1. By Muhammad Shahid Iqbal
Engineering
Economics
Module No. 11
Annual Equivalent Method
By Muhammad Shahid Iqbal

2. Introduction In annual equivalent method of comparison,
Calculate Annual equivalent revenue of each alternative
Calculate Annual equivalent cost of each alternative
Decision criteria:
The alternative with the maximum annual equivalent revenue in the case of revenue based comparison will be selected as best alternative.
The alternative with the minimum annual equivalent cost in the case of cost based comparison will be selected as best alternative.

3. Revenue-Dominated cash flow analysis
In the first step, find Present worth of Revenue-dominated cash flow diagram using the following expression:
PW = - P + R1[1/(1 +i)1] + R2[1/(1 +i)2] + …………………+ Rn[1/(1 +i)n] + S [1/(1 +i)n]
P = Initial investment
Rn = Net revenue at the end of nth year.
S = Salvage value at the end of nth year. S
R R2 …………… RJ Rn
…… ……………………. j n P

4. Annual Equivalent Revenue
In the second step, the annual equivalent revenue is computed using the following formula:
i(1 + i)n
A = PW (i)
(1 + i) n – 1
If there are more alternatives which are to be compared with this alternative, then the corresponding annual equivalent revenues are computed and compared.
The alternative with the maximum annual revenue should be selected as the best alternative

5. Cost-Dominated cash flow analysis
In the first step, find Present worth of cost-dominated cash flow diagram using the following expression:
PW (i) = P + C1 / (1 +i)1 + C2 / (1 +i)2 + …….…+ Cj / (1 +i)j +……….+ Cn / (1 +i)n - S / (1 +i)n
P = Initial investment
Cj = cost of operation &maintenance at the end of jth year.
S = Salvage value at the end of nth year. S
J n
C C CJ Cn P

6. Annual Equivalent Revenue
In second step, the annual equivalent cost is computed using the following formula:
i(1 + i)n
A = PW (i)
(1 + i) n – 1
If there are more alternatives which are to be compared with this alternative, then the corresponding annual equivalent costs are computed and compared.
The alternative with the minimum annual cost should be selected as the best alternative

7. Annual Equivalent Revenue
Alternatively annual equivalent amount can be calculated by using FW