1、4-1 Pearson Education Limited 2004Fundamentals of Financial Management,12/eCreated by:Gregory A.Kuhlemeyer,Ph.D.Carroll College,Waukesha,WI4-21.Distinguish among the various terms used to express value.2.Value bonds,preferred stocks,and common stocks.3.Calculate the rates of return(or yields)of diff
2、erent types of long-term securities.4.List and explain a number of observations regarding the behavior of bond prices.4-3uDistinctions Among Valuation ConceptsuBond ValuationuPreferred Stock ValuationuCommon Stock ValuationuRates of Return(or Yields)4-4represents the amount a firm could be sold for
3、as a continuing operating business.represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.4-5(2)a firm:total assets minus liabilities and preferred stock as listed on the balance sheet.represents either(1)an asset:the a
4、ccounting value of an asset-the assets cost minus its accumulated depreciation;4-6represents the price a security“ought to have”based on all factors bearing on valuation.represents the market price at which an asset trades.4-7uImportant TermsuTypes of BondsuValuation of BondsuHandling Semiannual Com
5、pounding4-8uThe()or face value of a bond is the stated value.In the case of a U.S.bond,the face value is usually$1,000.uA is a long-term debt instrument issued by a corporation or government.4-9uThe (capitalization rate)is dependent on the risk of the bond and is composed of the risk-free rate plus
6、a premium for risk.uThe bonds is the stated rate of interest;the annual interest payment divided by the bonds face value.4-10A is a bond that never matures.It has an infinite life.(1+kd)1(1+kd)2(1+kd)V=+.+III=S St=1(1+kd)tIor I(PVIFA kd,)V=/Reduced Form4-11Bond P has a$1,000 face value and provides
7、an 8%annual coupon.The appropriate discount rate is 10%.What is the value of the?=$1,000(8%)=.=.=/Reduced Form =/=.4-12N:“Trick”by using huge N like 1,000,000!I/Y:10%interest rate per period(enter as 10 NOT.10)PV:Compute(Resulting answer is cost to purchase)PMT:$80 annual interest forever(8%x$1,000
8、face)FV:$0(investor never receives the face value)NI/YPVPMTFVInputsCompute1,000,000 10 80 0 -800.04-13A is a coupon paying bond with a finite life.(1+kd)1(1+kd)2(1+kd)V=+.+II+MVI=S St=1(1+kd)tIV=I(PVIFA kd,)+MV(PVIF kd,)(1+kd)+MV4-14Bond C has a$1,000 face value and provides an 8%annual coupon for 3
9、0 years.The appropriate discount rate is 10%.What is the value of the coupon bond?=$80(PVIFA10%,30)+$1,000(PVIF10%,30)=$80(9.427)+$1,000(.057)=$754.16 +$57.00=.4-15N:30-year annual bondI/Y:10%interest rate per period(enter as 10 NOT.10)PV:Compute(Resulting answer is cost to purchase)PMT:$80 annual i
10、nterest(8%x$1,000 face value)FV:$1,000(investor receives face value in 30 years)NI/YPVPMTFVInputsCompute 30 10 80 +$1,000 -811.46(Actual,roundingerror in tables)4-16A is a bond that pays no interest but sells at a deep discount from its face value;it provides compensation to investors in the form of
11、 price appreciation.(1+kd)V=MV=MV(PVIFkd,)4-17=$1,000(PVIF10%,30)=$1,000(.057)=Bond Z has a$1,000 face value and a 30 year life.The appropriate discount rate is 10%.What is the value of the zero-coupon bond?4-18N:30-year zero-coupon bondI/Y:10%interest rate per period(enter as 10 NOT.10)PV:Compute(R
12、esulting answer is cost to purchase)PMT:$0 coupon interest since it pays no couponFV:$1,000(investor receives only face in 30 years)NI/YPVPMTFVInputsCompute 30 10 0 +$1,000 -57.31(Actual-roundingerror in tables)4-19(1)Divide by(2)Multiply by(3)Divide by Most bonds in the U.S.pay interest twice a yea
