(Individual or component costs of capital) Compute the cost of capital for the firm for the following: a. A bond that has a $1 comma 000 par value (face value) and a contract or coupon interest rate of 11.4 percent. Interest payments are $57.00 and are paid semiannually. The bonds have a current market value of $1 comma 120 and will mature in 10 years. The firm's marginal tax rate is 34 percet. b. A new common stock issue that paid a $1.82 dividend last year. The firm's dividends are expected to continue to grow at 6.5 percent per year, forever. The price of the firm's common stock is now $27.22. c. A preferred stock that sells for $142, pays a dividend of 8.8 percent, and has a $100 par value. d. A bond selling to yield 11.9 percent where the firm's tax rate is 34 percent.

The requirement is to calculate the cost of each finance instrument whose details were given in the question:

after tax cost of debt is 6.28%

cost of equity is 13.63%

cost of preferred stock is 6.20%

after tax cost of debt is 7.85%

Explanation:

1. after cost of debt:

The pretax cost of debt can be determined using the rate formula in excel:

=rate(nper,pmt,-pv,fv)

nper is the number of coupon payments the bond would make i.e 10*2=20

pmt is given as $57

pv is the current price of the bond $1120

fv is the par value of $1000

=rate(20,57,-1120,1000)=4.76%(semi-annually)

=9.52% annually

After cost of debt =9.52%*(1-0.34)=6.28%

2. cost of equity

share price=Do*(1+g)/r-g

r is the cost of equity

r=Do*(1+g)/share price+g

r=$1.82*(1+6.5%)/$27.22+6.5%

r=(1.94/27.22)+6.5%=13.63%

3. cost of preferred  share=dividend/market price

dividend=8.8%*$100=$8.8

market price is $142

cost of preferred share=$8.8/$142=6.20%

4.after tax cost of debt

pretax cost of debt is 11.9%

tax rate is 34%

after tax cost of debt =11.9%*(1-0.34)=7.85%