武汉大学公司金融课件(二)

GROWING PERPETUITY-An annuity in which the cash flowcontinues forever, but grows at aconstant rate of “g” per year.-The stream of income looks like: PV0 = C1+ C1(1+g) + C1(1+g)2+…1 + r (1+r)2(1+r)3-Fortunately, there is an easier wayto present and calculate this value.PV growing perpetuity = C1_r – g-This is a very important equationin the evaluation of common stock.FV t = PV * ( 1 + r )tPV = FV t * ___1____( 1 + r )tPV A(r,t) = C * 1 – (1/(1 + r)t)r FV A(r,t) = C * ( 1 + r )t- 1r PV perpetuity= CrPV growing perpetuity = __C1_r – g WHAT IS THE INTEREST RATE?Your banker offers the following 5 choices:7.75% compounded daily7.75% compounded weekly7.75% compounded monthly7.75% compounded quarterly8 % compounded annuallyWHICH OPTION DO YOU PREFER?STATED or QUOTED INTEREST RATE-the interest rate expressed in terms of the interest paymentmade each period.▪Example: a quoted rate of 7.75% per year, compoundedweekly.▪Example: a stated rate of 7.75% per year, compoundedmonthly.EFFECTIVE ANNUAL RATE:EAR: the interest rate expressed as ifit were compounded once peryear.EAR = ( 1 + QR/m)m– 1Where: QR= quoted rate per yearm = number of timescompounded per year.▪Example: a quoted rate of 7.75% per year, compoundedweekly.EAR = ( 1 + .0775/52)52– 1EAR = ( 1 + .00149)52– 1EAR = 8.052%EXAMPLEAt the local loan shark, you pay $1 per week compounded weekly for every $100 that you borrow. Actually sounds very lenient doesn’t it? What is the EAR? EXAMPLE:Mortgages are quoted in annual rates but are usually compoundedsemi-annually. What is the EAR for a 9% mortgage?DEFINITIONANNUAL PERCENTAGE RATE (APR)♦The interest rate charged per period multiplied by the number of periods per year.EXAMPLEA credit card requiring monthly payments carries an APR of 14.4% and interest is calculated and compounded monthly. What is the EAR?EXAMPLE:You are to receive $1,000 per month for 25 years.Interest is compounded monthly.The present value of this annuity is $155,206.86.(I)WHAT IS THE STATED OR QUOTED MONTHLY RATE?(II)WHAT IS THE EAR?LOANS & BONDSLOAN TYPESPure Discount Loans- e.g. Treasury billsInterest-only Loans- e.g. secured loans from banksAmortized LoansAMORTIZED LOANS♦Where the lender requires the borrower to repay parts of the loan amount over time.♦Two Basic Approaches:∙Simple method: pay the accrued interest plus some portion of theprincipal.Fixed payment per period, which is a blend of interest and principal. There is a constant fixed payment every period. SIMPLE AMORTIZATION▪7% interest compounded annually;▪$8,000 loan▪4-year termThis is a 4-year annuity with a present value of $8,000.PV A(7%,4) = C * PVIFA(7%,4)8,000 = C * 1 – (1/(1.07)4).078,000 = C * 3.38721C = $2,361.82The annual payment at the end of each year would be $2,361.82.Let’s call it $2,362.AMORTIZATION SCHEDULE7.25% interest rate. When presented in this manner, the 7.25% rate is anAPR, and might be called a stated or quoted annual rate.Remember that mortgages almost always compound every 6 months.Two questions:(i)What is the monthly mortgage payment with the 5-year term?(ii)What lump-sum payment (balloon payment) would be required to pay off the mortgage after 5 years?BONDS AND BOND EVALUATIONWhat are the features of a bond?How do we find bond prices and the yield to maturity?Why do bond prices and yields move in opposite directions?What do meant by the terms “discount” and “premium” bonds?What do we mean by interest rate risk and default risk?How do we determine the rate of return on a bond?What is the difference between a real and a nominal interest rate? FEATURES OF A BONDA BOND is:▪ A financial asset that acknowledges debt;▪It entitles the owner to specified periodic interest payments; and,▪The repayment of the principal (the face value) at the stated date of maturity.FACE V ALUE OR PAR V ALUE:The principal amount of a bond that is repaid at maturity (the end of the term of the bond).COUPON:The interest payments paid to the bondholder.COUPON RATE:The annual interest as a percentage of face value. MATURITY:Specified date at which the principal amount of a bond is paid.Example: a $1,000 bond with a 6% coupon maturing in 10 years.▪This bond will pay $60 in interest at the end of each year for 10 years and will then repay the $1,000 face value at the end of the10th year.(Note: most bonds pay interest semi-annually. This is a simple complication that we will deal with after understanding the basic valuation techniques)BOND V ALUESHow much would you pay for the $1,000 bond, maturing in 10 years with a 6% annual coupon, if the current market rate of interest were 6%?In other words, what is the Present Value of this bond?The Bond has two parts:i. A 10-year stream of interest payments of $60 per year; and,ii.The repayment of the face value of the bond, the $1,000, at the end of 10 years.BOND = Present Value + Present ValueV ALUE of the Coupons of the PrincipalPV bond = C * PVIFA6%,10 + P * PVIF6%,10In our example, then:PV bond = 60*( 1 – 1/(1.06)10) +1,000 * 1/(1.06)10.06= ( 60 * 7.3601) + (1,000 * .55839)= 441.61 + 558.39PV bond = $1,000You would be prepared to pay $1,000 for the bond.BUT:What if the market rate of interest for that type of bond was really 7%? Why would you pay $1,000 and earn only 6%?a YIELD TO MATURITY equal to the market rate of interest.That price is easily calculated:PV bond = C * PVIFA7%,10+ 1,000 * PVIF 7%,10=60 * 1 – (1/(1.07)10 + 1,000 * 1/(1.07)10.07= ( 60 * 7.02358) + (1,000 * .50835)= 421.41 + 508.35PV bond= $ 929.76YIELD TO MATURITY OR INTERNAL RATE OF RETURN OF THE BOND: The discount ra te that equates a bond’s present value of interest payments and principal repayment with its price.。