13、r(1/2 of the annual coupon).Adjustments needed:4-20(1+kd/)*(1+kd/)1A adjusted for semiannual compounding.V=+.+I/I/+MV=S S*t=1(1+kd/)tI/=I/(PVIFAkd/,*)+MV(PVIFkd/,*)(1+kd/)*+MVI/(1+kd/)24-21=$40(PVIFA5%,30)+$1,000(PVIF5%,30)=$40(15.373)+$1,000(.231)=$614.92 +$231.00=Bond C has a$1,000 face value and
14、provides an 8%semiannual coupon for 15 years.The appropriate discount rate is 10%(annual rate).What is the value of the coupon bond?4-22N:15-year semiannual coupon bond(15 x 2=30)I/Y:5%interest rate per semiannual period(10/2=5)PV:Compute(Resulting answer is cost to purchase)PMT:$40 semiannual coupo
15、n($80/2=$40)FV:$1,000(investor receives face value in 15 years)NI/YPVPMTFVInputsCompute 30 5 40 +$1,000 -846.28(Actual,roundingerror in tables)4-23Let us use another worksheet on your calculator to solve this problem.Assume that Bond C was purchased(settlement date)on 12-31-2004 and will be redeemed
16、 on 12-31-2019.This is identical to the 15-year period we discussed for Bond C.What is its percent of par?What is the value of the bond?4-24Press:2nd Bond 12.3104 ENTER 8 ENTER 12.3119 ENTER 10 ENTER CPT4-251.What is its percent of par?2.What is the value of the bond?u84.628%of par(as quoted in fina
17、ncial papers)u84.628%x$1,000 face value=$846.284-26 is a type of stock that promises a(usually)fixed dividend,but at the discretion of the board of directors.Preferred Stock has preference over common stock in the payment of dividends and claims on assets.4-27This reduces to a!(1+kP)1(1+kP)2(1+kP)=+
18、.+DivPDivPDivP=S St=1(1+kP)tDivPor DivP(PVIFA kP,)=DivP/kP4-28 =$100(8%)=.=.=/=/=Stock PS has an 8%,$100 par value issue outstanding.The appropriate discount rate is 10%.What is the value of the?4-29uPro rata share of future earnings after all other obligations of the firm(if any remain).uDividends
19、be paid out of the pro rata share of earnings.represents a residual ownership position in the corporation.4-30(1)Future dividends(2)Future sale of the common stock sharesWhat cash flows will a shareholder receive when owning shares of?4-31Basic dividend valuation model accounts for the PV of all fut
20、ure dividends.(1+ke)1(1+ke)2(1+ke)V=+.+Div1DivDiv2=S St=1(1+ke)tDivtDivt:Cash Dividend at time tke:Equity investors required return4-32The basic dividend valuation model adjusted for the future stock sale.(1+ke)1(1+ke)2(1+ke)V=+.+Div1Div +PriceDiv2:The year in which the firms shares are expected to
21、be sold.Price:The expected share price in year.4-33The dividend valuation model requires the forecast of all future dividends.The following dividend growth rate assumptions simplify the valuation process.4-34The assumes that dividends will grow forever at the rate g.(1+ke)1(1+ke)2(1+ke)V=+.+D0(1+g)D
22、0(1+g)=(ke-g)D1D1:Dividend paid at time 1.g:The constant growth rate.ke:Investors required return.D0(1+g)24-35Stock CG has an expected dividend growth rate of 8%.Each share of stock just received an annual$3.24 dividend.The appropriate discount rate is 15%.What is the value of the?=(1+.08)=/(-g)=/(-
23、.08)=4-36The assumes that dividends will grow forever at the rate g=0.(1+ke)1(1+ke)2(1+ke)VZG=+.+D1D=keD1D1:Dividend paid at time 1.ke:Investors required return.D24-37Stock ZG has an expected growth rate of 0%.Each share of stock just received an annual$3.24 dividend per share.The appropriate discou
24、nt rate is 15%.What is the value of the?=(1+0)=/(-0)=/(-0)=4-38D0(1+g1)tDn(1+g2)tThe assumes that dividends for each share will grow at two or more different growth rates.(1+ke)t(1+ke)tV=S St=1nS St=n+1+4-39D0(1+g1)tDn+1Note that the second phase of the assumes that dividends will grow at a constant
25、 rate g2.We can rewrite the formula as:(1+ke)t(ke-g2)V=S St=1n+1(1+ke)n4-40Stock GP has an expected growth rate of 16%for the first 3 years and 8%thereafter.Each share of stock just received an annual$3.24 dividend per share.The appropriate discount rate is 15%.What is the value of the common stock
