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What is the NPV of a project that costs $100,000 and returns $50,000 annually for 3 years if the opportunity cost of capital is 14%?

Question

What is the NPV of a project that costs 100,000andreturns100,000 and returns 50,000 annually for 3 years if the opportunity cost of capital is 14%?

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Solution

Sure, here's how you can calculate the Net Present Value (NPV) of the project:

  1. Identify the cash flows: The initial cost of the project is 100,000(thisisanoutflowsoitwillbenegative).Theprojectthenreturns100,000 (this is an outflow so it will be negative). The project then returns 50,000 annually for 3 years (these are inflows so they will be positive).

  2. Identify the discount rate: The opportunity cost of capital is 14%.

  3. Calculate the present value of each cash flow: The formula for present value is PV = CF / (1 + r)^n, where CF is the cash flow, r is the discount rate, and n is the year.

    • For the initial cost, n = 0 (as it is at the start of the project), so the present value is -100,000/(1+0.14)0=−100,000 / (1 + 0.14)^0 = -100,000.

    • For the first return, n = 1, so the present value is 50,000/(1+0.14)1=50,000 / (1 + 0.14)^1 = 43,859.65.

    • For the second return, n = 2, so the present value is 50,000/(1+0.14)2=50,000 / (1 + 0.14)^2 = 38,454.09.

    • For the third return, n = 3, so the present value is 50,000/(1+0.14)3=50,000 / (1 + 0.14)^3 = 33,732.89.

  4. Sum up all the present values: The NPV is the sum of all these present values, which is -100,000+100,000 + 43,859.65 + 38,454.09+38,454.09 + 33,732.89 = $16,046.63.

So, the NPV of the project is $16,046.63. Since the NPV is positive, the project is expected to add value and therefore could be considered a good investment.

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