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# CH24 - CHAPTER 24 Valuing Debt Answers to Practice...

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CHAPTER 24 Valuing Debt Answers to Practice Questions 1. Some reasons Fisher’s theory might not be true are: a. Taxes are levied on nominal interest. Therefore, if expected inflation is high, part of the tax is actually on the real principal. b. Inflation may be associated with the level of real economic activity, which, in turn, may affect real interest rates. c. It ignores uncertainty about inflation. 2. If expected real interest rates are negative, then individuals will be tempted to save by buying and storing real goods. This forces the prices of goods up and the prices of securities down until real rates are no longer negative. However, goods are costly to store and expensive to resell if you do not want them. Some goods are impossible to store, e.g., haircuts and appendectomies. Prices of these goods may be expected to rise faster than the interest rate. Note also that it is difficult for a country on its own to maintain a very low real rate without imposing exchange controls on its citizens. 3. The key here is to find a combination of these two bonds (i.e., a portfolio of bonds) that has a cash flow only at t = 6. Then, knowing the price of the portfolio and the cash flow at t = 6, we can calculate the 6-year spot rate. We begin by specifying the cash flows of each bond and using these and their yields to calculate their current prices: Investment Yield C 1 . . . C 5 C 6 Price 6% bond 12% 60 . . . 60 1,060 \$753.32 10% bond 8% 100 . . . 100 1,100 \$1,092.46 From the cash flows in years one through five, it is clear that the required portfolio consists of one 6% bond minus 60% of one 10% bond, i.e., we should buy the equivalent of one 6% bond and sell the equivalent of 60% of one 10% bond. This portfolio costs: \$753.32 – (0.6 × \$1,092.46) = \$97.84 The cash flow for this portfolio is equal to zero for years one through five and, for year 6, is equal to: \$1,060 – (0.6 × 1,100) = \$400 Thus: \$97.84 × (1 + r 6 ) 6 = 400 r 6 = 0.265 = 26.5% 220

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4. Downward sloping. This is because high coupon bonds provide a greater proportion of their cash flows in the early years. In essence, a high coupon bond is a ‘shorter’ bond than a low coupon bond of the same maturity. 5. Using the general relationship between spot and forward rates, we have: (1 + r 2 ) 2 = (1 + r 1 ) × (1 + f 2 ) = (1.060) × (1.064) r 2 = 0.062 = 6.2% (1 + r 3 ) 3 = (1 + r 2 ) 2 × (1 + f 3 ) = (1.062) 2 × (1.071) r 3 = 0.065 = 6.5% (1 + r 4 ) 4 = (1 + r 3 ) 3 × (1 + f 4 ) = (1.065) 3 × (1.073) r 4 = 0.067 = 6.7% (1 + r 5 ) 5 = (1 + r 4 ) 4 × (1 + f 5 ) = (1.067) 4 × (1.082) r 5 = 0.070 = 7.0% If the expectations hypothesis holds, we can infer—from the fact that the forward rates are increasing—that spot interest rates are expected to increase in the future. 6. In order to lock in the currently existing forward rate for year five (f 5 ), the firm should: Borrow the present value of \$100 million. Because this money will be received in four years, this borrowing is at the four-year spot rate: r 4 = 6.7% Invest this amount for five years, at the five-year spot rate: r 5 = 7.0% Thus, the cash flows are: Today: Borrow (100/1.067) 4 = \$77.151 million Invest \$77.151 million for 5 years at 7.0% Net cash flow: Zero In four years: Repay loan: (\$77.151 × 1.067 4 ) = \$100 million dollars Net cash flow: -\$100 million In five years: Receive amount of investment: (\$77.151 × 1.070 5 ) = \$108.2 million Net cash flow: +\$108.2 million
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