Question

1) Suppose a company will be in business for only the next 10 years and pays an annual dividend of $1.75 for those ten years? What is the present value of a share of stock for this company if we want a 9% return on the stock?

2) Your firm has issued 15- year zero coupon bonds with a $1000 face value. If the bonds are currently selling for $585, what is the annual yield to maturity, assuming semiannual compounding?

Answer 1

Answer 1.

Annual Dividend = $1.75
Number of Dividends = 10 years
Return = 9%

Present Value = $1.75/1.09 + $1.75/1.09^2 + ... + $1.75/1.09^10
Present Value = $1.75 * (1 - (1/1.09)^10) / 0.09
Present Value = $1.75 * 6.4177
Present Value = $11.23

Answer 2.

Face Value = $1,000
Current Price = $585
Semiannual Period to Maturity = 30 (15 years)

Let Semiannual YTM be i%

$585 = $1,000 / (1+i)^30
(1+i)^30 = 1.7094
1 + i = 1.018
i = 0.0180
i = 1.80%

Semiannual YTM = 1.80%
Annual YTM = 2 * 1.80%
Annual YTM = 3.60%