【正文】 1,200 / + $3,000 / = $ Project B should be chosen. a. Average Investment: ($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000 Average accounting return: $4,500 / $8,000 = = % b. 1. AAR does not consider the timing of the cash flows, hence it does not consider the time value of money. 2. AAR uses an arbitrary firm standard as the decision rule. 3. AAR uses accounting data rather than net cash flows. a Average Investment = (8000 + 4000 + 1500 + 0)/4 = Average Net Ine = 2000() = 1500 = AAR = 1500/3375=% a. Solve x by trial and error: $8,000 + $4,000 / (1 + x) + $3000 / (1 + x)2 + $2,000 / (1 + x)3 = 0 x = % b. No, since the IRR (%) is less than the discount rate of 8%. Alternatively, the NPV a discount rate of = $. a. Solve r in the equation: $5,000 $2,500 / (1 + r) $2,000 / (1 + r)2 $1,000 / (1 + r)3 $1,000 / (1 + r)4 = 0 By trial and error, IRR = r = % b. Since this problem is the case of financing, accept the project if the IRR is less than the required rate of return. IRR = % 10% Reject the offer. c. IRR = % 20% Accept the offer. d. When r = 10%: NPV = $5,000 $2,500 / $2,000 / $1,000 / $1,000 / = $ When r = 20%: NPV = $5,000 $2,500 / $2,000 / $1,000 / $1,000 / = $ Yes, they are consistent with the choices of the IRR rule since the signs of the cash flows change only once. PI = $40,000 / $160,000 = Since the PI exceeds one accept the project.Chapter 7: Net Present Value and Capital Budgeting Since there is uncertainty surrounding the bonus payments, which McRae might receive, you must use the expected value of McRae’s bonuses in the putation of the PV of his contract. McRae’s salary plus the expected value of his bonuses in years one through three is $250,000 + 180。 $2,000) = $80,000 + $20,000 () = $138,274 EAC = $138,274 / = $47,456 IOU PV(costs) = (11 180。 300,000) (340,000 + 180。ReturnRecessionModerate GrowthRapid ExpansionExpected Return = b. Return if State occursP180。 = 215%5% 180。} / dXB = (2 XB 2) sA2 + 2 XB sB2 + 2 Cov(RA, RB) 4 XB Cov(RA, RB) Set the derivative equal to zero, cancel the mon 2 and solve for XB. XB sA2 sA2 + XB sB2 + Cov(RA, RB) 2 XB Cov(RA, RB) = 0 XB = {sA2 Cov(RA, RB)} / {sA2 + sB2 2 Cov(RA, RB)} and XA = {sB2 Cov(RA, RB)} / {sA2 + sB2 2 Cov(RA, RB)} Using the data from the problem yields, XA = and XB = .a. Using the weights calculated above, the expected return on the minimum variance portfolio is E(RP) = E(RA) + E(RB) = (5%) + (10%) = % b. Using the formula derived above, the weights are XA = 2 / 3 and XB = 1 / 3 c. The variance of this portfolio is zero. sP 2 = XA2 sA2 + XB2 sB2 + 2 XA XB Cov(RA , RB) = (4 / 9) () + (1 / 9) () + 2 (2 / 3) (1 / 3) () = 0 This demonstrates that assets can be bined to form a riskfree portfolio. %= %+b(%) 222。 . sell short security one and buy security two.b. Follow the same logic as in part a, we have Where X is the proportion of security three in the portfolio. Thus, sell short security four and buy security three. this is a risk free portfolio!c. The portfolio in part b provides a risk free return of 10% which is higher than the 5% return provided by the risk free security. To take advantage of this opportunity, borrow at the risk free rate of 5% and invest the funds in a portfolio built by selling short security four and buying security three with weights (3,2).d. Assuming that the risk free security will not change. The price of security four ( that everyone is trying to sell short) will decrease and the price of security three ( that everyone is trying to buy ) will increase. Hence the return of security four will increase and the return of security three will decrease. The alternative is that the prices of securities three and four will remain the same, and the price of the riskfree security drops until its return is 10%. Finally, a bined movement of all security prices is also possible. The prices of security four and the riskfree security will decrease and the price of security four will increase until the opportunity disappears. E 20% 10% 5% 0 Chapter 12: Risk, Return, and Capital Budgeting a. To pute the beta of Mercantile Manufacturing’s stock, you need the product of the deviations of Mercantile’s returns from their mean and the deviations of the market’s returns from their mean. You also need the squares of the deviations of the market’s returns from their mean.The mechanics of puting the means and the deviations were presented in an earlier chapter. = / 12 = = / 12 = E( ) ( ) = rTMsTsM = ()()() = E( )2 = b = sTM/sM2 = / = b. The beta of the average stock is 1. Mercantile’s beta is slightly greater than 1, indicating that its stock has slightly greater than average risk. a. RM can have three values, , or . The probability that takes one of these values is the sum of the joint probabilities of the return pair that include the particular value of . For example, if is , RJ will be , or . The probability that is and RJ is is . The probability that RM is and RJ is is . The probability that is and RJ is is . The probability that is is, therefore, + + = . The same procedure is used to calculate the probability that is and the probability that is . Remember, the sum of the probability must be one. Probability b. i. = () + () + () = ii. = ( ) 2 () + ( ) 2 () + ( ) 2 () = iii. = = c. RJ Probability .16 .10 .