Solved problem on annual equivalent method – 2
Solved problem on annual equivalent method – 2
Find
the best alternative using the annual equivalent method of comparison. Assume
an interest rate of 12% compounded annually.
Details
|
Alternative A
|
Alternative B
|
Alternative C
|
Initial
cost (₹)
|
₹.
5,00,000
|
₹.
8,00,000
|
₹.
6,00,000
|
Annual
receipt (₹)
|
₹.
2,00,000
|
₹.
1,50,000
|
₹.
1,20,000
|
Life
(years)
|
10
|
10
|
10
|
Salvage
value (₹)
|
₹.
1,00,000
|
₹.
50,000
|
₹.
30,000
|
Given data
Method
= Annual equivalent method - Revenue dominated cash flow
i
= 12%
Alternative A
P
= ₹. 5,00,000
A1
= A2 = … = A10 = A = ₹.
2,00,000
n
= 10
S
= ₹. 1,00,000
Alternative B
P
= ₹. 8,00,000
A1
= A2 = … = A10 = A = ₹.
1,50,000
n
= 10
S
= ₹. 50,000
Alternative C
P
= ₹. 6,00,000
A1
= A2 = … = A10 = A = ₹.
1,20,000
n
= 10
S
= ₹. 30,000
Formula used
AE(i) = -P (A/P, i, n) + A + S (A/F, i, n)
Solution
Alternative A
AE(12%)1 = -5,00,000 (A/P, 12%, 10) + 2,00,000 + 1,00,000
(A/F, 12%, 10)
= -5,00,000 (0.1770) + 2,00,000 +
1,00,000 (0.0570)
= - 88,500 + 2,00,000 + 57,000
AE(12%)1 = ₹. 1,68,500
Alternative B
AE(12%)2 = -8,00,000 (A/P, 12%, 10) + 1,50,000 + 50,000
(A/F, 12%, 10)
= -8,00,000 (0.1770) + 1,50,000 +
50,000 (0.0570)
= -1,41,600+ 1,50,000 + 2,850
AE(12%)2 = ₹. 11,250
Alternative C
AE(12%)3 = -6,00,000 (A/P, 12%, 10) + 1,20,000 + 30,000
(A/F, 12%, 10)
= -6,00,000 (0.1770) + 1,20,000 +
30,000 (0.0570)
= -1,06,200 + 1,20,000 + 1,710
AE(12%)3 = ₹. 13,970
Result
In annual equivalent
revenue method, the alternative which has maximum annual equivalent revenue is
the best alternative. Therefore alternative A is the best alternative.