NPV – Perpetuity

Practice Question

Intro to Finance
Capital Budgeting
NPV
Short Answer

You are considering an investment at a price of $190,000, and its after-tax net cash flows will increase by $30,000 per year and remain at this level forever. If the appropriate cost of capital is 15%, what is the NPV?

Answer +
Final Answer: $10,000
Explanation +

Step 1: Identify relevant inputs

- Initial Investment = $190,000
- Perpetual annual cash flow = $30,000
- Discount rate (cost of capital) = 15%

Step 2: Calculate the present value of the perpetuity

Using the perpetuity formula:
\[ PV = \frac{C}{r} = \frac{30,000}{0.15} = 200,000 \]

Step 3: Compute the Net Present Value (NPV)

\[ NPV = PV - \text{Initial Investment} = 200,000 - 190,000 = 10,000 \]

Conclusion: The net present value of the investment is $10,000. Since the NPV is positive, this project would add value to the firm.