1. Because prices increased by a factor of 419/27, so would Pudge's salary: (419/27)$500 = $7,759.

2. a. A stronger economy could increase the rate of inflation; a higher inflation rate raises nominal interest rates, reducing bond prices. (The news story noted that short-term yields had risen more than long-term yields.)
   b. The Dow Jones Industrial index rose even while bond prices were falling (and interest rates rising), because of good news about the economy.
   c. Stock prices fell because bond prices were falling (and interest rates rising), and there was no good news about the economy.

3. Small changes in interest rates do not affect the future value and realized rate of return for a bond with a duration equal to the investor's horizon. The duration of a zero-coupon bond is equal to the bond's maturity. Therefore, the 20-year zero does the best job of guaranteeing a fixed future value 20 years from now. (However, its yield is relatively low because the term structure is downward sloping.)

4. According to the intrinsic value model, growth stocks are actually very sensitive to changes in required yields. As discussed in the text, growth stocks have long durations and high capital risk.
   One way to make sense of the quotation is that growth stocks are not good substitutes for the bonds whose interest rates have been observed rising. Perhaps only widows and orphans buy bonds and only riverboat gamblers buy growth stocks. If so, then bond rates could rise with little or no effect on the prices and yields of growth stocks. This is not a persuasive argument.

5. Long-term bonds have the most capital risk; short-term bonds the next most; and money-market securities the least. For long-term bonds to also have the highest yields to maturity, the term structure must be upward sloping.

6. Treasury bills aren't the only, or even the most logical, alternative to share repurchases. If we consider these share repurchases to be an investment (which "earns" dividends that would otherwise have to be paid on these repurchased shares), long-term bonds (not Treasury bills) are a more comparable alternative--and in October of 1992, interest rates on long-term Treasury bonds were 8 percent. Another alternative for the company is to retain these funds and expand by investing in new plant and equipment (which is often an attractive option when interest rates are low).

7. Debt can serve as a tax shield. A restructuring in which a company uses borrowed money to finance share repurchases can reduce a company's taxes and increase its after-tax cash flow to bond and stockholders.

8. The expected return is the anticipated long-run average return; even if the probabilities that underlie these expected returns are accurate, there is no assurance that the investment with the highest expected value will turn out to have highest actual return in the short run. Someone might invest in a particular stock with a sufficiently low beta even if another stock with the same standard deviation has a higher expected return.

9. Treasury bills are short-term bonds that mature in less than one year. Investors who buy Treasury bills are implicitly betting on an increase in interest rates so that they can roll over their investment at higher interest rates. (The article told how there had been aggressive buying the previous day at the U.S. Treasury's auction of 3-to-5 year Treasury notes, suggesting that, while the term structure was upward sloping at the time, with 1-year Treasury bonds paying 7.4%, 4-year Treasury bonds paying 7.8%, and 10-year Treasury bonds yielding 8.60%, these buyers expected interest rates to decline over the next three-to-five years. The headline writer mistakenly called these note buyers "T-bill investors.")

10. Rents will probably not be constant during the investment. The building may also appreciate in value. In addition, even if rents are constant and the value of building does not change, the investor will get more than a 10% return because the monthly mortgage payments include principal (the buildup of equity) as well as interest. At the end of 25 years, the investor will own a $444,076 building with no debt, in addition to the 10% annual income from the rent. (This is a substantial amount: $80,000(1 + R)^25 = $444,076 implies R = .071.)
   A reasonable way to calculate the implicit rate of return is to equate the present value of the cash flow to the initial $80,000 investment:

   Another (approximate) way to look at this situation is as follows. Neglecting the mortgage, the annual rate of return on the building is ($56,000 - $14,280)/$444,076 = .094. The (initial) leverage is $444,076/$80,000 = 5.55, suggesting a rate of return of .08 + 5.55(.094 - .08) = .158. The actual 12.95% return is somewhat lower than this because the leverage diminishes over time as the mortgage balance is reduced.

