In: Finance
Iron Works International is considering a project that will produce annual cash flows of $37,900, $46,600, $57,300, and $22,800 over the next four years, respectively. What is the internal rate of return if the project has an initial cost of $113,100?
Answer : Internal rate of return is 17.59%
Calculation of Internal Rate of Return
IRR is rate where PV of cash inflow is equal to PV of cash outflow.
IRR is calculated by Hit & Trial Method.
Lets assume two rates @16% & 18% for purpose of calculation of NPV.
Now, we calculate discounted cash flow @ 16%
Year | Cash Flow | PVF @16% | Discounted Cash Flow |
1 | 37900 | 0.862068966 | 32672.41379 |
2 | 46600 | 0.743162901 | 34631.3912 |
3 | 57300 | 0.640657674 | 36709.68469 |
4 | 22800 | 0.552291098 | 12592.23703 |
Present Value of Cash Inflow | 116605.7267 |
Present Value of Cash Otflow | -113100 |
Net Present Value | 3505.72672 |
Now, we calculate discounted cash flow @ 18%
Year | Cash Flow | PVF @18% | Discounted Cash Flow |
1 | 37900 | 0.847457627 | 32118.64407 |
2 | 46600 | 0.71818443 | 33467.39443 |
3 | 57300 | 0.608630873 | 34874.549 |
4 | 22800 | 0.515788875 | 11759.98635 |
Present Value of Cash Inflow | 112220.5739 |
Present Value of Cash Outflow | -113100 |
Net Present Value | (-879.4261473) |
where,By Interpolation,
IRR = Lower Rate + Lower Rate NPV /(Lower Rate NPV - Higher Rate NPV) * Difference in Rate
Lower Rate = 16%
Lower Rate NPV = 3505.72672
Higher Rate NPV = (879.4261473)
Difference in Rate = 2% (18%-16%)
IRR = 16% + 3505.72672 /[3505.72672 - (879.4261473)]* 2%
=17.59%