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The Millers are considering a $200,000 expansion for their existing retail outlet. The expansion would generate $35,000 in cash each year over the next 10 years.  Assuming that CompuTech’s weighted average cost of capital is 8%, calculate the project’s net present value.

Question

The Millers are considering a 200,000expansionfortheirexistingretailoutlet.Theexpansionwouldgenerate200,000 expansion for their existing retail outlet. The expansion would generate 35,000 in cash each year over the next 10 years.  Assuming that CompuTech’s weighted average cost of capital is 8%, calculate the project’s net present value.

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Solution

To calculate the net present value (NPV) of the project, we need to discount the future cash flows to their present value and then subtract the initial investment.

Here are the steps:

  1. Identify the cash inflows from the project. In this case, the Millers expect to generate $35,000 each year for the next 10 years.

  2. Identify the discount rate. The Millers' weighted average cost of capital is 8%.

  3. Calculate the present value of each year's cash inflow. The formula for the present value (PV) of a future cash flow is:

    PV = CF / (1 + r)^n

    where:

    • CF is the cash flow for the year
    • r is the discount rate
    • n is the year number

    Do this for each of the 10 years.

  4. Sum up the present values of all the cash inflows. This gives you the total present value of the cash inflows.

  5. Subtract the initial investment from the total present value of the cash inflows. This gives you the NPV of the project.

If the NPV is positive, the project is expected to generate more cash than the cost of the investment, and it would be a good investment. If the NPV is negative, the project is expected to generate less cash than the cost of the investment, and it would not be a good investment.

Let's calculate:

Year 1: PV = 35,000/(1+0.08)1=35,000 / (1 + 0.08)^1 = 32,407.41 Year 2: PV = 35,000/(1+0.08)2=35,000 / (1 + 0.08)^2 = 30,006.49 Year 3: PV = 35,000/(1+0.08)3=35,000 / (1 + 0.08)^3 = 27,783.42 Year 4: PV = 35,000/(1+0.08)4=35,000 / (1 + 0.08)^4 = 25,726.13 Year 5: PV = 35,000/(1+0.08)5=35,000 / (1 + 0.08)^5 = 23,821.05 Year 6: PV = 35,000/(1+0.08)6=35,000 / (1 + 0.08)^6 = 22,056.34 Year 7: PV = 35,000/(1+0.08)7=35,000 / (1 + 0.08)^7 = 20,421.24 Year 8: PV = 35,000/(1+0.08)8=35,000 / (1 + 0.08)^8 = 18,905.22 Year 9: PV = 35,000/(1+0.08)9=35,000 / (1 + 0.08)^9 = 17,498.35 Year 10: PV = 35,000/(1+0.08)10=35,000 / (1 + 0.08)^10 = 16,192.18

Total present value of cash inflows = 32,407.41+32,407.41 + 30,006.49 + 27,783.42+27,783.42 + 25,726.13 + 23,821.05+23,821.05 + 22,056.34 + 20,421.24+20,421.24 + 18,905.22 + 17,498.35+17,498.35 + 16,192.18 = $224,797.83

NPV = Total present value of cash inflows - Initial investment = 224,797.83224,797.83 - 200,000 = $24,797.83

So, the NPV of the project is $24,797.83. Since the NPV is positive, the project is expected to generate more cash than the cost of the investment, and it would be a good investment.

This problem has been solved

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