Question

​(Individual or component costs of​ capital)  Compute the cost of capital for the firm for the​ following:

a.  A bond that has a​$1,000par value​ (face value) and a contract or coupon interest rate of11.8percent. Interest payments are​$59.00and are paid semiannually. The bonds have a current market value of​$1124,and will mature in10years. The​ firm's marginal tax rate is34percet.b.  A new common stock issue that paid a​$1.79 dividend last year. The​ firm's dividends are expected to continue to grow at7.3 percent per​ year, forever. The price of the​ firm's common stock is now​$27.97 c.  A preferred stock that sells for​$132 pays a dividend of 9.2 ​percent, and has a​ $100 par value.  d.  A bond selling to yield11.4percent where the​ firm's tax rate is34percent.

a.  The​ after-tax cost of debt isnothing​%.​(Round to two decimal​ places.)

Answer 1

a. The cost of debt is the yield to maturity or YTM of the bond. we can use financial calculator for calculation of YTM with below key strokes.

Interest are paid semi-annually. so, maturity will also be semi-annual and calculated YTM will also be semi-annual. we need to multiply it by 2 to make it annual.

N = semi-annual maturity = 10*2 = 20; PMT = semi-annual interest = $59; FV = face value = $1,000; PV = current market value = -$1,124 > CPT = compute > I/Y = semi-annual YTM = 4.91%

PV needs to be entered as negative value because it's a cash outflow.

Annual YTM = 4.91%*2 = 9.82%

after-tax cost of debt = cost of debt*(1-marginal tax rate) = 9.82%*(1-0.34) = 9.82%*0.66 = 6.48%

b. cost of common stock = [last dividend paid*(1+dividend growth rate)/current stock price] + dividend growth rate

cost of common stock = [$1.79*(1+0.073)/$27.97] + 0.073 = [($1.79*1.073)/$27.97) + 0.073 = ($1.92067‬/$27.97) + 0.073 = 0.0687 + 0.073 = 0.1417 or 14.17%

c. cost of preferred stock = annual dividend/current stock price

annual dividend = par value*dividend rate = $100*9.2% = $9.2

cost of preferred stock = $9.2/$132 = 0.0697 or 6.97%

d. The cost of debt is the yield to maturity or YTM of the bond.

after-tax cost of debt = cost of debt*(1-tax rate) = 11.4%*(1-0.34) = 11.4%*0.66 = 7.52%