国际交流学院FIN第一次.doc

Xu Yanqi 1802102656Question 1 According to the subject, the FVn is $1000, the year is 8 and the coupon rate is 8.0% and pays interest twice per year. Its most recent coupon of $40.00 has just been paid. The present value of the interest-payment annuity is given by substitution in equation PV= PMT1-1+i-ni, PV= PMT(PVIFAi,n) and the present value of the maturity value is given by substitution in equation PV=FVn1+in , PV = FVn(PVIFi,n). So it could be calculated: A. I = jm= 8%2 = 4%N = mt = 28 = 16PV = PMT1-1+i-ni FVn1+in = PMT(PVIFAi,n)+ FVn(PVIFi,n) = $40(PVIFA4%,16)+$1000(PVIF4%,16) = $4011.652+$10000.534 = $ 466.08 + $534 = $1000.08 At the required annual bond yields of 8%, todays price of the bond is $1000.08B. I = jm= 7.5%2 = 3.75%N = mt = 28 = 16Pv = PMT1-1+i-ni FVn1+in = $40 1-1+3.75%-163.75% $10001+3.75%16 = $40 1-0.55480.0375 + $10001.8027 = $40 11.872 + $554.8773 = $1029.7573 At the required annual bond yields of 7.5%, todays price of the bond is $1029.7573C. I = jm= 8.5%2 = 4.25%N = mt = 28 = 16Pv = PMT1-1+i-ni FVn1+in =$40 1-1+3.75%-163.75% $10001+4.25%16 = $401-0.5130.0425 $10001.9463 = $4011.459 + $513.7954 = $972.1554 At the required annual bond yields of 8.5%, todays price of the bond is $975.1554. According to the aftermath, we could find when the required annual bond yields increased, the price of the bond decreased.Question 2 Estimate the expected future cash flows from share ownership. Since the $0.40 dividend has just been paid, we need to estimate the dividend amount to be received amount to be received at the end of the first period. a. With a 4% per annum growth rate of dividends, D1 is expected to be 4% more than the previous dividend amount of D0.D0 = $0.40 g = 4% RE = 14%D1 = D0(1+g) = $0.40(1+ 4%) = $0.416 Estimate the required rate of return which is 14% after assessing the riskiness of the the expected cash flows. VE = D1RE-g = $0.41614%-4%= $4.16b. With a 5% per annum growth rate of dividends, D1 is expected to be 4% more than the previous dividend amount of D0.D0 = $0.40 g = 5% RE = 13%D1 = D0(1+g) = $0.40(1+ 5%) = $0.42Estimate the required rate of return which is 13% after assessing the riskiness of the the expected cash flows.VE = D1RE-g = $0.4213%-5%= $5.25c. Constant-dividend-growth ordinary-share valuation model From the results of calculation, when the dividends rate increase, the required rate of return will increase, also the intrinsic value will increase.Question 3 As the current share price is $10, according to the equation: VE = D1RE-g a. The ordinary share dividend expected to be paid at the end of the current year is D1 = D0(1+g) = 0.6(1+0)= $0.6 and future earnings and dividends are expected to grow at a 0.The expected rate of return is: RE = D1VE + g = $0.6$10 + 0 = 0.06 = 6%b. The ordinary share dividend expected to be paid at the end of the current year is D1 = D0(1+g) = 0.6(1+2%)= $0.612 and future earnings and dividends are expected to grow at a 0.02.The expected rate of return is: RE = D1VE + g = $0.612$10 + 0.02 = 0.0812 = 8.12%c. The ordinary share dividend expected to be paid at the end of the current year is D1 = D0(1+g) = 0.6(1+4%)= $0.624 and future earnings and dividends are expected to grow at a 0.04.The expected rate of return is: RE = D1VE + g = $0.624$10 + 0.04 = 0.1024 = 10.24%Question4 a. I. According to the equation j = PjmA jAm , the correlation with market returns for A、B、B is 0.75、0.8 and 0.75; standard deviation for A、B、C and market is 30%、27$、24% and 18%. jA = PjmA jAm = 0.75 30%18% = 1.25jB = PjmA jAm = 0.8 27%18% = 1.2jC = PjmA jAm = 0.75 24%18% = 1 II. According to the equation Rf = R RP we could know Rf = 14% 8% = 6% and the equation: Rj = Rf + j(Rm Rf ) RjA = Rf + jA(Rm Rf ) = 6% + 1.25 ( 14% - 6%) = 0.06 + 1.25 0.08 = 0.16 = 16% RjB = Rf + jB(Rm Rf ) = 6% + 1.2 ( 14%6% ) = 0.0 6 + 1.2 0.08 = 0.156 = 15.6% RjC = Rf + jC(Rm Rf ) = 6% + 1 ( 14% 6% ) = 0.06 + 0.08 = 0.14 = 14%b. According to the equation V= DRP VA = 1RARjA = 16% 116% = 1 VB = 1RBRjB = 15% 115.6% = 0.962 VC = 1RCRjC = 113%14% = 0.929. According to the result of our calculation we could easily find out that the A is the correctly, the B and C is the under-price.Question 5 I .Net present value According to the equation : NPV = t=1nACFt(1+k)n -IO NPV = t=1nACFt(1+k)n IO = $2500001+0.12 + $200000(1+0.12)2 + $150000(1+0.12)3 + $100000(1+0.12)4 + $150000(1+0.12)5 $500000 =$223250 + $159400 + $106800 + $63600 + $85050 $500000 = $138100 Because $1381000 . So, we accept the proposed investment. II. Internal rate of returnAccording to the equation: IO= t=1nACFt(1+IRR)n First ,we use the trail and error . when IRR=20%, NPV = t=1nACFt(1+k)n IO = $2500001+0.2+ $200000(1+0.2)2+ $150000(1+0.2)3+ $100000(1+0.2)4+ $150000(1+0.2)5 $500000= $208250+$138800+$86850+$48200+$60300-$500000 = $42400 0 when IRR=25% NPV = t=1nACFt(1+k)n IO=$2500001+0.25+ $200000(1+0.25)2+ $150000(1+0.25)3+ $100000(1+0.25)4+ $150000(1+0.25)5-$500000 = $200000+$128000+$76800+$41000+$49200$500000 = -$5000 0 Second ,we use the interpolation 25%20%20%IRR= 500042400424000 IRR=24.47%Because IRR=24.47 required rate of return=12 , So , we accept the proposed investment.III. Modified internal rate of returnFV1= $ 250000 FVIF12%,4 = $393500FV2= $200000 FVIF12%,3 = $281000FV 3= $150000 FVIF12%,2= $188100FV 4= $100000 FVIF12%,1= $112000 FV 5= $150000So, the sum cash flow in five years is : FV= $393500+$281000+$188100+$112000+$150,000= $1124600According to the equation: MIRR=( terminal valuePV of cash outflows)151MIRR= ( terminal valuePV of cash outflows)151= ( $1124600$500000)151=1.176-1 = 0.176 =17.6% Because 17.6%12% So , we accept the proposed investment.IV. Average accounting rate of returnAccording to the equation,t=1nAPt = t=1nCost savings cost-tax expense t=1nAPt = t=1nCost savings cost-tax expense =($250000+$200000+$150000+$100000+$150000) （1-30%）-$500000= $850000 70%-500000= $95000According to the equation : AROR = t=1nAPtnIO+SV2 AROR = t=1nAPtnIO+SV2 = $950005$5