Suppose that Luther Industries is considering divesting one of its product lines

Question

Suppose that Luther Industries is considering divesting one of its product lines. The product line is expected to generate free cash flows of $2 million per year, growing at a rate of 3% per year. Luther has an equity cost of capital of 10%, a debt cost of capital of 7%, a marginal tax rate of 35%, and a debt-to-equity ratio of 2. If this product line is of average risk and Luther plans to maintain a constant debt-to-equity ratio, what after-tax amount must it receive for the product line in order for the divestiture to be profitable?

Explanation / Answer

Value of Operations = [Free Cash Flows (1 + growth rate)] / (WACC - growth rate) We know WACC = Kd*(1-T)*Wd + Ks*Ws where Ws&Wd are weights of Equity & Debt, Kd & Ks are Before Tax cost of Debt & Cost of equity. We also have D/E = 2 or D=2*E Tax Rate T=35%, Ks=10%, Kd =7%. So Kd*(1-T) = 7%*(1-35%) = 4.55% We can also write WACC eqn as WACC = Kd*(1-T)*(D/(D+E)) + Ks*(E/(D+E)) ie WACC = 4.55%*(2E/3E) + 10%*(E/3E) ie WACC = 4.55%*(2/3) + 10%*(1/3) ie WACC = 6.37% SO Value of Operations = [Free Cash Flows (1 + growth rate)] / (WACC - growth rate) ie Value of Ops = 2000000*(1+3%)/(6.37%-3%) = $61,127,596 So An after-tax amount of $61,127,596 it must receive for the product line in order for the divestiture to be profitable

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