1 The monthly payments are X such that

     Using this value of X, the effective annual interest rate R is such that

     If the loan is repaid after 5 years, the $5000 processing costs will be more imporrtant and the effective interest rate will be higher. It turns out that the monthly payments are $341.52. If it is not repaid early, the effective interest rate is 15.00%; if it is an repaid after 5 years, the effective interest rate is 17.21%.

2 "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 naivete, since the combined firms were [worth exactly the same no matter who did the acquiring]."

3 Because of their default risk, BBB bonds are priced to have higher interest rates than Treasury bonds. An increase in the unemployment rate would increase the chances of default, widening this spread.

4 Because there is no change in the number of shares, earnings per share will increase as long as the new capital makes a profit (r > 0); however, shareholders will not be better off unless this profit rate is larger than their required rate of return.

5 The cost of carry is equal to the interest on a perfectly safe investment (such as T-bills) minus the cash flow from the asset--dividends from stock, coupons from bonds. For a bond selling for par, the coupon rate is equal to the bond's yield to maturity. Because bond yields are higher than stock dividend yields, stocks have the higher cost of carry.

6 The stock has the shorter duration since the higher required rate of return reduces the present value of distant cash flows relative to the present value of near cash flows. Mathematically, the price of each is P = X/R and -(1/P)dP/dR = 1/R.

7 Sell a call option and put option with the same exercise date and the same exercise price (equal to the point of the kink in the profit picture):

     Buy one call option and sell one call option with a higher exercise price:

8 The two-year zero is most profitable:

9 The value of market and the stock did not necessarily increase monotonically over this time period. Perhaps the market rose above 10000 and then fell back to 10000, while StockB fell and then rose to 200; if so, the estimated beta coefficient would be negative. In the sample graph below, both prices have been scaled to equal 1 on January 1, 1995.

10 Long-term securities might have lower interest rates than short-term securities because the market expects interest rates to decline. If these expectations prove correct, the firm that borrows long-term will have locked itself in at what, in retrospect, turns out to be a high interest rate. Those who borrow long-term will be hurt financially if interest rates drop by more than the implicit interest-rate predictions embedded in the term structure.