any debris. If the outlet is blocked, the chamber will not empty and the first flush of water when it rains will not be diverted.Periodically:1.Remove the Hose Connection2.Remove and clean the Secondary Screen3.Remove the Threaded End Cap and Primary Screen, clean and replace4.Replace the Secondary Screen5.Make sure the Flow Control Washer is clear and refit the Hose Connection6.If the Sealing Ball falls out when the Primary Screen is removed be sure to replace the Ball BEFOREreplacing the Primary Screen.。