Question

Q Corporation and R Inc. are two companies with very similar characteristics. The only difference between the two companies is that Q Corp. is an unlevered firm, and R Inc. is a levered firm with debt of $5 million and cost of debt of 10%. Both companies have earnings before interest and taxes (EBIT) of $2 million and a marginal corporate tax rate of 40%. Q Corp. has a cost of capital of 15%

j. Both companies are now evaluating a project that requires an initial investment of $1.15 million and that will yield cash inflows of $500,000 per year for the next three years. Assume that this project has the same risk level as the individual firm’s assets. Should Q invest in this project? Should R invest in this project?

k.  Based on your results for part (j), discuss the effects of leverage and its tax shields effects on the future value of the two firms.

Answer 1

All financials below are in $ mn.

Before we get into solving this question we will have to calculate the WACC of R.

R is the levered firm, Q is the unlevered firm. The characteristics of both the firms are otherwise same.

Recall Modigliani and Miller Proposition:

Value of a levered firm = Value of an unlevered firm + present value of all the interest tax shield

Hence, Value of R = Value of Q + Present value of all the interest tax shield available to R

Value of Q = PV of all the future unlevered cash flows at unlevered cost of equity.

Since Q is unlevered, it's cost of capital = 15% is same as its unlevered cost of equity.

Unlevered cash flow of Q = EBIT x (1 - tax rate) = 2 x (1 - 40%) = 1.2 = FCFF

Value of Q = FCFF / Unlevered cost of equity = 1.2 / 15% = 8.00

Present value of all the interest tax shield available to R = Tax rate x Debt = 40% x 5 = 2

Hence, Value of R = Value of Q + Present value of all the interest tax shield available to R = 8 + 2 = 10

Value of R = FCFF / WACC of R

FCFF of R will be same as that of Q.

hence, 10 = 1.2 / WACC of R

Hence, WACC of R = 1.2 / 10 = 0.12 =12.00%

Let's now get into the question:

j. Both companies are now evaluating a project that requires an initial investment of $1.15 million and that will yield cash inflows of $500,000 per year for the next three years. Assume that this project has the same risk level as the individual firm’s assets. Should Q invest in this project? Should R invest in this project?

WACC of Q = 15% = 0.15

Post tax annual cash flows = $ 500,000 = 0.5 mn

Time frame = 3 years

NPV of this project for Q = - 1.15 + 0.5 / 1.15 + 0.5 / 1.15² + 0.5 / 1.15³ = - 0.0084

Since this project is NPV negative for Q, hence Q should not invest in this project.

WACC of R = 12% = 0.12

Post tax annual cash flows = $ 500,000 = 0.5 mn

Time frame = 3 years

NPV of this project for R = - 1.15 + 0.5 / 1.12 + 0.5 / 1.12² + 0.5 / 1.12³ = 0.0509

Since this project is NPV positive for R, hence R should invest in this project.

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k.  Based on your results for part (j), discuss the effects of leverage and its tax shields effects on the future value of the two firms.

Leverage leads to interest which is tax deductible. This reduces the tax burden of the firm. This tax shield has a value for the firm. Thus, leverage leads to incremental value creation for the firm through the tax shields. Because of this we saw the earlier equation that

Value of a levered firm = value of an unlevered firm + PV of all the tax shields

Leverage brings down the overall cost of capital of the firm.

Thus leverage increases the value of the firms in future, however only till a point called optimal leverage. Indebtedness beyond that point can lead to cost of bankruptcy and financial distress that may actually eat away the benefit due to interest tax shield. This will then lead to decline in the value of the firm.

Thus, leverage increase the value of a firm till a certain point, after which increasing leverage can reduce the value of the firm after accounting for cost of bankruptcy and financial distress.