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 comma 000 par value​ (face value) and a contract or coupon interest rate of 11.3 percent. Interest payments are ​$56.50 and are paid semiannually. The bonds have a current market value of ​$1 comma 125 and will mature in 10 years. The​ firm's marginal tax rate is 34 percent. b.  A new common stock issue that paid a ​$1.79 dividend last year. The​ firm's dividends are expected to continue to grow at 7.7 percent per​ year, forever. The price of the​ firm's common stock is now ​$27.83. c.  A preferred stock that sells for ​$124​, pays a dividend of 8.8 ​percent, and has a​ $100 par value.   d.  A bond selling to yield 11.7 percent where the​ firm's tax rate is 34 percent. a.  The​ after-tax cost of debt is nothing​%. ​(Round to two decimal​ places.) b.  The cost of common equity is nothing​%. ​(Round to two decimal​ places.) c.  The cost of preferred stock is nothing​%. ​(Round to two decimal​ places.) d.  The​ after-tax cost of debt is nothing​%. ​(Round to two decimal​ places.)

Answer 1

(a)-After-tax Cost of Debt

• The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value
• The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.
• The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 11.30% x ½]	PMT	56.50
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [10 Years x 2]	N	20
Bond Price/Current Market Price of the Bond [-$1,125]	PV	-1,125

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the semi-annual yield to maturity on the bond (1/Y) = 4.675%.

The semi-annual Yield to maturity = 4.675%

Therefore, the annual Yield to Maturity of the Bond = 9.35% [4.675% x 2]

After Tax Cost of Debt

After Tax Cost of Debt = Bond’s YTM x [ 1 – Tax Rate]

= 9.35% x (1 – 0.34)

= 9.35% x 0.66

= 6.17%.

(b)-Cost of Equity

As per Discounted cash flow model, The cost of common stock = [D0(1 + g) / P0] + g

Where, Dividend in next year (D0) = $1.79 per share

Dividend growth rate (g) = 7.70% per year

Current Share Price (P0) = $27.83 per share

Therefore, cost of common stock = [D0(1 + g) / P0] + g

= [$1.79(1 + 0.0770) / $27.83] + 0.0770

= [$1.9278 / $27.83] + 0.0770

= 0.0693 + 0.0770

= 0.1463 or

= 14.63%

(c)-Cost of Preferred Stock

Cost of Preferred Stock = [Annual Preferred Dividend / Selling Price] x 100

= [($100 x 8.80%) / $124] x 100

= [$8.80 / $124] x 100

= 7.10%

(d)-After-tax cost of Debt

After Tax Cost of Debt = Bond’s YTM x [ 1 – Tax Rate]

= 11.70% x (1 – 0.34)

= 11.70% x 0.66

= 7.72%.