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NPV Calculate the net present value (NPV) for the following 20-year projects.Comment on the acceptability of each. Assume that the firm has an opportunity costof 14%.a. Initial investment is $10,000; cash inflows are $2,000 per year.b. Initial investment is $25,000; cash inflows are $3,000 per year.c. Initial investment is $30,000; cash inflows are $5,000 per year.

Question

NPV Calculate the net present value (NPV) for the following 20-year projects.Comment on the acceptability of each. Assume that the firm has an opportunity costof 14%.a. Initial investment is 10,000;cashinflowsare10,000; cash inflows are 2,000 per year.b. Initial investment is 25,000;cashinflowsare25,000; cash inflows are 3,000 per year.c. Initial investment is 30,000;cashinflowsare30,000; cash inflows are 5,000 per year.

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Solution

To calculate the Net Present Value (NPV), we need to know the initial investment, the annual cash inflows, the discount rate (in this case, the opportunity cost), and the duration of the project. The formula for NPV is:

NPV = ∑ [Rt / (1+i)^t] - C0

where: Rt = net cash inflow during the period t i = discount rate or return that could be earned in alternative investments t = number of time periods C0 = initial investment

Let's calculate the NPV for each project:

a. Initial investment is 10,000;cashinflowsare10,000; cash inflows are 2,000 per year for 20 years; discount rate is 14%.

NPV = ∑ [2000 / (1+0.14)^t] - 10000 Calculate the sum from t=1 to t=20, then subtract the initial investment.

b. Initial investment is 25,000;cashinflowsare25,000; cash inflows are 3,000 per year for 20 years; discount rate is 14%.

NPV = ∑ [3000 / (1+0.14)^t] - 25000 Calculate the sum from t=1 to t=20, then subtract the initial investment.

c. Initial investment is 30,000;cashinflowsare30,000; cash inflows are 5,000 per year for 20 years; discount rate is 14%.

NPV = ∑ [5000 / (1+0.14)^t] - 30000 Calculate the sum from t=1 to t=20, then subtract the initial investment.

A positive NPV indicates that the projected earnings (in present dollars) are greater than the anticipated costs (also in present dollars). Generally, an investment is considered good if the NPV is positive.

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