304L Homework 5 Solutions

# 304L Homework 5 Solutions -...

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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 ૚૙ ൌ ૚૞ ሺ૚ ൅ ࢘ሻ ૚૙ሺ૚ ൅ ࢘ሻ ൌ૚૞ ሺ૚ ൅ ࢘ሻ ൌ૚ .૞ ૚൅࢘ൌ૚ .૞ ࢘ൌ૚ .૞ .૛૞ െ૚ ൌ૙ .૚૙૟ૠ 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

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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
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## This note was uploaded on 12/17/2010 for the course ECO 33530 taught by Professor Sadler during the Spring '10 term at University of Texas at Austin.

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304L Homework 5 Solutions -...

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