Economics 156 Second Test

Econ 156 Fall 1999 Second Test Answers

1. Letting the maturation value be F, the current price is P0 = F/1.06²⁰; a year from now, the price will be is P1 = F/1.05¹⁹, giving a capital gain of (P1 - P0)/P0 = P1/P0 - 1 = (F/1.05¹⁹)/(F/1.06²⁰) - 1 = 1.06²⁰/1.05¹⁹ - 1 = 0.269, or 26.9%.

2. a. A decline in interest rates increases the prices of fixed-income securities. The prices of long-term (actually long-duration) securities are most sensitive to interest rates.
     b. The Federal Reserve Board can reduce the discount rate, reduce reserve requirements, or make open market purchases to lower market interest rates.
     c. Lower interest rates reduces the cost of borrowing to buy cars, houses, and factories, and (for those who have cash to invest) make financial assets less attractive relative to real assets.
     d. A well-anticipated recession and decline interest rates should already be reflected in the term structure of interest rates.

3. For a horizon of one-year, the purchase of a one-year T-bill is a perfectly safe investment, with a rate of return equal to the current rate of return on a one-year T-bill.

4. If you pay 1400 for the S&P 500 now, you get about a d% dividend yield over the coming year; if you pay 1400 for an S&P 500 futures contract, you can invest 1400 in a 1-year T-bill for an r% rate of return; choose the S&P 500 if d > r; choose the futures contract if r > d.

5. The return on a stock depends on how well the overall market does and on factors specific to this particular company; the stock's beta coefficient measures the extent to which its return moves with the return on all stocks. A low-beta stock is not very sensitive to overall market movements, but still may be very volatile--the standard deviation of its e may be very large. While beta is not a good measure of risk for an individual stock, it is a good gauge for a diversified portfolio, since the firm-specific risk (the es) will probably cancel each other out.

7. Well, other things being equal, I'd prefer that the stock market love my stock.

8. 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.

9. We need to see if the present value of the cash flow is larger or smaller than $430,000. Using a required return r and letting her live n years:

10. 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.