26、under this scenario?4-41Stock GP has two phases of growth.The first,16%,starts at time t=0 for 3 years and is followed by 8%thereafter starting at time t=3.We should view the time line as two separate time lines in the valuation.0 1 2 3 4 5 6 D1 D2 D3 D4 D5 D6Growth of 16%for 3 yearsGrowth of 8%to i
27、nfinity!4-42Note that we can value Phase#2 using the Constant Growth Model 0 1 2 3 D1 D2 D3 D4 D5 D60 1 2 3 4 5 6Growth Phase#1 plus the infinitely long Phase#24-43Note that we can now replace all dividends from year 4 to infinity with the value at time t=3,V3!Simpler!V3=D4 D5 D60 1 2 3 4 5 6 D4k-gW
28、e can use this model because dividends grow at a constant 8%rate beginning at the end of Year 3.4-44Now we only need to find the first four dividends to calculate the necessary cash flows.0 1 2 3 D1 D2 D3 V30 1 2 3New Time Line D4k-g Where V3=4-45Determine the annual dividends.D0=$3.24(this has been
29、 paid already)=D0(1+g1)1=$3.24(1.16)1=D0(1+g1)2=$3.24(1.16)2=D0(1+g1)3=$3.24(1.16)3=D3(1+g2)1=$5.06(1.08)1=4-46Now we need to find the present value of the cash flows.0 1 2 3 3.76 4.36 5.06 780 1 2 3ActualValues 5.46.15-.08 Where$78=4-47We determine the PV of cash flows.PV()=(PVIF15%,1)=(.870)=PV()=
30、(PVIF15%,2)=(.756)=PV()=(PVIF15%,3)=(.658)=/(.15-.08)=$78 CG ModelPV()=(PVIF15%,3)=(.658)=4-48D0(1+.16)tD4Finally,we calculate the by summing all of cash flow present values.(1+.15)t(.15-.08)V=S St=13+1(1+.15)nV=$3.27+$3.30+$3.33+$51.324-49Steps in the Process(Page 1)Step 1:PressCF keyStep 2:Press2n
31、dCLR WorkkeysStep 3:For CF0 Press0Enter keysStep 4:For C01 Press3.76Enter keysStep 5:For F01 Press1Enter keysStep 6:For C02 Press4.36Enter keysStep 7:For F02 Press1Enter keys4-50Steps in the Process(Page 2)Step 8:For C03 Press83.06 Enter keysStep 9:For F03 Press 1Enter keysStep 10:Press keysStep 11:
32、PressNPVStep 12:Press 15Enter keysStep 13:PressCPTRESULT:Value=$61.18!(Actual-rounding error in tables)4-511.Determine the expected.2.Replace the intrinsic value(V)with the.3.Solve for the that equates the to the.Steps to calculate the rate of return(or Yield).4-52Determine the Yield-to-Maturity(YTM
33、)for the annual coupon paying bond with a finite life.P0=S St=1(1+kd)tI=I(PVIFA kd,)+MV(PVIF kd,)(1+kd)+MVkd=YTM4-53Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders(BW).BW has an issue of 10%annual coupon bonds with 15 years left to maturity.The bonds have a
34、 current market value of.4-54=$100(PVIFA9%,15)+$1,000(PVIF9%,15)=$100(8.061)+$1,000(.275)=$806.10+$275.00=4-55=$100(PVIFA7%,15)+$1,000(PVIF7%,15)=$100(9.108)+$1,000(.362)=$910.80+$362.00=4-56.07$1,273.02IRR$1,250$192.09$1,081 X$23.02$192$23X=4-57.07$1,273.02IRR$1,250$192.09$1,081 X$23.02$192$23X=4-5
35、8.07$1273.02$192.09$1081($23)(0.02)$192$23XX=X=.0024=.07+.0024=.0724 or 4-59N:15-year annual bondI/Y:Compute-Solving for the annual YTMPV:Cost to purchase is$1,250PMT:$100 annual interest(10%x$1,000 face value)FV:$1,000(investor receives face value in 15 years)NI/YPVPMTFVInputsCompute 15 -1,250 100
36、+$1,000 7.22%(actual YTM)4-60P0=S S2t=1(1+kd/2)tI/2=(I/2)(PVIFAkd/2,2)+MV(PVIFkd/2,2)+MV 1+(kd/2)2 -1=YTMDetermine the Yield-to-Maturity(YTM)for the semiannual coupon paying bond with a finite life.(1+kd/2)24-61Julie Miller want to determine the YTM for another issue of outstanding bonds.The firm ha
37、s an issue of 8%semiannual coupon bonds with 20 years left to maturity.The bonds have a current market value of.4-62N:20-year semiannual bond(20 x 2=40)I/Y:Compute-Solving for the semiannual yield nowPV:Cost to purchase is$950 todayPMT:$40 annual interest(8%x$1,000 face value/2)FV:$1,000(investor re
