財務管理基礎第二單元課后答案

1、2-1= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)= 11.40%.s2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)s2 = 712.44; s = 26.69%.CV = = 2.34.2-2 Investment Beta $35,000 0.8 40,000 1.4Total $75,000bp = ($35,000/

2、$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.2-3kRF = 5%; RPM = 6%; kM = ?kM = 5% + (6%)1 = 11%.k when b = 1.2 = ?k = 5% + 6%(1.2) = 12.2%.2-4kRF = 6%; kM = 13%; b = 0.7; k = ?k = kRF + (kM - kRF)b = 6% + (13% - 6%)0.7 = 10.9%.2-5a.k = 11%; kRF = 7%; RPM = 4%. k = kRF + (kM kRF)b11% = 7% + 4%b 4% =

3、 4%b b = 1.b.kRF = 7%; RPM = 6%; b = 1.k = kRF + (kM kRF)bk = 7% + (6%)1k = 13%.2-6a.= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)= 14% versus 12% for X.b.s = . = (-10% - 12%)2(0.1) + (2% - 12%)2(0.2) + (12% - 12%)2(0.4) + (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.sX = 12.20% versus 20

4、.35% for Y.CVX = sX/X = 12.20%/12% = 1.02, whileCVY = 20.35%/14% = 1.45.2-7a.ki = kRF + (kM - kRF)bi = 9% + (14% - 9%)1.3 = 15.5%.b.1.kRF increases to 10%:kM increases by 1 percentage point, from 14% to 15%.ki = kRF + (kM - kRF)bi = 10% + (15% - 10%)1.3 = 16.5%.2.kRF decreases to 8%:kM decreases by

5、1%, from 14% to 13%.ki = kRF + (kM - kRF)bi = 8% + (13% - 8%)1.3 = 14.5%.c.1.kM increases to 16%:ki = kRF + (kM - kRF)bi = 9% + (16% - 9%)1.3 = 18.1%.2.kM decreases to 13%:ki = kRF + (kM - kRF)bi = 9% + (13% - 9%)1.3 = 14.2%.2-8Old portfolio beta = (b) + (1.00) 1.12 = 0.95b + 0.05 1.07 = 0.95b 1.126

6、3 = b.New portfolio beta = 0.95(1.1263) + 0.05(1.75) = 1.1575 1.16.Alternative Solutions:1.Old portfolio beta = 1.12 = (0.05)b1 + (0.05)b2 + . + (0.05)b201.12 = (0.05)= 1.12/0.05 = 22.4.New portfolio beta = (22.4 - 1.0 + 1.75)(0.05) = 1.1575 1.16.2. excluding the stock with the beta equal to 1.0 is

7、22.4 - 1.0 = 21.4, so the beta of the portfolio excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:1.1263(0.95) + 1.75(0.05) = 1.1575 1.16.2-9Portfolio beta= (1.50) + (-0.50) + (1.25) + (0.75)bp= (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75)= 0.15 - 0.075 + 0.31

8、25 + 0.375 = 0.7625.kp= kRF + (kM - kRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.Alternative solution: First, calculate the return for each stock using the CAPM equation kRF + (kM - kRF)b, and then calculate the weighted average of these returns.kRF = 6% and (kM - kRF) = 8%.Stock Investment Beta k = k

9、RF + (kM - kRF)b Weight A $ 400,000 1.50 18% 0.10 B 600,000 (0.50) 2 0.15 C 1,000,000 1.25 16 0.25 D 2,000,000 0.75 12 0.50Total $4,000,000 1.00kp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.2-10We know that bR = 1.50, bS = 0.75, kM = 13%, kRF = 7%.ki = kRF + (kM - kRF)bi = 7% + (13% - 7%

10、)bi.kR = 7% + 6%(1.50) = 16.0%kS = 7% + 6%(0.75) = 11.5 4.5%2-11 = 10%; bX = 0.9; sX = 35%. = 12.5%; bY = 1.2; sY = 25%.kRF = 6%; RPM = 5%.a.CVX = 35%/10% = 3.5. CVY = 25%/12.5% = 2.0.b.For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more

11、 risky. Stock Y has the higher beta so it is more risky than Stock X.c.kX = 6% + 5%(0.9)kX = 10.5%.kY = 6% + 5%(1.2)kY = 12%.d.kX = 10.5%; = 10%.kY = 12%; = 12.5%.Stock Y would be most attractive to a diversified investor since its expected return of 12.5% is greater than its required return of 12%.

