7. Solving for the WACC Aa Aa The WACC is used as the discount rate to evaluate
ID: 2713427 • Letter: 7
Question
7. Solving for the WACC Aa Aa The WACC is used as the discount rate to evaluate various capital budgeting projects. However, it is important to realize that the WACC is an appropriate discount rate only for a project of average risk. Analyze the cost of capital situations of the following company cases, and answer the specific questions that finance professionals need to address. Consider the case of Turnbull Co. Turnbull Co. has a target capital structure of 45% debt, 4% preferred stock, and 51% common equity. It has a before-tax cost of debt of 8.2%, and its cost of preferred stock is 9.3%. If its current tax rate is 40%, how much higher will Turnbull's weighted average cost of capital (WACC) be if it has to raise additional common equity capital by issuing new common stock instead of raising the funds through retained earnings? If Turnbull can raise all of its equity capital from retained earnings, its cost of common equity will be 12.4%. However, if it is necessary to raise new common equity, it will carry a cost of 14.2%. 0.92% 1.24% 1.10% 1.0196 Turnbull Co. is considering a project that requires an initial investment of $270,000. The firm will raise the $270,000 in capital by issuing $100,000 of debt at a before-tax cost of 8.7%, $30,000 of preferred stock at a cost of 9.9%, and $140,000 of equity at a cost of 13.2%. The firm faces a tax rate of 40%, what will be the WACC for this project?Explanation / Answer
Excess in WACC for raising funds through new equity = 0.92%
Target Capital Structure
Debt = 45%
Prefered stock = 5%
Common Equity = 51%
Pre-tax Cost of Debt = 8.2%
Cost of Preferred Stock = 9.3%
Cost of Retained Earnings = 12.4%
Cost of new Common stock = 14.2%
Current Tax rate = 40%
WACC1 using Retained Earnings = 0.45 * 8.2% * (1-0.40) + 0.05 * 9.3% + 0.51 * 12.4%
= 0.45 * 8.2% * 0.6 + 0.05 * 9.3% + 0.51 * 12.4%
= 2.214% + 0.465% + 6.324%
= 9.003% or 9% (rounded off)
WACC2 using new common equity = 0.45 * 8.2% * 0.6 + 0.05 * 9.3% + 0.51 * 14.2%
= 2.214% + 0.465% + 7.242%
= 9.921% or 9.92% (rounded off)
Difference between WACC2 and WACC1 = 9.92% - 9.00% = 0.92%
WACC for the project = 9.88%
Initial investment = $270,000
Debt = $100,000 at a pre-tax cost of 8.7%
Preferred stock = $ 30,000 at a cost of 9.9%
Equity = $140,000 at a cost of 13.2%
Tax rate = 40%
Weight of Debt = Debt /Total investment = 100000/270000 = 0.3704
Weight of Preferred stock = Preferred stock / Total Investment = 30000/270000 = 0.1111
Weight of Common stock = 140000/270000 = 0.5185
Weighted Average cost of capital WACC = 0.3704 * 8.7% (1-0.4) + 0.1111 * 9.9% + 0.5185 *13.2%
WACC = 1.933488% + 1.09989% + 6.8442%
= 9.877578% or 9.88% (rounded off)
WACC of Kuhn Co = 15.87%
Initial Investment = $ 45 Million
Capital structure - 35% debt, 2% preferred stock, 63% common equity
Calculation of Cost of Debt
Face Value = $ 1000
Annual Coupon rate =10%
Time to maturity = 5 years
Annual Coupon amount =1000 * 10% = $100
Market Price = $1050.76
Let r be the rate of return on this bond, then
1050.76 = 100 * [(1-(1/(1+r)^5))/r] + 1000/(1+r)^5
1050.76 - 100 * [(1-(1/(1+r)^5))/r] - 1000/(1+r)^5 = 0
At r = 9%, LHS will be
= 1050.76 - 100 * [(1-(1/(1.09)^5))/0.09] - 1000/(1.09)^5
= 1050.76 – 100 * [(1-(1/(1.538624)/0.09] - 1000/1.538624
= 1050.76 – 100 * (1-0.649931)/0.09 – 1000 * 0.649931
= 1050.76 – 100 * (0.350069/0.09) – 1000 * 0.649931
= 1050.76 – 100* 3.889651 – 1000 * 0.649931
= 1050.76 – 388.9651 – 649.9314
= 11.86349
At r = 8.5%, LHS will be
= 1050.76 - 100 * [(1-(1/(1.085)^5))/0.085] - 1000/(1.085)^5
= 1050.76 – 100 * [(1-(1/1.503657))/0.085] - 1000/1.503657
= 1050.76 – 100 * (1-0.665045)/0.085 – 1000 * 0.665045
= 1050.76 – 100 * (0.334955/0.085) – 1000 * 0.665045
= 1050.76 – 100 * 3.940642 – 1000 * 0.665045
= 1050.76 – 394.0642 – 665.0454
= -8.34963
r = 0.085 + [(-8.34963) * (0.085-0.09)]/11.86343-(-8.34963)
r = 0.085 + 0.002065
r = 0.0871 or 8.71%
After tax cost of debt = 8.71% * ( 1- tax rate) = 8.71% * (1-0.4) = 8.71% * 0.6
= 5.226% or 5.23% (rounded off)
Annual Dividend on Preferred stock = $8
Price of Preferred stock = $ 95.70
Cost of Preferred stock =$8/$95.70 = 0.08359 or 8.36% (rounded off)
Current Price per share = $ 22.35
Expected dividend = $ 2.78
Floatation costs = 3%
Projected constant growth rate = 9.2%
Net realisation per share after floatation costs = 22.35 * (1-0.03) = $ 21.6795 or $ 21.68
Cost of equity = (Expected Dividend / Net realisation per share) + growth rate
Cost of Equity = (2.78/21.68) + 9.2%
= 0.1282 + 0.092 = 0.22023 or 22.02%
WACC of Kuhn Co = 0.35 * 5.23% + 0.02 * 8.36% + 0.63 * 22.02%
= 1.8305% + 0.1672% + 13.8726%
= 15.8703% or 15.87% (rounded off)
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