Solved problem on rate of return method - 1

Solved problem on Rate of Return Method - 1

Investment X has the net cash flows as follows:

Proposal	End of years
	0	1	2	3	4
Investment X (₹.)	- 10,000	3,000	4,000	5,000	6,000

Find the rate of return of the project.

Given data

P = ₹. 10,000

R1 = ₹. 3,000

R2 = ₹. 4,000

R3 = ₹. 5,000

R4 = ₹. 6,000

S = ₹. 0

Formula used

    PW(i) = -P + A (P/A, i, n) + S (P/F, i, n)

Solution

i₁ = 12%

PW(12%)      = - 10,000 + 3,000 (P/F, 12%, 1) + 4,000 (P/F, 12%, 2) + 5,000 (P/F, 12%, 3)

+ 6,000 (P/F, 12%, 4) + 0 (P/F, 12%, 4)

= - 10,000 + 3,000 (0.8929) + 4,000 (0.7972) + 5,000 (0.7118) + 6,000 (0.6355) + 0

= - 10,000 + 2678.70 + 3188.80 + 3,559 + 3,813

PW(12%)     = ₹. 3239.50

i₂ = 15%

PW(15%)      = - 10,000 + 3,000 (P/F, 15%, 1) + 4,000 (P/F, 15%, 2) + 5,000 (P/F, 15%, 3)

+ 6,000 (P/F, 15%, 4) + 0 (P/F, 15%, 4)

= - 10,000 + 3,000 (0.8696) + 4,000 (0.7561) + 5,000 (0.6575) + 6,000 (0.5718) + 0

= - 10,000 + 2,608.80 + 3,024.40 + 3,287.50 + 3,430.80

PW(15%)     = ₹. 2,351.50

i₃ = 18%

PW(18%)      = - 10,000 + 3,000 (P/F, 18%, 1) + 4,000 (P/F, 18%, 2)

+ 5,000 (P/F, 18%, 3) + 6,000 (P/F, 18%, 4) + 0 (P/F, 18%, 4)

= - 10,000 + 3,000 (0.8475) + 4,000 (0.7182) + 5,000 (0.6086) + 6,000 (0.5158) + 0

= - 10,000 + 2,542.50 + 2872.80 + 3,043 + 3094.8

PW(18%)     = ₹. 1,553.10

i₄ = 20%

PW(20%)     = - 10,000 + 3,000 (P/F, 20%, 1) + 4,000 (P/F, 20%, 2)

+ 5,000 (P/F, 20%, 3) + 6,000 (P/F, 20%, 4) + 0 (P/F, 20%, 5)

= - 10,000 + 3,000 (0.8333) + 4,000 (0.6944) + 5,000 (0.5787) + 6,000 (0.4823) + 0

= - 10,000 + 2,499.90 + 2,777.60 + 2,893.50 + 2,893.80

PW(20%)     = ₹. -4,490.40

Therefore Rate of return,

i           = 18% + [{( 1553.10 – 0) / (1553.10 – (-4490.40))}* (20% – 18%)]

            = 18% + 0.513%

i           = 18.513%

Result

Rate of return of the project = 18.513%.

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