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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
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
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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