Question

Tarrasa Mining Corporation has 11.2 million shares of common stock outstanding and 205,000 5.9% semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $37 per share and has a beta of 0.8. The bonds have 12 years to maturity and sell for 91% of par. The market risk premium is 5.5%, T-bills are yielding 4%, and Tarrasa Mining's tax rate is 30%.

What is the firm's market value weight of equity? 68.96 (Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).  

What is the firm's market value weight of debt? 31.04 (Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).  

What is the firm’s cost of equity?8.4 (Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).  

What is the firm’s cost of debt? ??????????(Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).  

I need help with the last question; I have done the first 3.

Topic: WACC

Answer 1

To find the cost of debt we have to find the yield to maturity of the bond with the following information

Par value , M = $1000

Coupon rate = 5.9% semi-annual = 0.059

Annual Coupon value,C = coupon rate* par value of bond = (0.059) * 1000 = 59

price of bond ,P= 91% of par value = 0.91*1000 = 910

Maturity, n = 12 years

approximate formula for Yield to maturity(YTM)

Yield to maturity = {(C/2) + [(M-P)/2*n]}/(0.4*M + 0.6*P

= {(29.5) + [(1000-910)/24]}/(400+546)

= 33.25/946 = 0.035147991 = 3.5147991%

cost of debt = YTM = 3.5147991%

Total after tax cost of debt = YTM*(1-T) = 3.5147991*(1-0.30) = 3.5147991*0.70 = 2.46035937%

Or 2.46% (after rounding off to two decimal places)