11. a. A company could buy oil futures, because the value of these futures increases as the price of oil increases.
   b. Even if the delivery date doesn't coincide with the company's need for oil, an increase in the price of oil will generally raise the price of oil and oil futures on nearby dates.
   c. The price of crude-oil futures should be higher than the price of crude oil because the cost of carry (storage expenses and interest rates) is positive.
   d. Neglecting commissions and other expenses, futures are a zero-sum game--gains by some require losses by others. Those who buy futures to hedge their positions cannot reasonably expect to make profits consistently while futures sellers have consistent losses. Taking commissions and other expenses into account, the average profit of buyers and sellers is negative. Unless the company consistently beats the market, the purchase of futures contracts will increase its average costs. Such hedges do reduce risk by effectively locking in the price of oil, insulating this cost from fluctuations--up or down--in the market price.

12. A bond's duration measures (approximately) the percentage change in the bond's market value when its yield to maturity changes by one percentage point. The cited estimate by the Vanguard Group indicates that this portfolio of 20-year bonds has a duration of about 9 years. For their duration to be less than 20 years, the 20-year bonds must have coupons. 13. She wants her investment in the 6-month and 2-year zeros to have the same duration as the 1-year zero, so that these two strategies will be affected equally by equal changes in interest rates. The 1-year zeros have a duration of 1 year. The duration of the other portfolio is a(0.5) + (1 - a)2.0. Equating the two durations,

14. If the market price P is above 95, the investor will make a profit of 5 + P - 98.5. If the market price is at or below 95, the investor will make a profit of 5 + 95 - 98.5 = 1.5. This graph is unrealistic because the market price will not fall below 95. (The horizontal axis of the graph could instead use the market value of an otherwise identical nonputable bond.)

15. Because the put gives the investor the right but not the obligation to sell the bond at a specified price, the putable bond should sell for more than otherwise identical nonputable bonds.
   a. An increase in the expected value of future interest rates implies an expectation (or reality) that bond prices will decline, making the put more valuable.
   b. An increase in uncertainty about the future level of interest rates increases the probability that the put will be exercised; therefore, the put is more valuable.

16. a. The yield on this zero can be determined by equating the present value of the $5,000 maturation value to the price:

   b. If RC is the before-tax return on a fully taxable corporate security, then the after-tax return is

RC – .123RC – .31(RC – .123RC) = (1 – .31)(1 – .123)RC

   The taxable equivalent yield is that value of RC that gives an after-tax return that is equal to RM, the return on a tax-exempt municipal security:

   For the mini-munis considered here, the taxable equivalent yield is

17. a. They used the usual measure of risk: the standard deviation of the annual returns.
   b. We need to look forward, not backward, and consequently should measure risk by uncertainty about future returns, not variability of past returns. Similarly, we should measure expected return by anticipated future returns, not the average of past returns.

18. a. The real rate of return r is (approximately) equal to the nominal rate of return R minus the rate of inflation p: r = R - p. Using the nominal and real returns given in the quotation, the inflation rates in these three countries were as follows:

United States: p = R – r = 6.55% – 3.5% = 3.05%
United Kingdom: p = R – r = 9.29% – 3.5% = 5.79%
Germany: p = R – r = 8.05% – 3.25% = 4.80%

  b. Purchasing power parity predicts that the value of dollar will increase by 2.74 percent annually relative to the pound, because this is the amount by which the U.K. annual rate of inflation exceeds the U.S. annual rate of inflation:

%De = %DPd – %DPf = 3.05% – 5.79% = –2.74%

   where Pd is the U.S. rate of inflation, Pf is the U.K. rate of inflation, and a decrease in e, the dollar price of pounds, represents an appreciation of the dollar.
   c. If this prediction that the value of the dollar will increase relative to the pound by 2.74% annually is correct, then the rate of return in dollars on a pound-denominated investment will be 6.55%, the same as a dollar denominated investment.

Rf + %De = 9.29% + (–2.74%) = 6.55%

  (This equality holds whenever the real rates of return are equal and purchasing power parity holds.)