Econ 156
Fall 2001

Second Test Answers

1. [David Leonhardt, “The Most Bang for Your MBA Buck,” Business Week, October 21, 1996, 154–155.] A payback period calculation ignores the time value of money and it ignores the extra income after the investment is paid back.

2. The upward sloping term structure indicates that investors expect interest rates to increase over time. If so, rolling over short-term debt may be as expensive (or more so) than issuing long-term debt.

3. U.S. stocks will still be held if they are sufficiently uncorrelated with the other assets. In practice, he estimates that the correlations are 0.45 between U.S. stocks and U.S. bonds, 0.30 between U.S. stocks and absolute return assets, and 0.35 between U.S. bonds and absolute return assets.

4. Using the given data
a. q = (stock price)/(book value per share) = $66/$7.83 = 8.4
b. The CAPM equation gives (Ei - R0) = b(EM - R0) = 1.83(4) = 7.32

5. The fundamental value model implies that the shareholder’s actual return, dividend yield plus capital gain, will equal their required return, here 10%.
a. Since the dividend yield is 0 for the first 10 years, the annual price increase will be 10%.
b. Thereafter, the stock price will be determined by D/(R - g) and will increase at the rate g, 5% a year.

6. The futures price should equal the spot price plus the cost of carry: F = P(1 + R - d). Since Microsoft stock doesn’t pay dividends, a one-year futures contract should cost P(1 + R - d) = $66(1 + 0.0188 - 0) = $67.24.

7. Selling a future for F > 67.24, buying a call, and selling a put would cost $12.00 - $9.80 = $2.20 and make a profit of F - $65 a year from now, a riskless return of (F - $65)/($2.20).

At F = $67.24, the profit is ($67.24 - $65)/($2.20) = 0.0182, which is 1.88% with a little rounding error.
(If stock transactions were considered, buying stock, selling call, and buying a put would cost $66.00 - $12.00 + $9.80 = $63.80 and be worth $65 a year from now, a riskless return of ($65 - $63.80)/$63.80 = 1.88%.)

8. You want the asset with the highest before-tax return in your retirement account and the asset with the highest after-tax return in your regular investment account. The after-tax returns are (1 - 0.5)8% = 4% for taxable bonds, 6% for tax-free bonds, and (1 - 0.3)10% = 7% for stocks. You should put stocks in both accounts.

9. If n = 10 years and r = 5%, the advisor’s value is X = R($1,000,000) + $1,000,000/n = 0.05($1,000,000) + $1,000,000/10 = $150,000.

a. The fund doesn’t earn R$1,000,000 each year, since the fund balance is declining each year. The value of X is too large and the fund runs out of money before n years. (In 8 years if n = 10 years and r = 5%.)

b. The correct value of X is determined by the fact that the present value of the n payments of X should equal $1,000,000. So solve this equation for X:

Using the mathematical simplification

we have

If n = 10 years and r = 5%, the correct value of X is $129,505.

10. The author calculates the yield by dividing the annual interest by the market price: $80/$870 = .092 (9.2%). This 9.2% figure is the not-very-informative “current yield,” which is not the same as the yield to maturity (or interest rate) unless the bond is selling for its maturation value. In the example here, the investor will get a capital gain at maturity in addition to the annual coupons. The yield to maturity y is given by the present value equation (assuming annual coupons),

For example, with m = 5 years until maturity, the yield to maturity is y = 11.57%.