Question

1. You are considering a project with an initial investment of $14 million and annual cash flow (before interest and taxes) of $2,000,000. The project’s cash flow is expected to continue forever. The tax rate is 34%, the firm’s unlevered cost of equity is 12% and its pre-tax cost of debt is 10%. The only side-effect from the use of debt that you are concerned about is related to the tax shield.

1. If the project were to be financed with 100% equity, would you accept the project?
2. If the project were to be financed with $5 million in perpetual debt and the rest with equity, use the APV method to help you decide whether to accept the project or not. Does your decision change from part (a)?
3. Redo part (b) by using the FTE approach.
4. Redo part (b) by using the WACC approach.
5. What is the minimum level of debt you would have to use in order to accept this project?

Answer 1

a.

If the project to be financed by 100% equity

Initial Investment = $14 million

Annual Cash Flow before interest and taxes= $2000000

Since interest is zero, as it is equity-financed

Annual Cash Flow after taxes (Free cash flow) = $2000000(1-0.34) = $1320000

Unlevered cost of Equity = 12%

Now Calculating Net Present Value (NPV)

NPV = -14000000 + 1320000/0.12 = -$3 million

Since net present Value is negative therefore we will not accept the project.

b.

As per Adjusted Present Value Method (APV)

APV = Unlevered Firm Value + Net effect of debt

Unlevered Firm Vale = NPV = -$3000000

Net effect of debt = Tax Rate * Debt Amount = 0.34*5000000 = $1700000

APV = -3000000 + 1700000 =-$1300000

Since APV is negative we will not accept the project.

The decision will not change.

c. FTE Approach

Since the firm is using $5 million of debt, the equity holders only have to come up with $9 million of the initial $14 million. Thus, CF0( cash flow at t=0) = –$9 million

Each period, the equity holders must pay interest expense. The after-tax cost of the interest is = (1 – 0.34) ×0.10 ×$5 million = $330000

So Cash Flow till perpetuity = $(2-0.33) million = $1.67 million

Now finding the discount rate

Discount Rate = Cost of Equity + [(Debt/S)(1- tax rate)(Cost of equity- Cost of debt)]

V = PV of after-tax cash flow + PV of the tax shield

V = 11000000 + 1700000 = $12700000

S = V- Debt = 12700000-5000000 = $7700000

Discount Rate = 0.12 + [(5000000/7700000)(1- 0.34)(0.12- 0.10)]

Discount Rate = 0.12 + 0.00857 = 12.85%

NPV = -$9million + ($1.67million /0.1285) = $3.99 million

d.

Debt = $5 million

Equity = $9 million

Annual Cash Flow before interest and taxes= $2000000

Interest = 0.10*5000000 = $0.5 million

Cash flow after Interest = $1.5 million

Annual Cash Flow after taxes (Free cash flow) = $1500000(1-0.34) = $0.99 million

WACC = (D/D+E)* After tax Cost of Debt + (E/D+E)* Cost of Equity

WACC = (5/14)*0.066 + (9/14)*0.12 = 10.07%

Now Calculating NPV

NPV = -$14 million + $0.99 million/0.1007 = -$4.168 million