## Problem Set # 1

1. Explain why a dollar today is worth more than a dollar 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.

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.

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?

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?

6. What is the Present Value of \$100 to be received in:
• a. three years, at a discount rate of 7% per year
• b. ten years, at a discount rate of 9% per year
• c. seventy two years, at a discount rate of 1% per year
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?

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?

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?

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)?