Question

Consider an investment opportunity that requires an upfront payment of $2,500. For the next 15 years (from t=1 to t=15), you expect annual cash flows of $500. Then, for the next 20 years thereafter (starting at t=16), you expect annual cash flows of $250. If the opportunity cost of capital is 8%, what is the NPV of this investment?

Answer 1

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Answer 2

First, the formula for calculating the net present value (NPV) is: NPV = -I0 + CFt (1 + r)^t, where I0 is the initial investment, CFt is the cash flow in period t, and r is the opportunity cost of capital. The initial investment is $2500, and r = 0.08. Then, calculate the present value of the cash flow in the first 15 years: PV = A times 1-(1 + r)^t, where A = 500, n = 15, and r = 0.08. \(PV_1=500\times\frac{1-(1 + 0.08)^{-15}}{0.08}\)\(\approx4279.74\) USD. Next, calculate the present value of the cash flow in the next 20 years at \(t = 15\): Also according to the present value formula of ordinary annuity, this time \(A = 250\) USD, \(n = 20\) years, \(r = 0.08\), first calculate the present value of the cash flow of these 20 years at \(t = 15\) \(PV_{15}=250\times\frac{1-(1 + 0.08)^{-20}}{0.08}\)\(\approx2454.54\) USD. Discount it to the moment \(t = 0\), according to the present value formula \(PV = \frac{PV_{15}}{(1 + r)^{15}}\), then \(PV_2=\frac{2454.54}{(1 + 0.08)^{15}}\)\(\approx773.77\) dollars. Finally, calculate the net present value NPV: \(NPV=-2500 + PV_1+PV_2\). Substituting \(PV_1\approx4279.74\) dollars and \(PV_2\approx773.77\) dollars, we get: \(NPV=-2500 + 4279.74+773.77\)\(= 2553.51\) dollars. Therefore, the net present value of this investment is \(2553.51\) dollars.