Economics 304L: Principles of Macroeconomics
Spring 2010
Sadler
Homework 5
Solutions
The following problems refer to the “Problems and Applications” section at the end of Chapter 14 of
Mankiw (pp. 307
‐
308).
1.
No. 2
a.
The present value of $15 million to be received in four years at an interest rate of 11% is $15
million/(1.11)
4
= $9.88 million. Because the present value of the payoff is less than the cost, the
project should not be undertaken.
The present value of $15 million to be received in four years at an interest rate of 10% is $15
million/(1.10)
4
= $10.25 million. Because the present value of the payoff is greater than the cost,
the project should be undertaken.
The present value of $15 million to be received in four years at an interest rate of 9% is $15
million/(1.09)
4
= $10.63 million. Because the present value of the payoff is greater than the cost,
the project should be undertaken.
The present value of $15 million to be received in four years at an interest rate of 8% is $15
million/(1.08)
4
= $11.03 million. Because the present value of the payoff is greater than the cost,
the project should be undertaken.
b.
The exact cutoff for the interest rate between profitability and nonprofitability is the interest
rate that will equate the present value of receiving $15 million in four years with the current
cost of the project ($10 million), or
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.
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Therefore, an interest rate of 10.67% would be the cutoff between profitability and
nonprofitability. At an interest rate higher than this, the present value of the future “payoff” is
less than the cost of the project, and therefore it should not be undertaken. At an interest rate
lower than this, the present value of the future payoff is more than the cost of the project, so
the project should be undertaken.
2.
No. 3
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Economics 304L: Principles of Macroeconomics
Spring 2010
Sadler
The value of the stock is equal to the present value of its dividends and its final sale price. The
dividend (“
Div”)
is $5 per year and the final sale price (
P,
which in reality would be unknown) is given
as $120. Let the interest rate be
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 Spring '10
 Sadler
 Interest Rates

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