1. Analysts had expected earnings to be even higher, 51 cents a share (a 76% increase), instead of 44 cents a share (a 63% increase). [Ralph T. King, Jr., "Adobe Posts 63% Increase in Earnings, But Figure Trails Analysts' Estimates," The Wall Street Journal, September 19, 1995.]
2. As the Journal article goes on to explain: "In other words, because interest is compounded and paid only at maturity, investors don't need to worry about where to reinvest money twice a year." The future value of the investment and the realized rate of return are consequently not affected by fluctuations in interest rates during the life of the bond.
3. There is no good reason to assume that earnings will stay constant, particularly since one of the primary explanations of differences in p/e ratios is anticipated differences in growth rates. This is like analyzing differences in Treasury and junk bond yields and saying "assuming that there are no defaults."
4. a. Interest rates will never be negative as long as holding cash gives a nonnegative return.
b. There will be substantial capital gains on 30-year Treasuries if interest rates decline, about a 13 percent capital gain if the yield drops by a percentage point.
c. Even if interest rates don't decline, investors in 30-year Treasuries will make much more than four-fifths of a percentage point if they hold the bond for more than one year.
5. a. They should have bought futures (as they did). They would lose money on their contracts to deliver fuel at fixed prices if the price of fuel increases. By buying futures, they make money on these futures if oil prices increase, in theory offsetting the losses on their delivery contracts.
b. To the extent crude oil and refined gasoline prices are related, an increase in the price of oil should be accompanied by an increase in the price of gasoline.
c. The difference between the futures price and the current spot price should reflect the cost of carry, which for oil is lost interest and storage costs. Thus people wanting oil in the future would normally pay more for a futures contract than for current delivery, in order to earn interest and avoid storage expenses. Similarly, a company with a large oil inventory could sell at the current spot price and buy futures to replenish its inventory in the future, in the meantime, earning interest and avoiding storage expenses
d. MG would make a profit on its futures if the spot price on the delivery date is above the futures price they paid for the contract. Because the futures price were backward (below the spot price at the time of purchase), MG would have made profits on its futures if spot prices had been constant.
e. In the long run (assuming they hedged correctly), MG should have made $1 billion in profits on its contracts to deliver fuel at what are now above-market prices. (If spot prices rise before the contracts come due, MG should make $1 billion on a continuing policy of rolling over oil futures. However, there were questions of whether the parties who had agreed to buy fuel from MG¾at fixed prices would have honored these contracts.)
6. The prime rate is higher than the Treasury-bill rate because private businesses have more default risk than does the U.S. Treasury. (Also, the interest on Treasury-bills is exempt from state-and-local income taxes.) Swapping a loan indexed to the prime rate for a loan indexed to the Treasury-bill rate is an implicit wager that the spread between the prime rate and the Treasury-bill rate will widen, so that this firm's interest payments will be lower than if the firm's loan were indexed to the prime rate.
7. Some of the buyers are institutions, not individuals, and may well be around 100-years from now. Either way, they can sell the bonds before maturity and, in any case, the present value of the principal 100 years from now is only a small part of the value of the bond. Of more concern is the default risk on A3/BBB+ bonds and the capital risk on such a long-duration bond.
8. The individual safety ratings are analogous to the standard deviations of individual stocks. In a well-diversified portfolio (and 15 stocks may be sufficient), the idiosyncratic risk will be diversified away, leaving only systematic risk, which is gauged by beta coefficients.
9. Stocks do pay dividends, which grow with the firm. Even if there were no uncertainty about a stock's return, it would still be priced to yield the same as other risk-free investments and people would still invest, just as they do with Treasury bills, savings accounts, and other risk-free investments.
10. a. The earnings yield is just the inverse of the P/E ratio. Fundamental analysis says that the price that investors are willing to pay for a company with a certain level of earnings per share should depend on (among other things) their required rate of return, which is strongly influenced by interest rates.
b. But other things matter, too, such as the anticipated growth rate of earnings. The constant-dividend-growth model says that the earnings yield will equal shareholders required rate of return if the firm pays no dividends or if its profit rate is equal to the shareholders' required rate of return. If the profit rate exceeds the shareholders' required rate of return, the P/E will be relatively high and the E/P relatively low--less than the shareholders' required rate of return. The E/P will be larger than the shareholders' required rate of return if the firm's profit rate is lower than the shareholders' required rate of return.
c. I would expect the earnings yield, on average, to equal the shareholders' required return, which should have a risk premium and consequently be above the 30-year Treasury bond yield.
d. The largest gap in this graph between these two time series was in 1987, before the October crash.
11. If the retired hold mostly short-term securities, a halving of interest rates cuts their interest income in half. When these investors roll over their short-term securities, the decline in income resulting from lower interest rates outweighs any temporary capital gains.
12. a. This German government agency has a dollar-denominated bond liability and mark-denominated assets (its tax revenue). If the mark appreciates relative to the dollar, its assets will appreciate relative to its liabilities, making the government agency better off financially. Alternatively, we can reason that the government agency will be able to spend fewer marks to pay the dollar-denominated coupons and principal on these bonds if the value of the mark appreciates relative to the dollar.
b. To hedge its exposure to exchange-rate risk on these bonds, the government agency should swap dollar liabilities for mark liabilities. Here is a figure depicting the appropriate transaction:
13. A dividend-reinvestment plan forces shareholders to pay taxes on their dividends; a share repurchase does not. A company with 100 million shares outstanding, valued at $5 apiece, has an aggregate market value of $500 million. A $1 dividend will reduce the firm's assets by $100 million, to $400 million, implying a per-share value of $400,000,000/100,000,000 = $4. In place of a share worth $5, stockholders have a share worth $4 plus $1 in dividends, on which they must pay taxes. If stockholder 1 participates in the dividend-reinvestment plan, the company's assets will increase by $50 million (to $450 million), and the number of shares outstanding will increase by $50,000,000/$4 = 12,500,000, to 112,500,000 implying a per share value of $450,000,000/112,500,000 = $4. These are all nonevents, except for the taxes. Stockholder 1 will own a slightly larger share (62,500,000/112,500,000 = 0.556) of a somewhat smaller company. Stockholder 2 will have $50 million in cash and own a slightly smaller share of a somewhat smaller company.
