CHAPTER 2 Present Values, The Objectives of the Firm, and Corporate Governance

Answers to Practice Questions 1. The face value of the treasury security is $1,000. If this security earns 5%, then in one year we will receive $1,050. Thus: NPV = C0 + [C1/(1 + r)] = −$1000 + ($1050/1.05) = 0 This is not a surprising result because 5 percent is the opportunity cost of capital, i.e., 5 percent is the return available in the capital market. If any investment earns a rate of return equal to the opportunity cost of capital, the NPV of that investment is zero. NPV = −$1,300,000 + ($1,500,000/1.10) = +$63,636 Since the NPV is positive, you would construct the motel. Alternatively, we can compute r as follows: r = ($1,500,000/$1,300,000) – 1 = 0.1539 = 15.39% Since the rate of return is greater than the cost of capital, you would construct the motel. 3. Investment (1) NPV Return

2.

− 10,000 +

18,000 = $5,000 1.20

18,000 − 10,000 = 0.80 = 80.0% 10,000 9,000 − 5,000 = 0.80 = 80.0% 5,000 5,700 − 5,000 = 0.14 = 14.0% 5,000
4,000 − 2,000 = 1.00 = 100.0% 2,000

(2)

− 5,000 +

9,000 = $2,500 1.20 5,700 = −$250 1.20
4,000 = $1,333.33 1.20

(3)

− 5,000 +

(4)

− 2,000 +

a. b.

Investment 1, because it has the highest NPV. Investment 1, because it maximizes shareholders’ wealth.

1

4.

a. b.

NPV = (−$50,000 + $20,000) + ($38,000/1.05) = $6,190.48 NPV = (−$50,000 + $20,000) + ($38,000/1.10) = $4,545.45

In Part (a), the NPV is higher than the NPV of the office building ($5,000); therefore, we should accept E. Coli’s offer. In Part (b), the NPV is less than the NPV of the office building, so we should not accept the offer. You can also think of this in another way. The true opportunity cost of the land is what you could sell it for, i.e., $56,190 (or $54,545). At $56,190, the office building has a negative NPV. At $54,545, the office