Solved problem on rate of return method - 2
Solved problem on Rate of Return Method - 2
A firm desires has identified three mutually exclusive investment proposals whose details are given below. The minimum attractive rate of return for the firm is 12%. The following data are to be used in the analysis:
Details
|
Alternative A1
|
Alternative A2
|
Alternative A3
|
First
cost (₹)
|
₹.
1,50,000
|
₹.
2,10,000
|
₹.
2,50,000
|
Estimated
life (years)
|
5
|
5
|
5
|
Annual
Revenue (₹)
|
₹.
45,570
|
₹.
58,260
|
₹.
69,900
|
Find the best alternative based on the rate of return of comparison.
Given data
Method = Rate of return method - Revenue dominated cash flow
i = 12%
Alternative A1
P = ₹. 1,50,000
n = 5
A1 = A2 = … = A5 = A = ₹. 45,570
Alternative A2
P = ₹. 2,10,000
n = 5
A1 = A2 = … = A5 = A = ₹. 58,260
Alternative A3
P = ₹. 2,50,000
n = 5
A1 = A2 = … = A5 = A = ₹. 69,900
Formula used
PW(i) = -P + A (P/A, i, n) + S (P/F, i, n)
Solution
Alternative A1
i = 12%
PW(12%)1 = - 1,50,000 + 45,570 (P/A, 12%, 5) + 0 (P/F, 12%, 5)
= - 1,50,000 + 45,570 (3.6048) + 0
= - 1,50,000 + 1,64,270.736 + 0
PW(12%)1 = ₹. 14,270.736
i = 15%
PW(15%)1 = - 1,50,000 + 45,570 (P/A, 15%, 5) + 0 (P/F, 15%, 5)
= - 1,50,000 + 45,570 (3.3522) + 0
= - 1,50,000 + 1,52,759.754 + 0
PW(15%)1 = ₹. 2,759.754
i = 18%
PW(18%)1 = - 1,50,000 + 45,570 (P/A, 18%, 5) + 0 (P/F, 18%, 5)
= - 1,50,000 + 45,570 (3.1272) + 0
= - 1,50,000 + 1,42,506.504 + 0
PW(18%)1 = ₹. -7,493.504
Therefore Rate of return,
i1 = 15% + [{( 2,759.754 – 0) / (2,759.754 – (-7,493.504))}* (18% – 15%)]
= 15% + 0.807%
i1 = 15.807%
Alternative A2
i = 12%
PW(12%)2 = - 2,10,000 + 58,260 (P/A, 12%, 5) + 0 (P/F, 12%, 5)
= - 2,10,000 + 58,260 (3.6048) + 0
= - 2,10,000 + 2,10,015.648 + 0
PW(12%)2 = ₹. 15.648
i = 15%
PW(15%)2 = - 2,10,000 + 58,260 (P/A, 15%, 5) + 0 (P/F, 15%, 5)
= - 2,10,000 + 58,260 (3.3522) + 0
= - 2,10,000 + 1,95,299.172 + 0
PW(15%)2 = ₹. -14,700.828
Therefore Rate of return,
i2 = 12% + [{( 15.648 – 0) / (15.648– (-14,700.828))}* (15% – 12%)]
= 12% + 0.00339%
i2 = 12.00339%
i2 ≈ 12%
Alternative A3
i = 12%
PW(12%)3 = - 2,50,000 + 69,900 (P/A, 12%, 5) + 0 (P/F, 12%, 5)
= - 2,50,000 + 69,900 (3.6048) + 0
= - 2,50,000 + 2,51,975.52 + 0
PW(12%)3 = ₹. 1,975.52
i = 15%
PW(15%)3 = - 2,50,000 + 69,900 (P/A, 15%, 5) + 0 (P/F, 15%, 5)
= - 2,50,000 + 69,900 (3.3522) + 0
= - 2,50,000 + 2,34,318.78 + 0
PW(15%)3 = ₹. -15,681.22
Therefore Rate of return,
i3 = 12% + [{( 1,975.52 – 0) / (1,975.52 – (-15,681.22))}* (15% – 12%)]
= 12% + 0.335%
i3 = 12.335%
Result
In rate of return method, the rate of return for all the given alternatives is higher than the minimum attractive rate of return 12%. There for all the alternatives are taken into consideration. Here the rate of return of alternative 1 is higher than the remaining two alternatives. Therefore alternative 1 should be selected.
