Question

In: Finance

Your firm is considering a project with no start-up costs that will generate $1 million in...

Your firm is considering a project with no start-up costs that will generate $1 million in FCF forever, starting in one year. Your debt-to-equity ratio is 1, your equity-holders require a return of 12%, and your debt-holders require a return of 8%. The tax rate is 20%. Using the Adjusted Present Value method, compute the unlevered value of the project, the value of the tax shield (assuming you maintain your current leverage ratio), and the levered value of the project.

a. V_u = $10 million, PV(Tax Shield) = $0.870 million, V_L = $10.870 million

b. V_u = $12 million, PV(Tax Shield) = $0.080 million, V_L = $12.080million

c. V_u = $10 million, PV(Tax Shield) = $1.740 million, V_L = $11.740 million

d. V_u = $11.740 million, PV(Tax Shield) = $0, V_L = $11.740 million

Solutions

Expert Solution

Hence, the correct answer is the first option i.e. option a. V_u = $10 million, PV(Tax Shield) = $0.870 million, V_L = $10.870 million

D/E = 1

Wd = D/(D + E) = 1 / (1 + 1) = 0.5

We = 1 - Wd = 0.5

Cost of equity for the unlevered firm, r = Wd x Kd + We x Ke = 0.5 x 8% + 0.5 x 12% = 10%

Hence, value of the unlevered firm = C/r = 1/10% = $ 10 million.

Let V be the value fo the levered firm. Then D = V x Wd = V x 50% = 0.5V

Interest = Kd x D = 8% x 0.5V = 0.04V

Interest tax shield = ITS = Interest x T = 0.04V x 20% = 0.008V

PV of ITS = ITS / r = 0.008V/10% = 0.08V

Also Value of the levered firm = Value of unlevered firm + PV of ITS

Hence, V = 10 + 0.08V

Hence, V = 10 / (1 - 0.08) = 10.870

and PV of ITS = 0.08V = 0.08 x 10.870 = 0.870

Hence, the correct answer is the first option i.e. option a. V_u = $10 million, PV(Tax Shield) = $0.870 million, V_L = $10.870 million


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