Question

​Ernst's Electrical has a bond issue outstanding with ten years to maturity. These bonds have a​ $1,000 face​ value, a 5 percent​ coupon, and pay interest semiminusannually. The bonds are currently quoted at 96 percent of face value. What is​ Ernst's pretax cost of​ debt?

Answer 1

Answer: 5.52%

Explanation:

Given the following :

Face value (f) = $1000

Bond price(p) = 96% of face value = 0.96 × 1000 = $960

Coupon rate = 5% Semi-annually = 0.05/2 = 0.025

Payment per period (C) = 0.025 × 1000 = $25

Period(n) = 10 years = 10 × 2 = 20

Semiannual Yield to maturity = [(((f-p)/n) + C) / (f + p)/2]

Semiannual YTM = [(((1000 - 960) / 20) + 25) / (1000 + 960)/2]

Semiannual Yield to maturity = [(((40 /20) + 25) / 1960/2]

= (2 + 25) / 980

= 27 / 980 = 0.02755 = 2.755% = 2.76%

Pretax cost of debt = Yield to maturity = 2 × Semiannual yield to maturity

Pretax cost of debt = 2 × 2.76% = 5.52%