Valuing Debt

Nếu dự kiến ​​tỷ lệ lãi suất thực tế là tiêu cực, sau đó các cá nhân sẽ bị cám dỗ đểtiết kiệm bằng cách mua và lưu trữ thực tế hàng hoá. Điều này đã khiến giá hàng hoá lêngiá chứng khoán xuống cho đến khi tỷ lệ thực sự là không còn tiêu cực.
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Valuing Debt CHAPTER 24 Valuing DebtAnswers to Practice Questions1. 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 C1 ... C5 C6 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 + r6)6 = 400 r6 = 0.265 = 26.5% 2204. 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 + r2)2 = (1 + r1) × (1 + f2) = (1.060) × (1.064) ⇒ r2 = 0.062 = 6.2% (1 + r3)3 = (1 + r2)2 × (1 + f3) = (1.062)2 × (1.071) ⇒ r3 = 0.065 = 6.5% (1 + r4)4 = (1 + r3)3 × (1 + f4) = (1.065)3 × (1.073) ⇒ r4 = 0.067 = 6.7% (1 + r5)5 = (1 + r4)4 × (1 + f5) = (1.067)4 × (1.082) ⇒ r5 = 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: r4 = 6.7% Invest this amount for five years, at the five-year spot rate: r 5 = 7.0%  Thus, the cash flows are: Borrow (100/1.067)4 = $77.151 million Today: Invest $77.151 million for 5 years at 7.0% Net cash flow: Zero In four years: Repay loan: ($77.151 × 1.0674) = $100 million dollars Net cash flow: -$100 million In five years: Receive amount of investment: ($77.151 × 1.0705) = $108.2 million Net cash flow: +$108.2 million Note that the cash flows from this strategy are exactly what one would expect from signing a contract today to invest $100 million in four years, for a time period of one year, at today’s forward rate for year 5 (8.2%). With $108.2 million available, the firm can cover the payment of $107 million at t = 5. 2217. We make use of the usual definition of the internal rate of return to calculate the yield to maturity for each bond. 5% Coupon Bond: 50 50 50 50 1050 NPV = −920.70 + + + + + =0 (1 + r) (1 + r) (1 + r ...