Question

What is the NPV of a project that costs $10,000 today and another $10,000 in one year, and is then expected to generate 8 annual cash inflows of $4,000 each starting at the end of year 6? The expected return on the market is 9.4%, the risk-free rate is 2% and the project’s beta is 1.4.

Answer 1

The NPV is computed as shown below:

= Initial investment + Present value of future cash flows

Present value is computed as follows:

= Future value / (1 + r)ⁿ

r is computed as follows:

= risk free rate + beta x (return on market - risk free rate)

= 0.02 + 1.4 (0.094 - 0.02)

= 12.36% or 0.1236

So, the present value will be computed as follows:

= - $ 10,000 - $ 10,000 / 1.1236 + $ 4,000 / 1.1236⁶ + $ 4,000 / 1.1236⁷ + $ 4,000 / 1.1236⁸ + $ 4,000 / 1.1236⁹ + $ 4,000 / 1.1236¹⁰ + $ 4,000 / 1.1236¹¹ + $ 4,000 / 1.1236¹² + $ 4,000 / 1.1236¹³

= - $ 7,942.53 Approximately

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