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Problem Set 5

1. Bobbi is the CEO of a large company. Her compensation is based on current

profitability. She is considering undertaking one of two investments available to

the company; (a) one that yields profits of $500 million in each of the next 5

years and none thereafter; (b) one that yields annual profits of $300 million over

20 years. She selects the first investment. How could this example illustrate the

agency problem?

2. You are a manager of a company that just spent $80,000 to purchase a piece of

equipment that is expected to function for six years. If you can borrow money at

7%, what is the PDV of the depreciation allowance under the following

circumstances?

a. You can expense the investment.

b. You depreciate using straight-line methods. That is, you depreciate the

investment in equal amounts each year over its expected life.

c. You depreciate over four years using accelerated straight-line methods.

3. Suppose that new machines cost $504 and the marginal benefit from new

machines is MB=246-6K, where K is the number of machines purchased. The

depreciation rate is 15%, and the dividend yield is 10%.

a. What amount of capital will you purchase? Why?

b. What amount of capital will you purchase if there were a 25% tax rate on

cash earnings minus labor costs?

4. (Chapter 21 # 1) Zach lives two periods. He earns $10,000 in the first period and

nothing in the second period. The rate of return is 10 percent and there is an

income tax (applied to labor and interest earnings) of 50 percent. Zach decides

to save half of his first period earnings, which he consumes (along with interest

earned) in the second period.

a. What is Zach’s income tax liability each period? What is the present

value of his lifetime tax payments?

b. Suppose that a consumption tax of 50 percent replaces the income tax in

the second period (after Zach has made his saving decision). How much

does he pay in taxes the second period? What is the present value of his

lifetime tax payments? Compare your answer to the present value of

2

lifetime tax payments in part (a), and explain the relevance of the

comparison to transitional problems in moving to a consumption tax.

5. (Chapter 21 # 4) In 2011, Derek Jeter hit a home run to become the 28th man to

exceed 3,000 hits. This presented an interesting set of tax questions for the fan

who caught the ball. In each case below, what are the tax consequences for the

fan who caught the ball?

a. The fan gives the ball back to the player who hit it (Jeter).

b. The fan keeps the ball and holds onto it until he dies.

c. The fan gives the ball to charity, and the charity sells the ball for a profit.

d. The fan sells the ball immediately.

e. The fan sells the ball after holding it for one year.

6. In “A Value-Added Tax for the United States: Part of the Solution,” Gale and

Harris suggest that a 10 percent federal VAT could be used to reduce the longterm

fiscal gap.

a. What do they suggest that states do with their retail sales taxes?

b. How can Canada’s experience with the implementation of a VAT in 1991

serve as a guide?

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