38、ceives face value in 15 years)NI/YPVPMTFVInputsCompute 40 -950 40 +$1,000 4.2626%=(kd/2)4-63 1+(kd/2)2 -1=YTMDetermine the Yield-to-Maturity(YTM)for the semiannual coupon paying bond with a finite life.1+(.042626)2 -1=.0871 or 8.71%Note:make sure you utilize the calculator answer in its DECIMAL form
39、.4-64Press:2nd Bond 12.3104 ENTER 8 ENTER 12.3124 ENTER 95 ENTER CPT=kd4-65 1+(kd/2)2 -1=YTMThis technique will calculate kd.You must then substitute it into the following formula.1+(.0852514/2)2 -1=.0871 or 8.71%(same result!)4-66-The market required rate of return exceeds the coupon rate(Par P0).T
40、he coupon rate exceeds the market required rate of return(P0 Par).The coupon rate equals the market required rate of return(P0=Par).4-67MARKET REQUIRED RATE OF RETURN(%)BOND PRICE($)1000 Par16001400120060000 2 4 6 8 12 14 16 184-68Assume that the required rate of return on a 15 year,10%annual coupon
41、 paying bond from 10%to 12%.What happens to the bond price?When interest rates,then the market required rates of return and bond prices will.4-69MARKET REQUIRED RATE OF RETURN(%)BOND PRICE($)1000 Par16001400120060000 2 4 6 8 12 14 16 184-70Therefore,the bond price has from$1,000 to$864.($863.78 on c
42、alculator)The required rate of return on a 15 year,10%annual coupon paying bond has from 10%to 12%.4-71Assume that the required rate of return on a 15 year,10%annual coupon paying bond from 10%to 8%.What happens to the bond price?When interest rates,then the market required rates of return and bond
43、prices will.4-72MARKET REQUIRED RATE OF RETURN(%)BOND PRICE($)1000 Par16001400120060000 2 4 6 8 12 14 16 184-73Therefore,the bond price has from$1000 to$1171.($1,171.19 on calculator)The required rate of return on a 15 year,10%coupon paying bond has from 10%to 8%.4-74Assume that the required rate of
44、 return on both the 5 and 15 year,10%annual coupon paying bonds from 10%to 8%.What happens to the changes in bond prices?The longer the bond maturity,the greater the change in bond price for a given change in the market required rate of return.4-75MARKET REQUIRED RATE OF RETURN(%)BOND PRICE($)1000 P
45、ar16001400120060000 2 4 6 8 12 14 16 184-76The 5 year bond price has from$1,000 to$1,080 for the 5 year bond(+8.0%).The 15 year bond price has from$1,000 to$1,171(+17.1%).The required rate of return on both the 5 and 15 year,10%annual coupon paying bonds has from 10%to 8%.4-77For a given change in t
46、he market required rate of return,the price of a bond will change by proportionally more,the the coupon rate.4-78Assume that the market required rate of return on two equally risky 15 year bonds is 10%.The annual coupon rate for Bond H is 10%and Bond L is 8%.What is the rate of change in each of the
47、 bond prices if market required rates fall to 8%?4-79The price for Bond H will rise from$1,000 to$1,171(+17.1%).The price for Bond L will rise from$848 to$1,000(+17.9%).The price on Bond H and L prior to the change in the market required rate of return is$1,000 and$848 respectively.4-80Determine the
48、 yield for preferred stock with an infinite life.P0=DivP/kP Solving for kP such thatkP=DivP/P0 4-81kP=$10/$100.=.Assume that the annual dividend on each share of preferred stock is$10.Each share of preferred stock is currently trading at$100.What is the yield on preferred stock?4-82Assume the consta
49、nt growth model is appropriate.Determine the yield on the common stock.P0=D1/(ke-g)Solving for ke such thatke=(D1/P0)+g 4-83ke=($3/$30)+5%=10%+5%=Assume that the expected dividend(D1)on each share of common stock is$3.Each share of common stock is currently trading at$30 and has an expected growth rate of 5%.What is the yield on common stock?
