1. a. The 39.5% figure was evidently arrived at by dividing the 257 return by 6.5 years: 257/6.5 = 39.5. This calculation ignores compound interest.
   b. The appropriate future-value equation $100(1+R)^6.5 = $357 gives an annual return of R = 0.2163 (21.63%).

2. a. This calculation incorrectly assumes that payments are made annually with no payment of principal until the very end.
   b. The actual total interest is much less than the reported $300,000 in interest because payments are, in fact, monthly with a continual repayment of principal. You pay less than the reported $300,000 interest because you don't borrow $100,000 for all 30 years. Equation 2 shows the monthly payments to be $877.57. The total payments are 360($877.57) = $315,925.20, implying that the total interest is $315,925.20 $100,000 = $215,925.20.

3. All of his calculations involve total payments and ignore the time value of money. He might consider whether he could refinance for 22 1/2 years at 9% to 10%, choosing to the size of this new loan to give him the same monthly payments he has now, and see if this new loan covers his unpaid balance plus the $3500 to $4000 in closing costs. In fact, it would. His current monthly payments are $630.69. He could borrow $67,631.09 at 10% (the high end of the stated range) for 22 1/2 years, with monthly payments of $630.69. The unpaid balance on the current loan is $54,173.34. The $13,457.75 difference between the new loan and the unpaid balance would allow him to pay $3000 to $4000 in closing costs and pocket nearly $10,000.

4. The taxable bond has the lower price and higher before-tax rate of return; the tax-exempt bond has the higher price and lower before-tax return. If the demand for tax-exempts surges, their prices will rise, widening the price and interest-rate differentials.

5. If the Omaha bank has lots of farms loans and the Houston bank has lots of oil loans, this swap provides needed diversification.

6. a. Shareholders prefer stock repurchases, which are voluntary, to dividends which are an involuntarily taxable event.
   b. The acquisition of a firm with a lower price/earnings ratio will boost earnings per share; however the conservation-of-value principle tells us that there is no effect on the stock price unless that the aggregate cash flow is affected by the merger, or the firm buys the shares at a premium or discount from their market value. Thus the payment of a premium for the shares of a low price/earnings company, with no economies of scale, management changes, or other real economic benefits from the merger would increase earnings per share while reducing the stock price.

7. Their value to the investor (the present value) still goes up and down with interest rates, even if the securities cannot be sold. If you buy a fixed-income security and interest rates go up substantially, it will not be worth as much to you and, in particular, may be worth much less than what you paid for it.

8. The law of one price Pd = ePf implies that a system with stable exchange rates without trade imbalances requires nations to have equal (not necessarily zero) rates of inflation.

9. In the depths of the Great Depression, earnings were depressed severely; prices did not fall as far as earnings for these blue-chip stocks because investors expected earnings to recover eventually.

10. MacKinnon is using the constant-dividend-growth model, where R = D/P + g with g the growth rate of dividends and prices. Here, R = 7% (ignoring a risk premium) and D/P = 2%+, so that g = 4% to 5%. Because g is the growth rate of both dividends and prices, the answer is (a).

11. a. The expected value is ($590 million)(0.95) + ($590 million - $1.5 billion)(0.05) = $590 million - ($1.5 billion)(0.05) = $515 million.
   b. The expected value calculation in the preceding part is smaller than the correct expected value. Taking the time value of money into account reduces the present value of Hathaway's potential $1.5 billion liability, but does not affect the value of its $590 million asset. The fact that the liability might be less than $1.5 billion also reduces Hathaway's potential expense.
   c. It is generally not a good idea to bet against Warren Buffett because he is one of the most successful investors ever.

12. a. ($1.5 billion)(1 + R)^4 = ($1.5 billion + $590 million), implies R = 0.086
   b. It doesn't make sense to consider the interest on the bonds to be the cost. If there is no catastrophic quake, the Authority can invest the $1.5 billion it raises from this bond sale and earn interest that roughly offsets the interest it is paying on these bonds, reducing the cost to virtually zero. If there is a catastrophic quake, the cost is this same net interest plus the $1.5 billion principal, not just the net interest. expected value of the quake. Thus if the authority takes the deal with Buffett, it pays $590 million now with certainty. If the authority sells bonds, it pays $590 million in interest four years from now less the interest that it earns on $1.5 billion in the meantime, and there is an 0.05 probability that it will have to pay $1.5 billion. If the net interest is zero, then the Authority would be taking the same gamble that Buffett would taking: a probability P of having to pay $1.5 billion and a probability 1 - P of having to pay nothing.
   Alternatively, we can reason that since this is a zero-sum game (except for the net interest), the Authority's expected value must be equal to Buffett's expected value, with the sign reversed. The Authority must be extremely risk averse (or irrational) to pay $590 million to avoid this gamble that has an expected cost of $75 million.

13. a. The value of Tobin's q, the ratio of market value to replacement cost (or, roughly, book value) should be larger than one when the firm's return on equity is larger than the stockholders' required return, and less than one in the reverse case.
   b. Market values will be highest relative to book value when investors are most bullish and will be lowest when investors are most bearish. According to contrarian logic, the latter case (Category 2) is the best time to buy stocks, and consequently should offer the highest average returns. This was in the fact the case in this study.

14. As the graph below shows, a married put is a a synthetic call option, an implicit wager that stock prices will rise.

15. a. The two macroeconomic forces that drive the stock market are profits and interest rates. Low unemployment means increased output and profits; low inflation means low interest rates. In addition, because the tax code is not indexed for inflation, the real value of corporate taxes is lower during low inflation than during high inflation.
   b. Changes in stock prices are driven by unexpected economic developments. If the current economic situation is as good as it gets, then the only possible change is a deterioration.

16. The Japanese paid $610 million for the Exxon building. The plunge in the value of the dollar against the yen meant that the Japanese paid fewer yen, not fewer dollars. As an investment, presumably the Japanese should compare the dollar rental income from this building with the dollar price, regardless of the value of the yen before or at the time of the purchase. The value of the yen does affect how much yen can be purchased with this future dollar rental income; but what matters here is the future change in the value of the yen relative to the dollar, not the past change. (The quotation's poor logic is illustrated by the fact that the 16-month period used to compare the current and past exchange rate is completely arbitrary.)

17. Swapping fixed-rate debts for variable-rate debts would shorten the duration of their liabilities, exacerbating the mismatch between their long-duration assets and short-duration liabilities--borrowing short in order to lend long.

18. Such index arbitrage, selling stocks and buying stock index futures, would be profitable if the difference between the index futures price and the spot price of the index is less than the cost of carry--the Treasury-bill rate minus the dividend yield.

19. a. Higher interest rates are bearish for both stocks and bonds
   b. Higher interest rates are definitely bearish for bonds, but effect on stocks is uncertain since the bullish effects of the higher profits that would result from an increase in economic growth might be stronger than the bearish effects of higher interest rates.
   c. An increase in pay and benefits would squeeze profits; to the extent these translate into more rapid inflation, interest rates might rise too. So, bearish for stocks and bonds.
   d. Weak profits are bearish for stocks, with no effect on bonds.

20. Because T-bills is a safe investment, its beta coefficient is zero. Using the CAPM equation, mi - R0 = b(mM - R0), the expected return for a zero-beta investment is equal to the risk-free rate. Thus, the expected return on commodities in this model is 5%. If the correlation coefficient between stocks and commodities is -0.03, then so is the correlation coefficient between commodities and stocks. The correlation coefficient between T-bills and stocks or commodities is 0. Thus, the complete table is