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Consider a project with free cash flows in one year of $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%.The NPV for this project is closest to:Group of answer choices$14,100.$6250.$10,000.$18,600.

Question

Consider a project with free cash flows in one year of 90,000inaweakeconomyor90,000 in a weak economy or 117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is 80,000,andtheproject′scostofcapitalis1580,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%.The NPV for this project is closest to:Group of answer choices14,100.6250.6250.10,000.$18,600.

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Solution

To calculate the Net Present Value (NPV) of the project, we first need to calculate the expected cash flow, then discount it to the present value using the project's cost of capital.

Step 1: Calculate the expected cash flow. Since each outcome (weak economy and strong economy) is equally likely, we can simply take the average of the two possible outcomes:

Expected cash flow = (Weak economy cash flow + Strong economy cash flow) / 2 Expected cash flow = (90,000+90,000 + 117,000) / 2 = $103,500

Step 2: Discount the expected cash flow to present value using the project's cost of capital:

Present value = Expected cash flow / (1 + cost of capital) Present value = 103,500/(1+0.15)=103,500 / (1 + 0.15) = 90,000

Step 3: Subtract the initial investment from the present value to get the NPV:

NPV = Present value - Initial investment NPV = 90,000−90,000 - 80,000 = $10,000

So, the NPV for this project is closest to $10,000.

This problem has been solved

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