12、e.bp = ($7,500/$10,000)0.9 + ($2,500/$10,000)1.2 = 0.6750 + 0.30 = 0.9750.kp = 6% + 5%(0.975)kp = 10.875%.f.If RPM increases from 5% to 6%, the stock with the highest beta will have the largest increase in its required return. Therefore, Stock Y will have the greatest increase.Check:kX = 6% + 6%(0.9

13、) = 11.4%.Increase 10.5% to 11.4%.kY = 6% + 6%(1.2) = 13.2%.Increase 12% to 13.2%.2-12kRF = k* + IP = 2.5% + 3.5% = 6%. ks = 6% + (6.5%)1.7 = 17.05%.2-13Using Stock X (or any stock): 9%= kRF + (kM kRF)bX 9%= 5.5% + (kM kRF)0.8(kM kRF)= 4.375%.2-14In equilibrium:kJ = = 12.5%. kJ= kRF + (kM - kRF)b 12

14、.5%= 4.5% + (10.5% - 4.5%)b b= 1.33.2-15bHRI = 1.8; bLRI = 0.6. No changes occur.kRF = 6%. Decreases by 1.5% to 4.5%.kM = 13%. Falls to 10.5%.Now SML: ki = kRF + (kM - kRF)bi.kHRI = 4.5% + (10.5% - 4.5%)1.8 = 4.5% + 6%(1.8) = 15.3%kLRI = 4.5% + (10.5% - 4.5%)0.6 = 4.5% + 6%(0.6) = 8.1%Difference 7.2

15、%2-16An index fund will have a beta of 1.0. If kM is 12.5 percent (given in the problem) and the risk-free rate is 5 percent, you can calculate the market risk premium (RPM) calculated as kM - kRF as follows: k = kRF + (RPM)b12.5% = 5% + (RPM)1.0 7.5% = RPM.Now, you can use the RPM, the kRF, and the

16、 two stocks betas to calculate their required returns.Bradford:kB= kRF + (RPM)b= 5% + (7.5%)1.45= 5% + 10.875%= 15.875%.Farley:kF= kRF + (RPM)b= 5% + (7.5%)0.85= 5% + 6.375%= 11.375%.The difference in their required returns is:15.875% - 11.375% = 4.5%.2-17Step 1:Determine the market risk premium fro

17、m the CAPM: 0.12= 0.0525 + (kM - kRF)1.25 (kM - kRF)= 0.054.Step 2:Calculate the beta of the new portfolio:The beta of the new portfolio is ($500,000/$5,500,000)(0.75) + ($5,000,000/$5,500,000)(1.25) = 1.2045.Step 3:Calculate the required return on the new portfolio:The required return on the new po

18、rtfolio is:5.25% + (5.4%)(1.2045) = 11.75%.2-18After additional investments are made, for the entire fund to have an expected return of 13%, the portfolio must have a beta of 1.5455 as shown below:13% = 4.5% + (5.5%)b b = 1.5455.Since the funds beta is a weighted average of the betas of all the indi

19、vidual investments, we can calculate the required beta on the additional investment as follows:1.5455 = + 1.5455 = 1.2 + 0.2X0.3455 = 0.2X X = 1.7275.2-19a.($1 million)(0.5) + ($0)(0.5) = $0.5 million.b.You would probably take the sure $0.5 million.c.Risk averter.d.1.($1.15 million)(0.5) + ($0)(0.5)

20、 = $575,000, or an expected profit of $75,000.2.$75,000/$500,000 = 15%.3.This depends on the individuals degree of risk aversion.4.Again, this depends on the individual.5.The situation would be unchanged if the stocks returns were perfectly positively correlated. Otherwise, the stock portfolio would

21、 have the same expected return as the single stock (15 percent) but a lower standard deviation. If the correlation coefficient between each pair of stocks was a negative one, the portfolio would be virtually riskless. Since r for stocks is generally in the range of +0.6 to +0.7, investing in a portf

22、olio of stocks would definitely be an improvement over investing in the single stock.2-20a.M = 0.1(7%) + 0.2(9%) + 0.4(11%) + 0.2(13%) + 0.1(15%) = 11%.kRF = 6%. (given)Therefore, the SML equation iski = kRF + (kM - kRF)bi = 6% + (11% - 6%)bi = 6% + (5%)bi.b.First, determine the funds beta, bF. The

23、weights are the percentage of funds invested in each stock.A = $160/$500 = 0.32B = $120/$500 = 0.24C = $80/$500 = 0.16D = $80/$500 = 0.16E = $60/$500 = 0.12bF= 0.32(0.5) + 0.24(2.0) + 0.16(4.0) + 0.16(1.0) + 0.12(3.0)= 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8.Next, use bF = 1.8 in the SML determined in Part a: = 6% + (11% - 6%)1.8 = 6% + 9% = 15%.c.kN = Required rate of return on new stock = 6% + (5%)2.0 = 16%.An expected return of 15 percent on the new