2. The implicit interest rate R on the first loan is determined by

Trial and error gives R = 0.1050 (10.50%). The implicit interest rate R on the second loan is determined by

The trial-and-error solution is R = 0.1144 (11.44%). Thus the implicit interest rate on the second loan is nearly a full percentage point higher than the rate on the first loan.

3. Record profits just means that profits are growing, not that they are necessarily growing very fast; similarly, with the increased dividend for the seventh year in a row. The payment of a stock dividend has nothing to do with the firm’s profitability. This simply doubles the number of shares and halves the value of each share.

4. The Fed should have bought long-term bonds (pushing bond prices up and yields down) and sold short-term bonds (pushing prices down and yields up). The Expectations Hypothesis implies that long-term rates won’t fall below short-term rates unless investors believe that interest rates are going to fall in the future. Thus, to maintain this twisted term structure, the Fed had to convince investors of an implausible scenario in which interest rates stay high while investors continue to believe that they will decline.

5. “Firms that commanded [high] price-to-earnings ratios could purchase firms with [lower] P/Es because in an equity exchange the buyer's EPS increased. But the reverse transaction was anathema in the boardroom because it lowered earnings per share. This was the height of naiveté, since the combined firms were [worth exactly the same no matter who did the acquiring].”

6. There is capital risk for the bank that holds a fixed-rate mortgage, but there is also capital risk for the mortgage borrower: a decline in interest rates is advantageous for the holder of a fixed-rate mortgage, disadvantageous for the borrower. Adjustable-rate mortgages have very little capital risk, but there is still income risk for both sides: an increase in interest rates benefits the lender and hurts the borrower. Fixed-rate and adjustable-rate mortgages are each risky, for both the borrower and lender.

It would be more accurate to say that a fixed-rate mortgage is implicitly a wager on rising interest rates by the borrower and a bet on falling interest rates by the lender. An adjustable-rate mortgage is a bet on declining interest rates by the borrower, a bet on rising interest rates by the lender.

7. Since the firm’s return on assets (and equity) is equal to the shareholders’ required rate of return, each firm’s market value is equal to its assets, 100 for Firm 1 and 200 for Firm 2. The conservation-of-value principle tells us that the total value of the merged firms is equal to the sum of the pre-merger values: 100 + 200 = 300.

8. Using the constant-dividend-growth model, we have

where P is the stock price, D is the next dividend, w is the tax-rate on dividends, and g is the growth rate of dividends. A change in w from 0.40 to 0.15 will change P from

a percentage increase of (0.85 - 0.60)/0.60 = 0.4166 (41.66%)

9.

a. Government securities are free of default risk.

b. The value of corporate stock depends on the interest rate on a government bond, because bonds are an alternative asset for investors.

c. You might use a bond with a duration comparable to that on stocks because they then have comparable amounts of capital risk.

d. Treasury bills have a year or less until maturity and consequently have a duration of less than a year. The cash flow from corporate stocks is much more distant, and they consequently have a duration closer to that on ten-year Treasury bonds. (McKinsey says “the ten-year rate approximates the duration of the stock market index portfolio—for example, the S&P 500.” This is actually only true if it is a ten-year zero, since stock have a duration of around 10 years.

10.This sounds like regression towards the mean: those teams that won more than 100 games were more likely to have been lucky than unlucky that year (with regard to injuries, close calls, etc.)