Annual Equivalent Method
ANNUAL EQUIVALENT METHOD
In
the annual equivalent method of comparison, first the annual equivalent cost or
the revenue of each alternative will be computed.
Then
the alternative with the maximum annual equivalent revenue in the case of revenue-based
comparison or with the minimum annual equivalent cost in the case of cost-
based comparison will be selected as the best alternative.
Revenue-Dominated Cash Flow Diagram
The profit/revenue, salvage value of all
inflows to an organization will be assigned with positive sign and the cost
outflows will be assigned with negative sign is called revenue dominated cash
flow.
A generalized revenue-dominated cash flow
diagram to demonstrate the present worth method of comparison is presented in
Fig.
 |
| Revenue dominated cash flow diagram |
Here,
P
= Initial investment
Rj
= Revenue at the end of the ‘j’th year
i
= Interest rate compounded annually
S
= Salvage value at the end of ‘n’th year
First step:
The
present worth amount of the above revenue dominated cash flow diagram for a
given interest rate i is
PW(i) = -P + R1[1/(1 + i)1]
+ R2[1/(1 + i)2] + ... + Rj[1/(1 + i) j] + Rn[1/(1 + i)n]
+ S[1/(1 + i)n]
The above equation can be simplified
as,
PW(i) = -P + R1 (P/F, i, 1) + R2
(P/F, i, 2) + . . . + Rj (P/F, i, J) + Rn (P/F, i, n) + S (P/F, i, n)
Incase if revenue is equal for all the
given years (R1 = R2 = … = Rj = Rn = A) then the above formula is rewritten as,
PW(i) = -P + A (P/A, i, n) + S
(P/F, i, n)
Second step:
The annual equivalent revenue is
calculated using the following formula,
A = PW(i) (A/P, i, n)
Alternative approach:
For comparing various alternatives
following equation is used.
AE(i)
= - P (A/P, i, n) +
A + S (A/F, i, n)
The corresponding annual equivalent
revenues of different alternatives are calculated and compared. The alternative
which has maximum annual equivalent revenue should be selected as the
best alternative.
Cost-Dominated Cash Flow Diagram
The cost outflows of an organization will
be assigned with positive sign and the profit/revenue, salvage value of all
inflows to an organization will be assigned with negative sign is called cost
dominated cash flow.
A generalized cost - dominated cash flow
diagram to demonstrate the present worth method of comparison is presented in
Fig.
 |
| Cost dominated cash flow diagram |
Here,
P
= Initial investment
Cj
= Revenue at the end of the ‘j’th year
i
= Interest rate compounded annually
S
= Salvage value at the end of ‘n’th year
First step:
The
present worth amount of the above cash flow diagram for a given interest rate i
is
PW(i)
= P + C1[1/(1 + i)1] + C2[1/(1 + i)2] + ... + Cj[1/(1 +
i) j] + Cn[1/(1 + i)n] – S[1/(1 + i)n]
The above equation can be simplified
as,
PW(i) = P + C1 (P/F, i, 1) + C2
(P/F, i, 2) + . . . + Cj (P/F, i, J) + Cn (P/F, i, n) - S (P/F, i, n)
Incase if the cost is equal for all the
given years (C1 = C2 = … = Cj = Cn = A) then the above equation is rewritten
as,
PW(i) = P + A (P/A, i, n) - S
(P/F, i, n)
Second step:
The annual equivalent cost is
calculated using the following formula,
A = PW(i) (A/P, i, n)
Alternative approach:
For comparing various alternatives
following equation is used.
AE(i)
= P (A/P, i, n) + A -
S (A/F, i, n)
The corresponding annual equivalent cost of different
alternatives are calculated and compared. The alternative which has minimum
annual equivalent cost should be selected as the best alternative.
