Economic Concepts Christopher R. Bennett Director - Data Collection Ltd. The World Bank Economic Concepts

Present Value Period Flow A0 PV(A0) = A0 A5 PV(A5) = A5 / (1 + i ) ^ 5 1 2 3 4 5 A5 PV(A5) = A5 / (1 + i ) ^ 5 6 7 PV(Aj) = Aj / (1+ i ) ^ j PV(Aj) = Present Value of Aj Aj = Amount at year j i = Discount rate j = Year

Present Value at 12.0% Discount Rate 1.00 in Year 1 = 1.00 in Year 1 Year 2 0.89 Year 3 0.80 Year 4 0.71 1.00 in Year 5 = 0.64 in Year 1 Year 6 0.57 Year 7 0.51 Year 8 0.45 Year 9 0.40 1.00 in Year 1 0 = 0.36 in Year 1 1.00 in = in Year 1 Year 15 0.20 1.00 in Year 20 = 0.12 in Year 1

Net Present Value & Internal Rate of Return

Net Present Value & Internal Rate of Return The Net Present Value (NPV) of a project alternative relative to the without project alternative is the sum of the discounted net annual benefits or costs. The Internal Rate of Return (IRR) is the discount rate at which NPV is zero.

NPV Decision Rule 1. If the NPV is positive, for the chosen discount rate, then the alternative is acceptable. 2. If the NPV is negative, for the chosen discount rate, then the alternative is unacceptable. 3. If the NPV is zero, for the chosen discount rate, then the alternative is indifferent to the without project alternative.

Internal Rate of Return

Multiples Rates of Return

No Rate of Return

IRR Reinvestment Assumption

Modified Internal Rate of Return

Incremental Rate of Return

Benefits vs Costs

Net Benefits vs Costs