+ (1,500, 000) (1 + 0,10) (1,10) Since the NPV of the project is positive, you would construct the motel.

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1 CHAPTER 2: Practice questions 0. A parcel of land costs $500,000. For an additional $800,000 you can build a motel on the property. The land and the motel should be worth $,500,000 next year. Suppose that common stocks with the same risk as this investment offer a 0 percent expected return. Would you construct the motel? Why or why not? Land = $500,000 Motel = $800, 000 FV (exp) =,500, 000 r = 0% C = Co + ( + r) (,500, 000) = (500, ,000) + ( + 0,0) (,500, 000) =,00,000 + (,0) = 6,66.6 Since the of the project is positive, you would construct the motel. Alternatively, we can compute the return of the project as follows: r,500,000,00,000 = = 0,59 = 5,9%,00,000 Since the rate of return is greater than the cost of capital, you would construct the motel.. Calculate the and rate of return for each of the following investments. The opportunity cost of capital is 20% for all four investments. Investment Initial Cash Flow Cash Flow Year (0.000,00) 8.000,00 2 (5.000,00) 9.000,00 (5.000,00) 5.700,00 4 (2.000,00) 4.000,00

2 By using the formula C ( r) = Co + + where r=20% you obtain: Investment Return 8,000 8,000 0,000 0,000 + = $5,000 = 0.80 = 80.0%.20 0, ,000 9,000 5,000 5,000 + = $2,500 = 0.80 = 80.0%.20 5,000 5,700 5,700 5,000 5,000 + = $250 = 0.4 = 4.0%.20 5, ,000 4,000 2,000 2,000 + = $,. =.00 = 00.0%.20 2,000 (a) Which investment is most valuable? Investment is the most valuable for shareholders because it has the highest. (b) Suppose each investment would require use of the same parcel of land. Therefore you can take only one. Which one? Investment is the best choice because it has the highest (combined) IRR and. Although project and 2 offer the same rate of return, project maximizes shareholders wealth by offering also the highest.. Norman Gerrymander has just received a $ million bequest. How should he invest it? There are four immediate alternatives. a. Investment in one-year U.S. government securities yielding 5%. b. A loan to nephew Gerald, who has for years aspired to open a big Cajun restaurant in Duluth. Gerald has arranged a one-year bank loan for $900,000 at 0%, but asks for a $ million loan from Norman at 9%. c. Investment in the stock market. The expected rate of return is 2%. d. Investment in local real estate, which Norman judges is about as risky as the stock market. The opportunity at hand would cost $ million and is forecasted to be worth $. million after one year. Which of these investments have positive s? Which would you advise Norman to take? By using the formula C ( r) = Co + + obtain: 2

3 (a) a,050,000 = + = 0 (, 05) (b) Assuming that 0% is the appropriate discount rate for an investment with the level of risk inherent in Gerald s restaurant: b (,09) =, 000, = 9, (,0) (c) (d) c d,20, 000 = + = 0 (,2),00, 000 =, 000, = 7,857. (,2) Norman shouldn t invest in projects (b) and (d) because they yield a negative. On the other hand, projects (a) and (c) investing in a government bond or the stock marketwould yield him a =0 (this is because correctly priced securities always have an = 0). 4. Show that your answers to question are consistent with the rate of return rule for investment decisions. The following table summarizes the results obtained in question : Investment One-year U.S. government securities $0 Loan to nephew Gerald -$9,090.9 Investment in the stock market $0 Investment in local real estate -$7,857. *** Note that none of the investment projects has a positive. The investment in the government securities and the stock market have = 0 because correctly priced securities always have an = 0. Now, to compute the rate of return of each project we proceed: (a) Expected rate of return on project A: r a,050,000 = = 5.0% *** r a is equal to the return on the government securities (which is consistent with a =0).

4 (b) Expected rate of return on project B: r b,090,000 = = 9.0% *** r b is less than the return for investments with similar risk paying 0% (which is consistent with a negative ).,20,000 (c) Expected rate of return on project C: r c = = 2.0% *** r c is equal to the rate of return of the stock market (which is consistent with a =0).,00,000 (d) Expected rate of return on project = r d = = 0.0% *** r d is less than the 2% rate of return for investment in the equally risky stock market (which is consistent with a negative ). 9. For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered in Rotterdam one year hence. Unfortunately the net cash flow from selling the tanker load will be very sensitive to the growth rate of the world economy: Slump Normal Boom $8 $2 $6 (a) What is the expected cash flow? Assume the three outcomes for the economy are equally likely. Expected cash flow = /*(8+2+6) =2 (b) What is the expected rate of return on the investment in the project? Expected rate of return = (2-8)/8 = 0.5 (c) One share of stock Z is selling for $0.The stock has the following payoffs after one year Slump Normal Boom $8 $2 $6 Calculate the expected rate of return offered by stock Z. Explain why this is the opportunity cost of capital for your bucolic acid project. Expected rate of return = (2-0)/0 = 0.2 4

5 This is the return foregone by investing in the project and not in a share with identical risk (d) Calculate the project s. Is the project a good investment? Explain why. = 2/(+0.2)-8 = 2 > 0. It is a good project, since its has positive. CHAPTER 2: Challenge questions 20. (Tutorial) In real life the future health of the economy cannot be reduced to three equally probable states like slump, normal, and boom. But we ll keep that simplification for one more example. Your company has identified two more projects, B and C. Each will require a $5 outlay immediately. The possible payoffs at year, are in millions: Slump Normal Boom Project B $4 $6 $8 Project C 5 5,5 6 You have identified the possible payoffs to investors in three stocks X, Y, and Z: Current Price Payoff at Year per Share Slump Normal Boom X $95,65 $80 $0 $40 Y Z (a) What are the expected cash inflows of project B and C? Expected cash inflow of project B = /*(4+6+8) = 6 Expected cash inflow of project C = /*( ) = 5.5 5

6 (b) What are the expected rates of return offered by stocks X,Y, and Z? ( ) Expected rate of return for stock X = ( ) 40 Expected rate of return for stock Y = = ( ) 0 Expected rate of return for stock Z = = (c) What are the opportunity costs of capital for projects B and C? (Hint: Calculate the percentage differences, slump versus normal and boom versus normal, for stocks X,Y, and Z. Match up to the percentage differences in B s and C s payoffs.) Notice that 0.5 times stock Z has the same payoffs as project B and /8 of stock Y has the same payoffs as project C. Therefore we can choose 0.2 and 0. respectively as discount rates. (d) What are the s of projects B and C? Project B: = 6/(+0.2) 5 = 0 Project C: = 5.5/(+0.) 5 = 0 (e) Suppose B and C are launched and $5 million are invested in each. How much will they add to the market value of your company s shares? Since the is zero no value would be added to the company. 6