6-Discussion Questions - Solutions

# 6-Discussion Questions - Solutions - Lecture 6...

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Lecture 6: Intertemporal Choice Suggested questions and exercises (Pindyck and Rubinfeld Ch. 15). Questions: 6 Exercises: 2, 3, 4, 11 Additional Discussion Question. QUESTIONS 6. You have noticed that bond prices have been rising over the past few months. All else equal, what does this suggest has been happening to interest rates? Explain. This suggests that interest rates have been falling because bond prices and interest rates are inversely related. When the price of a bond (with a fixed coupon payment) rises, then the effective yield on the bond will fall. The only way people will be willing to hold the bond is if interest rates in general are also falling. If interest rates are lower than the effective yield on the bond for example, then people will prefer to hold the bond. When more people move into bonds, the price of the bond will rise and the effective yield will fall. Bond prices therefore adjust to bring the effective yield in line with interest rates. EXERCISES 2. You are offered the choice of two payment streams: (a) \$150 paid one year from now and \$150 paid two years from now; (b) \$130 paid one year from now and \$160 paid two years from now. Which payment stream would you prefer if the interest rate is 5 percent? If it is 15 percent? To compare two income streams, we calculate the present discounted value of each and choose the stream with the highest present discounted value. We use the formula PDV = FV (1 + R ) - t for each cash flow. See Exercise (2) above. Stream (a) has two payments: PDV a 1 (1 + R ) -1 + 2 (1 + R ) -2 PDV a = (\$150)(1.05) -1 + (\$150)(1.05) -2 , or PDV a = \$142.86 + 136.05 = \$278.91. Stream (b) has two payments: PDV b = (\$130)(1.05) -1 + (\$160)(1.05) -2 , or PDV b = \$123.81 + \$145.12 = \$268.93. At an interest rate of 5 percent, you should select (b).

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If the interest rate is 15 percent, the present discounted values of the two income streams would be: PDV a = (\$150)(1.15) -1 + (\$150)(1.15) -2 , or PDV a = \$130.43 + \$113.42 = \$243.85, and PDV b = (\$130)(1.15) -1 + (\$160)(1.15) -2 , or PDV b = \$113.04 + \$120.98 = \$234.02. You should still select (b). 3. Suppose the interest rate is 10 percent. What is the value of a coupon bond that pays \$80 per year for each of the next five years and then makes a principal repayment of \$1,000 in the sixth year? Repeat for an interest rate of 15 percent.
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6-Discussion Questions - Solutions - Lecture 6...

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