(weighted average cost of capital) As a consultant to GBH Skiwear, you have been
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Question
(weighted average cost of capital) As a consultant to GBH Skiwear, you have been asked to compute the appropriate discount rate to use in the evaluation of the purhase of a new warehouse facility. You have determined the market value of the firm's current capital structure as followed: Source of capital Bonds, Maket Value $460,000. Source of capital Preferred Stocks, Market value $110,000. Source of capital Common Stock, Market value $450,000. To finance the purchase GBH will sell 20-year bonds with a $1,000 par value paying 7.6 percent per year(paid semianually) at the market price of $973. Preferred stock paying a $2.45 dividend can be sold for $34.67. Common stock for GBH is currently selling for $49.43 per share. The firm paid a $4.02 dividend last year and expects dividends to continue growing at a rate of 3.7 percent per year ito the indefinite future. The firm's maginal tax rate is 34 percent. What discount rate should you use to evaluate the warehouse project?
a.Calculate component weights of capital.
The weight of debt in the firm's capital structure is ? %. The weight of preferred stock in the firm's capital is ?%. The weight of common stock in the firm's capital structure is ?%.
b. Calculate component cost of capital
The after-tax cost of debt for the firm is ?%. The cost of preferred stock for the firm is ?%. The cost of common equity for the firm is ?%.
c. Calculate the firm's weighted average cost of capital.
The discount rate you should use to evaluate the warehouse project is ? %.
Explanation / Answer
Market Value of Capital Bonds = $ 460,000
Market Value of Preferred stocks = $ 110,000
Market Value of Common stocks = $ 450,000
Marginal Tax Rate = 34%
Bonds
20 year Bonds to sold with Par Value $ 1000 coupon at 7.6% semi-annual at a price $ 973
Preferred Stock
Dividend on Preferred stock = $ 2.45 Sale Price = $ 34.67
Common Stocks
Dividend paid last year D0 = $ 4.02
Dividend growth rate g = 3.7% indefinitely
Current market price = $ 49.43
Answer (a)
Total Capital = Bonds + Preferred Stock + Common Stock
= 460,000 + 110,000 + 450,000
= $ 1,020, 000
Weight of Debt in Total Capital = (460000/1020000) *100 = 45.098% or 45.10% (rounded off)
Weight of Preferred Stock in Total Capital = (110000/1020000)*100 = 10.784% or 10.78% (rounded off)
Weight of Common stock in Total Capital = (450000/1020000) *100 = 44.117% or 44.12% (rounded off)
Answer (b)
Preferred Stocks
Dividend on Preferred stock = $ 2.45 Sale Price = $ 34.67
If cost of preferred capital is rp then Sale Price = Dividend / rp
34.67 = 2.45 / rp -> rp = 2.45/34.67 -> rp = 0.070666 or 7.0666%
Cost of Preferred Capital rp = 7.07% (rounded off)
Common Stocks
Dividend paid last year D0 = $ 4.02
Dividend growth rate g = 3.7% indefinitely
Current market price = $ 49.43
Dividend for current year = D0 * (1+g) = 4.02 * (1+0.037) = 4.02*1.037 = $ 4.1687
If rc is cost of common stocks, then
Current Market Price = D1 / (rc – g) - > 49.43 = 4.1687 / rc – 0.037
rc – 0.037 = 4.1687/49.43 -> rc – 0.037 = 0.08434 -> rc = 0.08434 – 0.037 = 0.04734
Cost of common stocks rc = 4.734% or 4.73% (rounded off)
Bonds
20 year Bonds to sold with Par Value $ 1000 coupon at 7.6% semi-annual at a price $ 973
Semi Annual Coupon Payment A = 1000 * 0.076/2 = 38
Total Discounting periods = 20*2 = 40
Face Value F = 1000 Present price P = 973
The bond yield comes around 3.94% semi annually or 7.88% annually based on following calculations and reducing the value
[If required rate of return is i then the present value Pof bond will be equal to
P = A * { 1-(1/1+i)^40)/i} + F /(1+i)^40
973 = 38* {1-(1/1+r)^40)/i} + 1000 / (1+i)^40
973 = (38 * 1/i) – 38* 1/(1+i)^40/i) + 1000/(1+i)^40
973 = 38/i – 38/(i*(1+i)^40) + 1000 /(1+i)^40
Taking logarithms on both sides
log 973 = log (38/i) – log (38/(1+i)^40/i) + log (1000/(1+i)^40)
(as per logarithm rules log (x/y) = log x – log y , log (xy) = log x + log y and log x^n = n log x)
log 973 = log 38 – log i – log (38 /(1+i)^40) – log i + log 1000 – log (1+i)^40
log 973 = log 38 – log i – log 38 – log i – log (1+i)^40 + log 1000 – log (1+i)^40]
After tax cost of debt i = 0.0788 (1-0.34) = 0.052008
After tax cost of debt = 5.20%
Answer ( c )
Weighted average cost of capital = weight of debt * after tax rate + weight of preferred stock * cost of preferred stock + weight of equity capital * cost of equity
WACC = 0.451* 0.052 + 0.1078 * 0.0707 + 0.4412 * 0.0473
= 0.0235 + 0.0076 + 0.021 = 0.0521 or 5.21%
The discount rate that should be applied to evaluate the warehouse project is 5.21%
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