Question

A project has two possible outcomes. The good outcome returns $8,000 next year and occurs 88% of the time. The bad outcome is total failure, returning $0, the rest of the time. If the risk free interest rate is 4.8%, the expected market return is 10.4%, and the project beta is 1.1, what is the price of the project today?

Answer 1

The price of the project today, taking into account the possible outcomes and adjusting for risk and time value of money using CAPM is approximately $6,341.73.

Step-by-step explanation:

The price of the project today can be calculated using the expected return and the project's beta to determine the required rate of return, then discounting the expected outcome by this rate. First, we calculate the expected return of the project:

• Expected return = ($8,000 * 88%) + ($0 * 12%) = $7,040.

Now we apply the Capital Asset Pricing Model (CAPM) to find the required rate of return:

• Required rate of return = Risk-free rate + [Beta * (Market return – Risk-free rate)]
• Required rate of return = 4.8% + [1.1 * (10.4% - 4.8%)] = 10.96%.

Finally, we discount the expected return by the required rate of return to find the present value, which will be the price today:

• Price today = Expected return / (1 + Required rate of return)
• Price today = $7,040 / (1 + 10.96%) ≈ $6,341.73

The price of the project today is approximately $6,341.73.