A ﬁrm has a target debt-equity ratio of .37. The cost of debt is 9% and the cost of equity is 15%. The company has a 34% tax rate. A project has an initial cost of $70,000 and an annual after-tax cash
ﬂow of $21,000 for six years. There is no salvage value or net working capital requirement. What is
The net present value of the project using the WACC?

Question

Quizplus · Accepted Answer

1. Calculate the WACC:
WACC = (E / V) × Re + (D / V) × Rd × (1 - Tc)
where:
E = Market value of equity
D = Market value of debt
V = Total value (E + D)
Re = Cost of equity
Rd = Cost of debt
Tc = Corporate tax rate

Assuming the market values of equity and debt are equal to the book values, we have:
E = V × Equity portion = V × (1 - Debt portion) = V × (1 - 0.37) = 0.63V
D = V × Debt portion = V × 0.37 = 0.37V
V = E + D = 1V
Plug in the values:
WACC = 0.63 × 15% + 0.37 × 9% × (1 - 34%) = 11.06%

2. Calculate the present value of the after-tax cash flows:
PV = ∑ [CF / (1 + WACC) ^ t]
where:
CF = after-tax cash flow
t = time period

PV = $21,000 / (1 + 11.06%) ^ 1 + $21,000 / (1 + 11.06%) ^ 2 + ... + $21,000 / (1 + 11.06%) ^ 6
PV = $15,011

Since the initial cost of the project is already accounted for in the present value calculation, the net present value (NPV) of the project is equal to the present value of the after-tax cash flows ($15,011). Therefore, the correct answer is C) $15,011.

A ﬁRm Has a Target Debt-Equity Ratio of