文档介绍：SOLUTIONS MANUAL
CHAPTER 2
Present Value and the Opportunity Cost of Capital
Answers to Practice Questions
1. Let INV = investment required at time t = 0 (., INV = -C0) and let x = rate of
return. Then x is defined as:
x = (C1 – INV)/INV
Therefore:
C1 = INV(1 + x)
It follows that:
NPV = C0 + {C1/(1 + r)}
NPV = -INV + {[INV(1 + x)]/(1 + r)}
NPV = INV {[(1 + x)/(1 + r)] – 1}
a. When x equals r, then:
[(1 + x)/(1 +r)] – 1 = 0
and NPV is zero.
b. When x exceeds r, then:
[(1 + x)/(1 + r)] – 1 > 0
and NPV is positive.
2. 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/) = 0
This is not a surprising result, because 5 percent is the opportunity cost of
capital, ., 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.
1
3. NPV = -$1,300,000 + ($1,500,000/) = +$63,636
Since the NPV is positive, you would construct the motel.
Alternatively, we pute r as follows:
r = ($1,500,000/$1,300,000) – 1 = = %
Since the rate of return is greater than the cost of capital, you would construct the
motel.
4.
Investment NPV Return
1) 18,000 18,000 −10,000
−10,000 + = $5,000 = = %
10,000
2) 9,000 9,000 − 5,000
− 5,000 + = $2,500 = = %
5,000
3) 5,700 5,700 − 5,000
− 5,000 + = −$250 = = %
5,000
4) 4,000 4,000 − 2,000
− 2,000 + = $1, = = %
2,000
a. Investment 1, because it has the highest NPV.
b. Investment 1, because it maximizes shareholders’ wealth.
5. a. NPV = (-50,000 + 30,000) + (30,000/) = $8,
b. NPV = (-50,000 + 30,000) + (30,000/) = $7,
Since, in each case, the NPV is higher than the