Question

​(Weighted average cost of​ capital)  As a member of the Finance Department of Ranch​ Manufacturing, your supervisor has asked you to compute the appropriate discount rate to use when evaluating the purchase of new packaging equipment for the plant. Under the assumption that the​ firm's present capital structure reflects the appropriate mix of capital sources for the​ firm, you have determined the market value of the​ firm's capital structure as​ follows:  

To finance the​ purchase, Ranch Manufacturing will sell

1010​-year

bonds paying interest at a rate of

7.47.4

percent per year​ (with semiannual​ payment) at the market price of

​$1 comma 0261,026.

Preferred stock paying a

​$2.072.07

dividend can be sold for

​$25.3925.39.

Common stock for Ranch Manufacturing is currently selling for

​$54.9254.92

per share and the firm paid a

​$3.053.05

dividend last year. Dividends are expected to continue growing at a rate of

5.55.5

percent per year into the indefinite future. If the​ firm's tax rate is

3030

​percent, what discount rate should you use to evaluate the equipment​ purchase?

laces.)

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Data Table

Source of Capital	Market Values
Bonds	​$4 comma 300 comma 0004,300,000
Preferred stock	​$1 comma 700 comma 0001,700,000
Common stock	​$6 comma 200 comma 0006,200,000

a.  Calculate component weights of capital.

The weight of debt in the​ firm's capital structure is

​(Round to two decimal​ places.)

The weight of preferred stock in the​ firm's capital structure is

​(Round to two decimal​ places.)

The weight of common stock in the​ firm's capital structure is

​(Round to two decimal​ places.)

b.  Calculate component costs of capital.

The​ after-tax cost of debt for the firm is

​(Round to two decimal​ places.)

The cost of preferred stock for the firm is

​(Round to two decimal​ places.)

The cost of common equity for the firm is

​(Round to two decimal​ places.)

c.  Calculate the​ firm's weighted average cost of capital.

The discount rate you should use to evaluate the equipment purchase is

​(Round to three decimal​ places.)

Answer 1

a). Total Market Value = Market Value of Debt + Market Value of Preferred Stock + Market Value of Common Stock

= $4,300,000 + $1,700,000 + $6,200,000 = $12,200,000

wD = Market Value of Debt / Total Market Value = $4,300,000 / $12,200,000 = 35.25%

wP = Market Value of Preferred Stock / Total Market Value = $1,700,000 / $12,200,000 = 13.93%

wE = Market Value of Common Stock / Total Market Value = $6,200,000 / $12,200,000 = 50.82%

b). To find the kD. we need to put the following values in the financial calculator:

INPUT	10*2=20		-1,026	(7.4%/2)*1,000=37	1,000
TVM	N	I/Y	PV	PMT	FV
OUTPUT		3.52

kD = 2r = 2 x 3.52% = 7.03%

After-tax kD = kD x (1 - t) = 7.03% x (1 - 0.30) = 4.92%

kP = Annual Dividends / Selling Price = $2.07 / $25.39 = 8.15%

kE = [{D0 x (1 + g)} / P0] + g

= [{$3.05 x 1.055} / $54.92] + 0.055 = 0.0586 + 0.055 = 0.1136, or 11.36%

c). WACC = [wD x After-tax kD] + [wP x kP] + [wE x kE]

= [0.3525 x 4.92%] + [0.1393 x 8.15%] + [0.5082 x 11.36%]

= 1.73% + 1.14% + 5.77% = 8.643%