London School of Business and Finance

• FINANCE 156

• CHAPTER 2 Present Values, The Objectives of the Firm, and Corporate Governance Answers to Practice Questions 1. The face value of the treasury security is $1,000. If this security earns 5%, then in one year we will receive $1,050. Thus: NPV = C0 + [C1/(1 + r)] = −$1000 + ($1050/1.05) = 0 This is not a surprising result because 5 percent is the opportunity cost of capital, i.e., 5 percent is the return available in the capital market. If any investment earns a rate of return equal to the opportunity cost of capital, the NPV of that investment is zero. 2. NPV = −$1,300,000 + ($1,500,000/1.10) = +$63,636 Since the NPV is positive, you would construct the motel. Alternatively, we can compute r as follows: r = ($1,500,000/$1,300,000) – 1 = 0.1539 = 15.39% Since the rate of return is greater than the cost of capital, you would construct the motel. 3. Investment NPV Return (1) $5,000 1.20 18,000 −10,000 + = 0.80 80.0% 10,000 18,000 10,000 = = − (2) $2,500 1.20 9,000 − 5,000 + = 0.80 80.0% 5,000 9,000 5,000 = = − (3) $250 1.20 5,700 − 5,000 + = − 0.14 14.0% 5,000 5,700 5,000 = = − (4) $1,333.33 1.20 4,000 − 2,000 + = 1.00 100.0% 2,000 4,000 2,000 = = − a. Investment 1, because it has the highest NPV. b. Investment 1, because it maximizes shareholders’ wealth. 2 4. a. NPV = (−$50,000 + $20,000) + ($38,000/1.05) = $6,190.48 b. NPV = (−$50,000 + $20,000) + ($38,000/1.10) = $4,545.45 In Part (a), the NPV is higher than the NPV of the office building ($5,000); therefore, we should accept E. Coli’s offer. In Part (b), the NPV is less than the NPV of the office building, so we should not accept the offer. You can also think of this in another way. The true opportunity cost of the land is what you could sell it for, i.e., $56,190 (or $54,545). At $56,190, the office building has a negative NPV. At $54,545, the office building has a positive NPV. 5. a. NPV = −$2,000,000 + [($2,000,000 × 1.05)/1.05] = $0 b. NPV = −$900,000 + [($900,000 × 1.07)/1.10] = −$24,545.45 The correct discount rate is 10% because this is the appropriate rate for an investment with the level of risk inherent in Norman’s nephew’s restaurant. The NPV is negative because Norman will not earn enough to compensate for the risk. c. NPV = −$2,000,000 + [($2,000,000 × 1.12)/1.12] = $0 d. NPV = −$1,000,000 + ($1,100,000/1.12) = −$17,857.14 Norman should invest in either the risk-free government securities or the risky stock market, depending on his tolerance for risk. Correctly priced securities always have an NPV = 0. 6. a. Expected rate of return on project = This is equal to the return on the government securities. b. Expected rate of return on project = This is less than the correct 10% rate of return for restaurants with similar risk. c. Expected rate of return on project = This is equal to the rate of return in the stock market. 0.05 5.0% $2,000,000 $2,100,000 $2,000,000 = = − 0.07 7.0% $900,000 $963,000 $900,000 = = − 0.12 12.0% $2,000,000 $2,240,000 $2,000,000 = = − 3 d. Expected rate of return on project = This is less than the return in the equally risky stock market. 7. $17,857.14 1.12 $1,100,000 ($1,600,000 1.12) NPV $2,600,000 = − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + × = − + The rate at which Norman can borrow does not reflect the opportunity cost of the investments. Norman is still investing $1,000,000 at 10% while the opportunity cost of capital is 12%. 8. The investment’s positive NPV will be reflected in the price of Scaled Composites stock. In order to derive a cash flow from her investment that will allow her to spend more today, Ms. Espinoza can sell some of her shares at the higher price or she can borrow against the increased value of her holdings. 9. a. Let x = the amount that Casper should invest now. Then ($200,000 – x) is the amount he will consume now, and (1.08x) is the amount he will consume next year. Since Casper wants to consume exactly the same amount each period: 200,000 – x = 1.08x 0.10 10.0% $1,000,000 $1,100,000 $1,000,000 = = − 203,704 200,000 220,000 216,000 Dollars Next Year Dollars Now 4 Solving, we find that x = $96,153.85 so that Casper should invest $96,153.85 now, he should spend ($200,000 - $96,153.85) = $103,846.15 now, and he should spend (1.08 × $96,153.85) = $103,846.15 next year. b. Since Casper can invest $200,000 at 10% risk-free, he can consume as much as ($200,000 × 1.10) = $220,000 next year. The present value of this $220,000 is: ($220,000/1.08) = $203,703.70 Therefore Casper can consume as much as $203,703.70 now by first investing $200,000 at 10% and then borrowing, at the 8% rate, against the $220,000 available next year. If we use the $203,703.70 as the available consumption now, and again let x = the amount that Casper should invest now, we can then solve the following for x: $203,703.70 – x = 1.08x x = $97,934.47 Therefore, Casper should invest $97,934.47 now at 8%, he should spend ($203,703.70 – $97,934.47) = $105,769.23 now, and he should spend ($97,934.47 × 1.08) = $105,769.23 next year. [Note that this approach leads to the result that Casper borrows $203,703.70 at 8% and then invests $97,934.47 at 8%. We could simply say that he should borrow ($203,703.70 - $97,934.47) = $105,769.23 at 8% against the $220,000 available next year. This is the amount that he will consume now.] c. The NPV of the opportunity in (b) is: ($203,703.70 - $200,000) = $3,703.70 5 Challenge Questions 1. a. Expected cash flow = ($8 million + $12 million + $16 million)/3 = $12 million b. Expected rate of return = ($12 million/$8 million) – 1 = 0.50 = 50% c. Expected cash flow = ($8 + $12 + $16)/3 = $12 Expected rate of return = ($12/$10) – 1 = 0.20 = 20% The net cash flow from selling the tanker load is the same as the payoff from one million shares of Stock Z in each state of the world economy. Therefore, the risk of each of these cash flows is the same. d. NPV = −$8,000,000 + ($12,000,000/1.20) = +$2,000,000 The project is a good investment because the NPV is positive. Investors would be prepared to pay as much as $10,000,000 for the project, which costs $8,000,000. 2. a. Expected cash flow (Project B) = ($4 million + $6 million + $8 million)/3 Expected cash flow (Project B) = $6 million Expected cash flow (Project C) = ($5 million + $5.5 million + $6 million)/3 Expected cash flow (Project C) = $5.5 million b. Expected rate of return (Stock X) = ($110/$95.65) –1 = 0.15 = 15.0% Expected rate of return (Stock Y) = ($44/$40) –1 = 0.10 = 10.0% Expected rate of return (Stock Z) = ($12/$10) –1 = 0.20 = 20.0% c. Percentage Differences Slump v. Normal Boom v. Normal Project B 4/6 = 66.67% 8/6 = 133.33% Project C 5/5.5 = 90.91% 6/5.5 = 109.09% Stock X 80/110 = 72.73% 140/110 = 127.27% Stock Y 40/44 = 90.91% 48/44 = 109.09% Stock Z 8/12 = 66.67% 16/12 = 133.33% Project B has the same risk as Stock Z, so the cost of capital for Project B is 20%. Project C has the sa