Question

What is the price of a bond with a coupon rate of 6%, payable semi-annually, a face value of $1000, 5 years to maturity, and a yield to maturity of 5.7%?

Consider a firm that has a debt-equity ratio of 1/3. The rate of return for debt is 7% and the rate of return for equity is 14%. The corporate tax rate is 30%. What is the weighted average cost of capital? Enter your answer as a percentage and rounded to 2 DECIMAL PLACES.

Answer 1

Given,

Face value = $1000

Coupon rate = 6%

Years to maturity = 5 years

Yield to maturity = 5.7% or 0.057

Solution :-

Semi annual coupon payment (C) = $1000 x 6% x 6/12 = $30

Semi annual periods (n) = 5 years x 2 = 10

Semi annual yield to maturity (r) = 0.057/2 = 0.0285

Price of the bond

= C/r x [1 - (1 + r)^-n] + [face value (1 + r)ⁿ]

= $30/0.0285 x [1 - (1 + 0.0285)^-10] + [$1000 (1 + 0.0285)¹⁰]

= $30/0.0285 x [1 - (1.0285)^-10] + [$1000 (1.0285)¹⁰]

= $30/0.0285 x [1 - 0.7550175378] + [$1000 1.32447254518]

= $30/0.0285 x 0.2449824622 + [$755.017537841]

= $257.876275998 + $755.017537841

= $1012.89