Econ 156 Spring 2000 Midterm Answers

1. For a 10-year $100,000 monthly amortized loan at 10% + 7% = 17%, the monthly payments X are $1,737.98:

     The borrower only receives $100,000 - 7%($100,000) = $93,000 and $1,737.98 monthly payments on a $93,000 loan implies an effective annual interest rate of 19.03%:
     With a 5-year loan, the initial 7% fees become more burdensome, raising the effective interest rate (to 20.41%).

2. 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. Two much more important concerns are the default risk for a BBB+ bond and the interest-rate risk for a bond with such a long duration

3. 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 x = y.

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. A company that retains 20% of its earnings grow faster than one that retains all of its earnings if its return on equity is sufficiently larger. In the constant dividend-growth model, g = (1 - d)ROE, and 0.2ROE1 > 1.0ROE2 if ROE1 > 5.0ROE2.

6. New earnings per share are (E1 + E2)/(n1 + x). The change in earnings per share is

     This is nonnegative if and only if
     That is, the exchange ratio must be less than or equal to the ratio of Company 2's earnings per share to Company 1's earnings per share. In this problem, the exchange ratio must be less than or equal to 2.75/1.50 = 11/6 = 1.83. It is a bad idea because 1.83 shares of Company 1's stock is worth $44 and 1 share of Company 2's stock is only worth $36.

7. The stock exchanges are a secondary market. Unlike depositors withdrawing money from a bank, stockholders who sell their shares do not constitute a run on industries, because businesses are not obligated to redeem these shares. The value of the shares derives not from the firm having redeemable assets, but from the profits generated by the firm.

8. Tobin's q depends on firm profit rates relative to shareholders' required returns. When interest rates (and shareholder required returns) decrease, the value of Tobin's q should increase. If businesses judge expansion plans by seeing if the profit rate is larger than shareholders' required return (or, equivalently, seeing whether Tobin's q is greater than 1), then the drop in interest rates and rise in Tobin's q encouraged business investment. Such a stimulus could well be explained by the decline in interest rates (and shareholder required rates of return), even if the economy and profit expectations are unchanged.

9. 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%).

10. If r = R, then there would be no economic value added, and P = K.The economic value added each period is the profitsrK minus the cost of capital, RK: EVA = (r - R)K Using the present value of a perpetuity, the value of the firm is

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