Fall 2002 midterm answers

Econ 156
Fall 2002

Midterm Answers

1. 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%.

2. With daily compounding, the effective annual return is (1 + 0.0925/365)³⁶⁵ = 1.0969 (9.69%). With quarterly compounding, (1 + 0.0940/4)⁴ = 1.0974 (9.74%). The reader is right.

3. 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.

4. 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.

5. Unless it is a new issue, the money you spend to purchase shares of stock are not used to pay the company’s expenses or expand its operations. Instead, theis money goes to whoever you buy the stock from.

6. One way to look at it is how much could she borrow at a 5.75% interest rate with monthly payments of $1798.65? The answer is $308,213.44—not enough to pay the $10,000 cost.

8. As the stock goes ex-dividend, the price of the stock will drop by (approximately) the size of the dividend.

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:

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