Solved problem on rate of return method - 3
Solved problem on Rate of Return Method - 3
A company is planning to expand its present business activity. It has two alternatives for the expansion programme and the corresponding cash flows are tabulated below. The minimum attractive rate of return for the company is 12%. The following data are to be used in the analysis:
Details
|
Alternative 1
|
Alternative 2
|
Initial
Investment (₹)
|
₹.
5,00,000
|
₹.
8,00,000
|
Estimated
life (years)
|
5
|
5
|
Yearly
revenue (₹)
|
₹.
2,00,000
|
₹.
3,00,000
|
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 1
P = ₹. 5,00,000
n = 5
A1 = A2 = … = A5 = A = ₹. 2,00,000
Alternative 2
P = ₹. 8,00,000
n = 5
A1 = A2 = … = A5 = A = ₹. 3,00,00
Formula used
PW(i) = -P + A (P/A, i, n) + S (P/F, i, n)
Solution
Alternative 1
i = 12%
PW(12%)1 = - 5,00,000 + 2,00,000 (P/A, 12%, 5) + 0 (P/F, 12%, 5)
= - 5,00,000 + 2,00,000 (3.6048) + 0
= - 5,00,000 + 7,20,960 + 0
PW(12%)1 = ₹. 2,20,960
i = 15%
PW(15%)1 = - 5,00,000 + 2,00,000 (P/A, 15%, 5) + 0 (P/F, 15%, 5)
= - 5,00,000 + 2,00,000 (3.3522) + 0
= - 5,00,000 + 6,70,440 + 0
PW(15%)1 = ₹. 1,70,440
i = 18%
PW(18%)1 = - 5,00,000 + 2,00,000 (P/A, 18%, 5) + 0 (P/F, 18%, 5)
= - 5,00,000 + 2,00,000 (3.1272) + 0
= - 5,00,000 + 6,25,440 + 0
PW(18%)1 = ₹. 1,25,440
i = 20%
PW(20%)1 = - 5,00,000 + 2,00,000 (P/A, 20%, 5) + 0 (P/F, 20%, 5)
= - 5,00,000 + 2,00,000 (2.9906) + 0
= - 5,00,000 + 5,98,120 + 0
PW(20%)1 = ₹. 98,120
i = 22%
PW(22%)1 = - 5,00,000 + 2,00,000 (P/A, 22%, 5) + 0 (P/F, 22%, 5)
= - 5,00,000 + 2,00,000 (2.8636) + 0
= - 5,00,000 + 5,72,720 + 0
PW(22%)1 = ₹. 72,720
i = 24%
PW(24%)1 = - 5,00,000 + 2,00,000 (P/A, 24%, 5) + 0 (P/F, 24%, 5)
= - 5,00,000 + 2,00,000 (2.7454) + 0
= - 5,00,000 + 5,49,080 + 0
PW(24%)1 = ₹. 49,080
i = 26%
PW(26%)1 = - 5,00,000 + 2,00,000 (P/A, 26%, 5) + 0 (P/F, 26%, 5)
= - 5,00,000 + 2,00,000 (2.6351) + 0
= - 5,00,000 + 5,27,020 + 0
PW(26%)1 = ₹. 27,020
i = 28%
PW(28%)1 = - 5,00,000 + 2,00,000 (P/A, 28%, 5) + 0 (P/F, 28%, 5)
= - 5,00,000 + 2,00,000 (2.5320) + 0
= - 5,00,000 + 5,06,400 + 0
PW(28%)1 = ₹. 6,400
i = 30%
PW(30%)1 = - 5,00,000 + 2,00,000 (P/A, 30%, 5) + 0 (P/F, 30%, 5)
= - 5,00,000 + 2,00,000 (2.4356) + 0
= - 5,00,000 + 4,87,120 + 0
PW(30%)1 = ₹. -12,880
Therefore Rate of return,
i1 = 28% + [{( 6,400 – 0) / (6,400 – (-12,880))}* (30% – 28%)]
= 28% + 0.663%
i1 = 28.663%
Alternative 2
i = 12%
PW(12%)2 = - 8,00,000 + 3,00,000 (P/A, 12%, 5) + 0 (P/F, 12%, 5)
= - 8,00,000 + 3,00,000 (3.6048) + 0
= - 8,00,000 + 10,81,440 + 0
PW(12%)2 = ₹. 2,81,440
i = 15%
PW(15%)2 = - 8,00,000 + 3,00,000 (P/A, 15%, 5) + 0 (P/F, 15%, 5)
= - 8,00,000 + 3,00,000 (3.3522) + 0
= - 8,00,000 + 10,05,660 + 0
PW(15%)2 = ₹. 2,05,660
i = 18%
PW(18%)2 = - 8,00,000 + 3,00,000 (P/A, 18%, 5) + 0 (P/F, 18%, 5)
= - 8,00,000 + 3,00,000 (3.1272) + 0
= - 8,00,000 + 9,38,160 + 0
PW(18%)2 = ₹. 1,38,160
i = 20%
PW(20%)2 = - 8,00,000 + 3,00,000 (P/A, 20%, 5) + 0 (P/F, 20%, 5)
= - 8,00,000 + 3,00,000 (2.9906) + 0
= - 8,00,000 + 8,97,180 + 0
PW(20%)2 = ₹. 97,180
i = 22%
PW(22%)2 = - 8,00,000 + 3,00,000 (P/A, 22%, 5) + 0 (P/F, 22%, 5)
= - 8,00,000 + 3,00,000 (2.8636) + 0
= - 8,00,000 + 8,59,080 + 0
PW(22%)2 = ₹. 59,080
i = 24%
PW(24%)2 = - 8,00,000 + 3,00,000 (P/A, 24%, 5) + 0 (P/F, 24%, 5)
= - 8,00,000 + 3,00,000 (2.7454) + 0
= - 8,00,000 + 8,23,620 + 0
PW(24%)2 = ₹. 23,620
i = 26%
PW(26%)2 = - 8,00,000 + 3,00,000 (P/A, 26%, 5) + 0 (P/F, 26%, 5)
= - 8,00,000 + 3,00,000 (2.6351) + 0
= - 8,00,000 + 7,90,530 + 0
PW(26%)2 = ₹. -9,470
Therefore Rate of return,
i2 = 24% + [{( 23,620 – 0) / (23,620 – (-9,470))}* (26% – 24%)]
= 24% + 1.428%
i2 = 25.428%
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 alternative 2. Therefore alternative 1 should be selected.
