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Chapter 4: 18BP (page 283)
Rita Gonzales won the \(41 million lottery. She is to receive \)1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14 percent. What is the current value of her winnings?
The current value is $10,862,407.79.
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Wilson Oil Company issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point in time as described next:
Real rate of return ........................ 8%
Inflation premium ......................... 3
Risk premium .............................. 4
Total return ............................... 15%
Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond.
The Short-Line Railroad is considering a \(140,000 investment in either of two companies. The cash flows are as follows:
Year | Electric Co | Water works |
1 | \)85,000 | $30,000 |
2 | 25,000 | 25,000 |
3 | 30,000 | 85,000 |
4-10 | 10,000 | 10,000 |
a. Using the payback method, what will the decision be?
b. Explain why the answer in part a can be misleading.
Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 14 percent.
a. What is the current price of the bonds?
b. By what percent will the price of the bonds increase between now and maturity?
c. What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.)
The Caffeine Coffee Company uses the modified internal rate of return. The firm has a cost of capital of 11 percent. The project being analyzed is as follows (\(26,000 investment):
Year | Cash flow |
1 | \)12,000 |
2 | 11,000 |
3 | 9,000 |
a. What is the modified internal rate of return? An approximation from Appendix B is adequate. (You do not need to interpolate.)
b. Assume the traditional internal rate of return on the investment is 17.5 percent. Explain why your answer in part a would be lower.
Dixie Dynamite Company is evaluating two methods of blowing up old buildings for commercial purposes over the next five years. Method one (implosion) is relatively low in risk for this business and will carry a 12 percent discount rate. Method two (explosion) is less expensive to perform but more dangerous and will call for a higher discount rate of 16 percent. Either method will require an initial capital outlay of \(75,000. The inflows from projected business over the next five years are shown next. Which method should be selected using net present value analysis?
Year Method 1 Method 2
1 .................................... \)18,000 $20,000
2 .................................... 24,000 25,000
3 .................................... 34,000 35,000
4 .................................... 26,000 28,000
5 .................................... 14,000 15,00
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