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Business Administration 130
Problem Set # 1 Answers
http://www.j-bradford-delong.net/Intro_Finance/BA130PS1A.html
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?
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?
- 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?
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.
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