Question

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

a.  A bond that has a ​$1,000 par value​ (face value) and a contract or coupon interest rate of 10.2 percent. Interest payments are $51.00 and are paid semiannually. The bonds have a current market value of $1,130 and will mature in 10 years. The​ firm's marginal tax rate is 34 percet.

b.  A new common stock issue that paid a $1.81 dividend last year. The​ firm's dividends are expected to continue to grow at 6.8 percent per​ year, forever. The price of the​ firm's common stock is now $27.45.

c.  A preferred stock that sells for $143 pays a dividend of 9.3 ​percent, and has a​ $100 par value.  

d.  A bond selling to yield 12.1 percent where the​ firm's tax rate is 34 percent.

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

b.  The cost of common equity is......​%. ​(Round to two decimal​ places.)

c.  The cost of preferred stock is ....%. ​(Round to two decimal​ places.)

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

Answer 1

a

Cost of debt

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

1130 =∑ [(10.2*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM = 8.26

b

Cost of equity

As per DDM

Price = recent dividend* (1 + growth rate )/(cost of equity - growth rate)

27.45 = 1.81 * (1+0.038) / (Cost of equity - 0.038)

Cost of equity% = 10.64

c

cost of preferred equity

cost of preferred equity = Preferred dividend/price*100

cost of preferred equity = 9.3/(143)*100

=6.5

d

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 8.2644112067*(1-0.34)

= 5.46