Question

A project requires an investment of $20 million today. Every year in the next 15 years the project will yield a cash flow of $5 million, with the first $5 million arriving one year from today. The beta of the project is 1.5. The risk-free interest rate is 1% and the expected return on the market portfolio is 10%. Assume that the CAPM holds. What is the NPV of the project?

Answer 1

I apologize for the confusion. I reviewed my previous response and noticed that I made a mistake in my calculations. The correct NPV value using a discount rate of 14.5% is actually $40.38 million, not $45.355 million. Therefore, my previous response was incorrect and I apologize for any confusion it may have caused.

To clarify, the correct NPV calculation using the formula I provided earlier is:

NPV = -$20 + (5 / (1 + 0.145)^1) + (5 / (1 + 0.145)^2) + ... + (5 / (1 + 0.145)^15)

NPV = -$20 + $60.38 million

NPV = $40.38 million

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Answer 2

Answer: 45.355

To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows using the appropriate discount rate. In this case, we can use the Capital Asset Pricing Model (CAPM) to determine the discount rate.

The CAPM formula is as follows:

Expected Return = Risk-Free Rate + Beta * (Expected Market Return - Risk-Free Rate)

Given that the risk-free interest rate is 1% and the expected return on the market portfolio is 10%, we can substitute these values along with the project's beta (1.5) into the CAPM formula:

Expected Return = 0.01 + 1.5 * (0.10 - 0.01)
Expected Return = 0.01 + 1.5 * 0.09
Expected Return = 0.01 + 0.135
Expected Return = 0.145 or 14.5%

Now, let's calculate the NPV of the project by discounting the cash flows. We'll assume a discount rate of 14.5% since it represents the expected return of the project.

Year 1 Cash Flow: $5 million / (1 + 0.145)^1 = $4.357 million
Years 2-15 Cash Flows: $5 million / (1 + 0.145)^2 + $5 million / (1 + 0.145)^3 + ... + $5 million / (1 + 0.145)^15 = $4.357 million + $4.357 million + ... + $4.357 million (15 times)

Now, let's calculate the NPV using the above calculations:

NPV = -$20 million + $4.357 million + $4.357 million + ... + $4.357 million (15 times)

Simplifying the equation:

NPV = -$20 million + $4.357 million * 15

NPV = -$20 million + $65.355 million

NPV = $45.355 million

Therefore, the Net Present Value (NPV) of the project is approximately $45.355 million.