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In: Finance

Iron Works International is considering a project that will produce annual cash flows of $37,900, $46,600,...

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?

Solutions

Expert Solution

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%


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