Question

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

a. A bond that has ​$1,000 par value​ (face value) and a contract or coupon interest rate of 7 percent. A new issue would have a floatation cost of 7 percent of the ​$1,135 market value. The bonds mature in 7 years. The​ firm's average tax rate is 30 percent and its marginal tax rate is 38 percent.

b. A new common stock issue that paid a ​$1.50 dividend last year. The par value of the stock is​ $15, and earnings per share have grown at a rate of 7 percent per year. This growth rate is expected to continue into the foreseeable future. The company maintains a constant​ dividend-earnings ratio of 30 percent. The price of this stock is now $31​,but 6 percent flotation costs are anticipated.

c. Internal common equity when the current market price of the common stock is $44. The expected dividend this coming year should be ​$3.20 increasing thereafter at an annual growth rate of 9 percent. The​ corporation's tax rate is 38 percent.

d. A preferred stock paying a dividend of 9 percent on a $140 par value. If a new issue is​ offered, flotation costs will be 11 percent of the current price of $172.

e. A bond selling to yield 9 percent after flotation​ costs, but before adjusting for the marginal corporate tax rate of 38 percent. In other​ words, 9 percent is the rate that equates the net proceeds from the bond with the present value of the future cash flows​ (principal and​ interest).

Answer 1

1-
before tax cost of debt =Using rate function in M S excel	rate(nper,pmt,pv,fv,type) nper = 7 pmt =1000*8% =80 pv = 1135*(1-.07) =1055.55 fv =1000 type =0	RATE(7,-80,1055.55,-1000,0)	6.97%
after tax cost of debt = before tax cost of debt*(1-average tax rate)	6.97*(1-.3)	4.88
2-
cost of common stock	(expected dividend/net proceeds)+growth rate	(1.605/29.14)+7%	12.51%
expected dividend = last year dividend*(1+growth rate)		1.5*1.07	1.605
net proceeds = market price*(1-flotation cost)	31*(1-.06)	29.14
3-
cost of common stock	(expected dividend/net proceeds)+growth rate	(3.2/44)+9%	16.27%
expected dividend			3.2
market price			44
growth rate			9%
4-
cost of preferred stock	(preferred dividend/net proceeds)*100	12.6/153.08	8.23%
preferred dividend	140*9%	12.6
net proceeds =market price*(1-flotation cost)	172*(1-.11)	153.08
5-
after tax cost of debt	Yield on bond*(1-tax rate)	9*(1-.38)	5.58

Answer 2

a. The cost of the bond can be calculated as follows:

First, we need to calculate the current market value of the bond: Coupon payment = 7% x $1,000 = $70 Floatation cost = 7% x $1,135 = $79.45 Current market value = $1,000 + $70 - $79.45 = $990.55

Next, we need to calculate the after-tax cost of debt: Effective annual interest rate = (Coupon payment / Current market value) x (1 - Marginal tax rate) Effective annual interest rate = ($70 / $990.55) x (1 - 0.38) = 4.90%

Therefore, the cost of the bond is 4.90%.

b. The cost of new common stock can be calculated as follows:

First, we need to calculate the expected dividend for the current year: Expected dividend = Dividend payout ratio x Earnings per share Expected dividend = 30% x $1.50 = $0.45

Next, we need to calculate the expected growth rate of dividends: Expected dividend growth rate = Retention ratio x Return on equity Expected dividend growth rate = (1 - Dividend payout ratio) x Return on equity Expected dividend growth rate = (1 - 0.30) x 0.07 = 0.049 or 4.9%

Next, we can calculate the cost of new common stock using the constant growth model: Cost of new common stock = (Expected dividend / Current market price) + Expected dividend growth rate Cost of new common stock = ($0.45 / $31) + 0.049 = 0.064 or 6.4%

After considering flotation costs, the cost of new common stock is 6.81% (6.4% / (1 - 0.06)).

c. The cost of internal common equity can be calculated using the dividend growth model:

Expected dividend for the next year = $3.20 Expected dividend growth rate = 9% Current market price = $44 Flotation costs = 0%

Cost of internal common equity = (Expected dividend / Current market price) + Expected dividend growth rate Cost of internal common equity = ($3.20 / $44) + 0.09 = 0.163 or 16.3%

d. The cost of preferred stock can be calculated as follows:

Current price = $172 Par value = $140 Dividend = 9% x $140 = $12.60 Floatation cost = 11% x $172 = $18.92

Net proceeds = Current price - Floatation cost = $172 - $18.92 = $153.08

After-tax cost of preferred stock = Dividend / Net proceeds x (1 - Marginal tax rate) = ($12.60 / $153.08) x (1 - 0.38) = 6.22%

Therefore, the cost of preferred stock is 6.22%.

e. The after-tax cost of debt can be calculated as follows:

Before-tax cost of debt = 9% Marginal tax rate = 38%

After-tax cost of debt = Before-tax cost of debt x (1 - Marginal tax rate) = 9% x (1 - 0.38) = 5.58%