## Question

###### Determine the Rate of Return (196) for the cash flow shown below, if the MARR is...

Determine the Rate of Return (196) for the cash flow shown below, if the MARR is 7%: Year 0 1-5 6-8 Cash Flow - 200,000 +50,000 +30,000 over 15% less than 10% 13% 11%

## Answers

Let IRR is I%, then

-200000 + 50000 * (P/A, I%,5) + 30000 * (P/A, I%,3) * (P/F, i%,5) = 0

50000 * (P/A, I%,5) + 30000 * (P/A, I%,3) * (P/F, i%,5) = 200000

Dividing by 10000

5 * (P/A, I%,5) + 3 * (P/A, I%,3) * (P/F, i%,5) = 20

using trail and error method

When I = 15%, value of 5 * (P/A, I%,5) + 3 * (P/A, I%,3) * (P/F, i%,5) = 5 * 3.352155 + 3*2.283225 * 0.497177 = 20.166274

When I = 16%, value of 5 * (P/A, I%,5) + 3 * (P/A, I%,3) * (P/F, i%,5) = 5 * 3.274294 + 3*2.245890 * 0.476113 = 19.579362

using interpolation

i = 15% + (20.166274 - 20) / (20.166274 - 19.579362)*(16%-15%)

I = 15% + 0.28%

I = 15.28%

First option is correct ie. IRR is over 15%

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