Corporate Finance

MBAC 6060

Jaime Zender

Problem Set #2

1) If $50,000 is invested in a company that earns 7% per year on invested capital, and if the earnings are reinvested at the end of each year, how much is the investment worth at the end of 12 years?

2) What is the present value of (current balance in) a fund that earns 11% on its balance and pays out $50,000 at the end of each of the next years. At the end of five years, the balance of the fund is zero.

3) With a 12 percent annual interest rate (assume annual compounding for each case), calculate the present value of the following streams of payments:

a. $5,000 per year forever, with the first payment today.

b. $3,000 every other year forever, with the first payment 1 year from today.

c. $4,000 per year forever, with the first payment 2 years from today.

4) You see an ad reading "pay us $2,000 a year at the end of each year for 5 years then receive $4,000 at the end of each year in perpetuity." Ignoring taxes, what interest rates would make this investment worthwhile?

5) Compute the present value of $25,000 to be received in 20 years if interest of 15% per year is compounded (a) annually, (b) quarterly, (c) continuously. Why do these values differ?

6) A department store offers the following credit terms on a new appliance "slashed" to a price of $300: only $100 down, and the balance in 24 monthly installments of $12.50. What monthly rate of interest is the company implicitly charging its credit customers? What is the stated annual rate? The effective annual rate?


7) Compute the stock returns below for the years indicated.

End of Year Dividend Paid Stock Stock

Year Stock Price During Year Split Return

2002 $125 $3.00* 2 for 1 ______

2001 170 4.50 None ______

2000 270 4.25 None ______

1999 375 4.00 None ______

1998 250 3.50 None ______

*Assume that all of the dividends in 2002 were paid after the stock split.

8) Jean Lafitte wants to save money to meet two objectives. First, he would like to purchase a fishing camp in five years at an estimated cost of $40,000. Second, he would like to retire twenty years from now and have a retirement income of $60,000 per year at the beginning of year 21 for the next 30 years.

Jean currently has zero savings and can save only $10,000 per year at the end of each year for the next 10 years and expects to earn 7% on any future investments. What must his constant annual savings be from the end of years 11 through 20 to meet his objectives?

The following problems may appear as if you have not had the material you need to solve them. This is an illusion, look past the labels to the ideas and use the tools you have.

9) It is now January 1, 1990. Bayou Transit's 1989 dividend, which was paid yesterday, was $2 per share. Earnings and dividends are expected to grow at a rate of 12 percent per year for the next five years (beginning in 1990), followed by a three-year period of 10 percent growth, and thereafter to grow indefinitely at 6 percent. The required rate of return on the stock is 15 percent. The growth rates and discount rates are all in nominal terms. What is the market value of Bayou's stock today?

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10) With no additional investments, the Fried Brain Pharmaceutical (FBP) Company will generate perpetual after-tax earnings per share of $6.00 per year, beginning at the end of this year, and paid out in their entirety as dividends. FBP is about to receive a decision by the FDA on whether the firm can begin marketing a new line of mind altering over-the-counter drugs at the end of this year. The new product line would boost the perpetual earnings to $7.50 per share per year, but would require a once only marketing investment during the coming year that would consume this year’s expected dividend distribution. After foregoing this year’s dividend, however, shareholders would again receive a 100% distribution (dividends become $7.50 per share per year). The market's required rate of return on FBP's equity is 17 percent.

a. What will be the current value of a share of FBP if the FDA turns down the new product? (Hint: Ignore the labels. Share value derives from what you get from owning it.)

b. What will be the current value if the product is approved and FBP makes the investment?

c. What is the return on investment of this new product?

d. Should FBP undertake this investment? Why or why not?

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