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

2. Present Value Period Flow A0 PV(A0) = A0 A5 PV(A5) = A5 / (1 + i ) ^ 51 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

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

4. Net Present Value & Internal Rate of Return

5. 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.

6. 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.

7. Internal Rate of Return

8. Multiples Rates of Return

9. No Rate of Return

10. IRR Reinvestment Assumption

11. Modified Internal Rate of Return

12. Incremental Rate of Return

13. Benefits vs Costs

14. Net Benefits vs Costs