The Marginal Cost of Capital

The cost of capital should ideally reflect the riskiness of the future cash flows of a project. For an average-risk project, the opportunity cost of capital is the same as the weighted average cost of capital (WACC) of the company. If the risk of the project is above or below average, then an upward or downward adjustment should be made to the WACC of the company.

The marginal cost of capital corresponds to the average risk of a company while appropriately adjusting to the riskiness of a given project. It plays a key role in capital budget decision-making based on the net present value (NPV) of the project.

Determining the Net Present Value (NPV) of a Project

You may recall that NPV = Present value of cash inflows – Present value of cash outflows

If a project’s NPV > 0, a company should undertake the project, while if NPV < 0, the project should not be undertaken.

If the the WACC of a company is used in the calculation of the NPV of a project, the assumption being made is that the project:

• has the same level of risk as the average-risk project of the company; and
• will have a constant target capital structure for the entirety of its useful life.

Question

Company XYZ is considering an investment of $50 million in a project. The project will return after-tax cash flows of $15 million per year for the first 2 years and another $35 million in year 3, the final year of the project. If the company’s marginal cost of capital is 5%, the NPV of the project is closest to:

1. $8.125 million.
2. $20.245 million.
3. $13.115 million.

Solution

The correct answer is A.

$$ \begin{align*}
\text{NPV} & = \cfrac {15}{1.05^{1}}+ \cfrac {15}{1.05^{2}}+\cfrac {35}{1.05^{3}} -50 \\
& = 14.286 + 13.605 + 30.234 – 50 = $8.125 \text{ million} \\
\end{align*} $$