Harold Stone, CFA, is an analyst for Spartacus Venture Capital. Stone is considering investing $3 million in a project with a potential $150 million return over a ten year life. The current risk-free rate is 5%, the equity risk premium is 5%, and the project's beta is 2.0. Stone believes that the project has a 22% probability of failure in the first four years and 13% thereafter. The expected net present value of the project is closest to:
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A. B. C.C
To calculate the expected net present value (NPV) of the project, we need to consider the cash flows associated with the investment and discount them to the present value.
Step 1: Calculate the cash flows: The project is expected to generate a $150 million return over a ten-year period. Since the investment is $3 million, the net cash flow from the project can be calculated as follows: Net Cash Flow = Return - Investment Net Cash Flow = $150 million - $3 million Net Cash Flow = $147 million
Step 2: Calculate the discount rate: The discount rate is used to determine the present value of future cash flows. It consists of the risk-free rate and the equity risk premium, which reflects the additional return expected for bearing the risk of investing in equities. Given that the risk-free rate is 5% and the equity risk premium is 5%, the discount rate can be calculated as follows: Discount Rate = Risk-Free Rate + Equity Risk Premium Discount Rate = 5% + 5% Discount Rate = 10%
Step 3: Calculate the present value of cash flows: To calculate the present value of the expected cash flows, we discount each cash flow by the discount rate and then weigh them by their respective probabilities of occurrence.
For the first four years, there is a 22% probability of failure. Therefore, the expected cash flow for these four years is calculated as: Expected Cash Flow (First Four Years) = Probability of Success * Cash Flow Expected Cash Flow (First Four Years) = (1 - 0.22) * $147 million Expected Cash Flow (First Four Years) = 0.78 * $147 million Expected Cash Flow (First Four Years) = $114.66 million
For the remaining six years, there is a 13% probability of failure. Therefore, the expected cash flow for these years is calculated as: Expected Cash Flow (Remaining Six Years) = Probability of Success * Cash Flow Expected Cash Flow (Remaining Six Years) = (1 - 0.13) * $147 million Expected Cash Flow (Remaining Six Years) = 0.87 * $147 million Expected Cash Flow (Remaining Six Years) = $127.89 million
Now we can calculate the present value of the expected cash flows by discounting them using the discount rate: Present Value (First Four Years) = Expected Cash Flow (First Four Years) / (1 + Discount Rate)^4 Present Value (First Four Years) = $114.66 million / (1 + 10%)^4 Present Value (First Four Years) = $114.66 million / (1.1)^4 Present Value (First Four Years) = $81.23 million
Present Value (Remaining Six Years) = Expected Cash Flow (Remaining Six Years) / (1 + Discount Rate)^6 Present Value (Remaining Six Years) = $127.89 million / (1 + 10%)^6 Present Value (Remaining Six Years) = $127.89 million / (1.1)^6 Present Value (Remaining Six Years) = $81.36 million
Step 4: Calculate the expected net present value: The expected NPV is calculated by subtracting the initial investment from the sum of the present values of the cash flows: Expected NPV = Present Value (First Four Years) + Present Value (Remaining Six Years) - Investment Expected NPV = $81.23 million + $81.36 million - $3 million Expected NPV = $159.59 million - $3 million Expected NPV = $156.59 million
Therefore, the expected net present value of the project is closest to $156.59 million