If the project's cost of capital were to increase, what would be the most likely effect on the project's net present value (NPV)?

• A. The NPV would decrease.
• B. The NPV would become positive.
• C. The NPV would remain unchanged.
• D. The NPV would increase.

Answer: (A)

Verified step by step guidance

1. Understand the concept of Net Present Value (NPV): NPV is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It is calculated using the formula: $\mathrm{NPV}=\sum _{t=1}^n\frac{{\mathrm{CF}}_t}{{\left(}^1}-\mathrm{Initial}\mathrm{Investment}$, where CFt is the cash flow at time t, r is the discount rate (cost of capital), and t is the time period.
2. Recognize the relationship between the cost of capital and NPV: The cost of capital (r) is used as the discount rate in the NPV formula. As the cost of capital increases, the denominator in the formula (${\left(}^1$) becomes larger, which reduces the present value of future cash inflows.
3. Analyze the impact of an increased cost of capital: Since the present value of cash inflows decreases with a higher discount rate, the overall NPV (which is the sum of discounted cash inflows minus the initial investment) will also decrease.
4. Evaluate the options provided: Based on the relationship between the cost of capital and NPV, the most likely effect of an increase in the cost of capital is that the NPV would decrease. The other options (NPV becoming positive, remaining unchanged, or increasing) are inconsistent with this relationship.
5. Conclude the reasoning: The correct answer is that the NPV would decrease because a higher cost of capital reduces the present value of future cash inflows, leading to a lower NPV.