If, instead, the firm uses $50 million to repurchase 10 million shares, it will have $450 million in assets (the same as in case a) and each share will be worth $450,000,000/9,000,000 = $5, a nonevent. Stockholder 1 does not sell shares and now owns a slightly larger share (50,000,000/90,000,000 = 0.556) of a somewhat smaller company. Stockholder 2 will have $50 million in cash and own a slightly smaller share of a somewhat smaller company.
14. High-yield bonds are junk bonds.
a. Treasuries and high-yields are both bonds with promised future coupons and principal; the present values (and market prices) decline when market interest rates go up and rise when market interest rates fall.
b. Stocks, too, have a future cash flow (dividends), with a present value that is inversely related to market interest rates.
c. The correlation between Treasuries and stocks is far from perfect because, unlike Treasuries with their fixed coupons, the future cash flow from stocks is uncertain and fluctuates with the strength of the economy.
d. Evidently, high-yields are more closely correlated with stocks than with Treasuries because their returns are sensitive to the strength of the economy in the same direction as stocks. This makes sense, since a strong economy will not only increase stock dividends, but also make it more likely that junk-bond issuers will be able to pay their promised coupons and principal.
15. a. Looking at the means and standard deviations, we see that Asset 2 is high-yield bonds.
b. Evidently, due to the relatively low correlation coefficients among these three assets, no point on the Markowitz frontier is 100% invested in high-yield bonds. Except for the extremes (with 100 percent in either Treasuries or stocks,) no point is 0% in high-yields either.
c. A risk-neutral investor maximizes expected return and would buy nothing but stocks.
d. We need to draw a straight line that intersects the vertical axis at 4% and is tangent to the Markowitz frontier.
16. The next-year dividend will be D = $4 instead of $2 and the required rate of return R is still 12 percent. Instead of plowing $2 per share back into the company, the firm must raise $2 a share by selling an additional 0.04 shares of stock (per share) at $50: 0.04($50) = $2. Thus while the company's aggregate earnings and dividends continue to grow by 8 percent a year, the number of shares grows by 4 percent a year, implying that dividends per share grow by 4 percent a year. Therefore, the price per share is not affected:
17. The retiree will be able to spend the annual principal from the maturing bonds in addition to the interest from the portfolio: "That combination of interest and principal produces much more [annual cash flow than a portfolio of 20-year bonds], where you still have all the principal left when you die." However, as Mr. MacKinnon goes on to explain, "The main risk of this approach is that you outlive the principal." If you live more than 20 years, your portfolio will be exhausted and provide no additional income.
18. a. If you buy 20 Treasury zeros, you want the future value of each (the annual cash flow) to be a constant amount F. The respective prices are
These prices must add up to the $500,000 that you have to invest:
Because this is a constant cash flow, we can use this equation from the textbook:
Solving this equation for the constant annual cash flow F,
b. What if you instead buy a 20-year Treasury bond with 10 percent annual coupons? The term structure in this exercise is flat with all Treasury bonds priced to yield 10 percent. If its yield to maturity is 10 percent, the price of a bond with 10 percent coupons will be equal to its maturation value. Thus $500,000 buys a 20-year Treasury bond with (10 percent)($500,000) = $50,000 annual coupons and a $500,000 maturation value.
Therefore, MacKinnon's strategy provides an additional $58,729.81 † $50,000 = $8,729.81 in annual cash flow in comparison with buying a 20-year $500,000 Treasury bond with 10 percent annual coupons. The additional $8,729.81 represents a 17.5 percent increase in the annual cash flow:
Of course, with the 20-year coupon bond you still have the $500,000 maturation value left at the end of 20 years. (It would not matter if, instead of zeros, you implemented MacKinnon's strategy with coupon bonds with maturities of 1 year, 2 years, and so on up to 20 years. The constant annual cash flow--coupons plus the principal on maturing bonds--would still have to be $59,729.81 for their total present value to be $500,000.)
19. (Other combination strategies will work too.) Sell one call and sell one put with the same exercise price:
Buy one call option and sell one call option with a higher exercise price:
20. The conservation-of-value principle suggests that selling shares for their market value is a nonevent. With the infusion of $40(2,000) = $80,000 in cash, the total market value of the company should increase from $400,000 to $480,000--implying a per-share market value of $480,000/12,000 = $40 as before.
If, however, they use the proceeds to make a crummy investment, the market price will decline. The value of Tobin's q for existing assets is q = 4,000,000/500,000 = 0.8. If the $80,000 in new cash is invested similarly and valued by the market similarly, then its market value will be 0.8($80,000) = $64,000--implying a per share price of $464,000/12,000 = $38.67, as in the exercise. Thus it is not the sale of additional shares of stock that depresses the stock's price; it the investment of this money in insufficiently profitable ventures.
