Question

The complete question is ABC Co has a target debt ratio of 40% and it keeps this target. The cost of equity is 10% and the cost of debt is 4%. It is considering expanding its business and requires $1 million investment. After expansion, ABC expects additional free cash flows of $0.2 million per year in perpetuity. ABC decides to issue equity to finance this expansion. The equity issuance cost is 5%. The corporate tax rate is 30%. Assume that ABC will maintain the target debt ratio. What's the NPV of the expansion project?

Answer 1

Step-by-step explanation:

To calculate the NPV (Net Present Value) of the expansion project, we need to determine the cash flows associated with the project and discount them to their present values.

Given information:

Target debt ratio = 40%

Cost of equity (Ke) = 10%

Cost of debt (Kd) = 4%

Equity issuance cost = 5%

Tax rate = 30%

Investment required = $1 million

Additional free cash flows per year = $0.2 million

Step 1: Calculate the weighted average cost of capital (WACC).

WACC is the weighted average of the cost of equity and the after-tax cost of debt, considering the target debt ratio.

Weight of equity (We) = 1 - Target debt ratio = 1 - 0.40 = 0.60

Weight of debt (Wd) = Target debt ratio = 0.40

WACC = (We * Ke) + (Wd * Kd * (1 - Tax rate))

WACC = (0.60 * 0.10) + (0.40 * 0.04 * (1 - 0.30))

WACC = 0.06 + 0.0112

WACC = 0.0712 = 7.12%

Step 2: Calculate the present value of the additional free cash flows.

Since the additional free cash flows are expected to continue indefinitely, we can use the perpetuity formula.

PV = CF / r

PV = $0.2 million / 0.0712

PV ≈ $2.81 million

Step 3: Calculate the present value of the investment required.

The investment required is $1 million.

PV = CF / r

PV = -$1 million / 0.0712

PV ≈ -$14.04 million (negative sign indicates cash outflow)

Step 4: Calculate the net present value (NPV).

NPV = PV of cash inflows - PV of cash outflows

NPV = $2.81 million - $14.04 million

NPV ≈ -$11.23 million

Therefore, the NPV of the expansion project is approximately -$11.23 million. This indicates a negative NPV, suggesting that the project may not be financially viable or profitable given the specified assumptions and costs.