## Problem Set # 1 Answers

1. Explain why a dollar today is worth more than a dollar tomorrow.
• Time-value of money; capital scarcity; you can take a dollar's command over purchasing power today and use it to commit resources to a project that will yield more than a dollar's worth of value tomorrow.
2. You must invest in a US government security yielding 5.5% or in a Russian government security also yielding 5.5% on an annual basis. Pick one. Justify your selection. Both bonds are denominated in United States dollars.
• U.S. government is less likely to default
3. Write down three reasons why capital markets are not actually "perfect." Then explain why, for purposes of this course and for their purposes, Brealey and Myers (and I) assume that they are perfect.
• There are many such reasons: information isn't free and freely-flowing; not everyone can borrow and lend unlimited amounts at (or near) the riskless rate; it's difficult to take large short positions. However, these are second-order corrections to a first order truth--that the market is nearly efficient.
4. Suppose that you have just won \$22,000,000 in the lottery. If you put all of this in the bank at 2%, what will be your annual income?
• \$440,000 a year
5. You are negotiating to purchase a typewriter company, and you need to know what a fair value for the company would be. Daisy Typewriters, Inc., had a positive cash flow of \$31,427,000 last year. Your researchers--whom you trust--tell you that these cash flows will be stable for the next three years, and after three years will then decline by 9% a year forever. Suppose that the appropriate cost of capital is 15%. What is the fair market value of this typewriter company?
• \$168,521,000
6. What is the Present Value of \$100 to be received in:
• a. three years, at a discount rate of 7% per year
• \$82
• b. ten years, at a discount rate of 9% per year
• \$42
• c. seventy two years, at a discount rate of 1% per year
• \$49
7. Why might actual corporation managers in the real world maximize their companies' net present value? Why might they not maximize their companies' net present value?
• Brealey and Myers give a bunch of different answers, all of which boil down to the principle that maximizing NPV maximizes their shareholders' opportunities. For a reason not to maximize, suppose maximizing dictates that the company liquidate itself? Unlikely to be accomplished.
8. Which would you prefer: (a) an investment paying interest of 8% per year compounded annually; (b) an investment paying interest of 7.8% per year compounded semi-annually; (c) an investment paying interest of 7.75% per year compounded quarterly?
The annual yields are: 1.08, 1.0795, and 1.0798--so pick the first
9. Suppose that the required rate of return on annuities is 6% per year. How much would it cost in a fair capital market to buy an annuity that would pay you \$100,000 per year for the next twenty years?
• \$1,146,992
10. Suppose you win a state lottery. You are told that the prize is \$20,000,000--\$1,000,000 a year will be paid to you for each of the next twenty years. If the appropriate rate of discount is 7% per year, what is the present value of this annuity? Suppose that the lottery has sold only 15,000,000 one-dollar lottery tickets for this prize. Has it made money on this transaction? How much money has it made (or lost)?
• Cost of the annuity is only \$10,594,000--so the lottery has made about \$4,406,000.