1、Xu Yanqi 18021026561 / 8Question 1According 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= PM
2、T , PV= PMT(PVIFAi,n) and the 1-(1+)-present value of the maturity value is given by substitution in equation PV= , (1+)PV = FVn(PVIFi,n). So it could be calculated: A. I = = = 4%8%2N = mt = 28 = 16PV = PMT 1-(1+)- (1+)= PMT(PVIFAi,n)+ FVn(PVIFi,n)= $40(PVIFA4%,16)+$1000(PVIF4%,16)= $4011.652+$10000
3、.534= $ 466.08 + $534= $1000.08At the required annual bond yields of 8%, todays price of the bond is $1000.08B. I = = = 3.75%7.5%2N = mt = 28 = 16Pv = PMT 1-(1+)- (1+)= $40 1-(1+3.75%)-163.75% $1000(1+3.75%)16= $40 + 1-0.55480.0375$10001.8027= $40 11.872 + $554.8773= $1029.7573At the required annual
4、 bond yields of 7.5%, todays price of the bond is $1029.7573Xu Yanqi 18021026562 / 8C. I = = = 4.25%8.5%2N = mt = 28 = 16Pv = PMT 1-(1+)- (1+)=$40 1-(1+3.75%)-163.75% $1000(1+4.25%)16= $40 1-0.5130.0425 $10001.9463= $4011.459 + $513.7954= $972.1554At the required annual bond yields of 8.5%, todays p
5、rice 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 2Estimate the expected future cash flows from share ownership. Since the $0.40 dividend has just been paid, we need to estimate the divide
6、nd 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%) = $0.416Estimate the required rate of return whic
7、h is 14% after assessing the riskiness of the the expected cash flows. VE = = $4.161- $0.41614%-4%= b. 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%) = $0.42Xu Yanqi 18021026563
8、/ 8Estimate the required rate of return which is 13% after assessing the riskiness of the the expected cash flows.VE = = $5.251- $0.4213%-5%= c. Constant-dividend-growth ordinary-share valuation modelFrom the results of calculation, when the dividends rate increase, the required rate of return will
9、increase, also the intrinsic value will increase.Question 3As the current share price is $10, according to the equation: VE = 1-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
10、 a 0.The expected rate of return is:RE = + g = + 0 = 0.06 = 6%1 $0.6$10b. 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 = + g = + 0.
11、02 = 0.0812 = 8.12%1 $0.612$10c. 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 = + g = + 0.04 = 0.1024 = 10.24%1 $0.624$10Question4
12、Xu Yanqi 18021026564 / 8a. I. According to the equation j = PjmA , the correlation with market returns for A、B、B is 0.75、0.8 and 0.75; standard deviation for A、B、C and market is 30%、27$、24% and 18%. jA = PjmA = 0.75 = 1.25 30%18%jB = PjmA = 0.8 = 1.2 27%18%jC = PjmA = 0.75 = 1 24%18% II. According t
13、o 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、14%Xu Yanqi 18021026565 / 8b. According to the equation V= VA = = = 1116% 116%VB = = = 0.9621RBRjB 15% 115.6%VC = = = 0.929.1RCRjC 113%14%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 valueAcc
15、ording to the equation : NPV = -IO=1(1+)NPV = IO=1(1+)= + + + + $500000$2500001+0.12 $200000(1+0.12)2 $150000(1+0.12)3 $100000(1+0.12)4 $150000(1+0.12)5=$223250 + $159400 + $106800 + $63600 + $85050 $500000= $138100Because $1381000 . So, we accept the proposed investment. II. Internal rate of return
16、Xu Yanqi 18021026566 / 8According to the equation: IO= =1 (1+)First ,we use the trail and error . when IRR=20%,NPV = IO=1(1+)= + + + + $500000$2500001+0.2 $200000(1+0.2)2 $150000(1+0.2)3 $100000(1+0.2)4 $150000(1+0.2)5= $208250+$138800+$86850+$48200+$60300-$500000= $42400 0 when IRR=25%NPV = IO=1(1+
17、)= + + + + -$500000$2500001+0.25 $200000(1+0.25)2 $150000(1+0.25)3 $100000(1+0.25)4 $150000(1+0.25)5= $200000+$128000+$76800+$41000+$49200$500000= -$5000 0Second ,we use the interpolation=25% 20%20% 5000 4240042400 0IRR=24.47%Because IRR=24.47 required rate of return=12 , So , we accept the proposed
18、 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= $1124600Xu Yanqi 1802
19、1026567 / 8According to the equation: MIRR= 1 ( )15MIRR= 1= 1=1.176-1 = 0.176 =17.6% ( )15 ( $1124600$500000)15Because 17.6%12% So , we accept the proposed investment.IV. Average accounting rate of returnAccording to the equation, = cost-tax =1 =1 expense = cost-tax expense =1 =1 =($250000+$200000+$
20、150000+$100000+$150000) （1-30%）-$500000= $850000 70%-500000= $95000According to the equation : AROR = =1+2AROR = =1+2= = = 0.069=6.9%$950005$500000+$500002 $19000$275000Because the AROR =6.9% the minimum acceptable level 12%So , we reject the proposed investmentV.Payback periodFrom d. we can get : =
21、 $950000=1The net cash flows are: $250000(1-30%)=$175000 $200000(1-30%)=$140000Xu Yanqi 18021026568 / 8 $150000(1-30%)=$105000 $100000(1-30%)=$70000 $150000(1-30%)=$105000Because $175000+$140000+$105000+$70000=$490000 .It can be return$490000 in four year.However $500000-$490000=$10000So =0.09523 $10000$1050000.0952312=1.14In conclusion, the payback period on this project is 4years and 2 months ,which is shorter than the desired payback period 5years.So , the firm could accept the this investment
