Question

cleopatra inc. uses 58 percent common stock and 42 percent debt to finance its operations. the after-tax cost of debt is 5.4 percent and the cost of equity is 15.3 percent. management is considering a project that will produce a cash inflow of $49,600 in the first year. the cash inflows will then grow at 2.5 percent per year forever. what is the maximum amount the firm can initially invest in this project to avoid a negative net present value for the project?

Answer 1

The maximum initial investment Cleopatra Inc. can make in the project without resulting in a negative net present value is approximately $565,007.96, which is calculated by using the weighted average cost of capital and the perpetuity growth model.

Step-by-step explanation:

The student's question is related to calculating the maximum initial investment that Cleopatra Inc. can make in a project without resulting in a negative net present value when considering a specific mix of equity and debt financing. To find this, we must use the weighted average cost of capital (WACC) which incorporates the given after-tax cost of debt and the cost of equity, weighted by the firm's capital structure percentages.

The WACC can be calculated using the formula:

WACC = (% of equity × cost of equity) + (% of debt × after-tax cost of debt).

Plugging in the values provided:

WACC = (0.58 × 15.3%) + (0.42 × 5.4%)

= 11.274%.

With the WACC and the project's cash flow growth, the terminal value of the project's cash flows can be found using the formula for a perpetuity growth model:

Terminal Value = Cash Flow Year 1 / (WACC - growth rate).

The terminal value will give us the maximum amount the firm can invest initially (Initial Investment):

Initial Investment = Terminal Value

= $49,600 / (11.274% - 2.5%)

= $49,600 / 8.774%

≈ $565,007.96.

This is the maximum amount the firm can invest without creating a negative NPV for the project.