. The project rate of return is also the discount rate that would give the proje
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. The project rate of return is also the discount rate that would give the project a zero NPV The rate of return is the discount rate at which NPV equlas zero. This discount rate is known as the project's internal rate of return (IRR). If the opportunity cost of capital is less than the project rate of return, then the NPV of project is positive. $18.3 ? Internal Rate of Return - Example You can purchase a building for $375,000. The investment will generate $25,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?Explanation / Answer
Initial investment in the project = $375,000
Annual cash flows = $25,000 for 3 years
Sale price of building after 3 years = $450,000
To find IRR of a project, we need to calculate NPV of the project at 2 different discount rates.
Let us assume first discount rate to be 10%.
Present value of cash inflows(at 10%) = Annual cash inflows x PVAF(10% , 3 ) + Sale price of building x (PVF10% , 3 )
= 25,000 x 2.487 + 450,000 x 0.751
= 62,175 + 337,950
= $400,125
NPV (at 10%) = Present value of cash inflows - Present value of cash outflows
= 400,125 - 375,000
= $25,125
Since at 10% discount rate, NPV of the project is positive, we must take a higher discount rate so that NPV becomes negative.
Let second discount rate be 13%.
Present value of cash inflows(at 13%) = Annual cash inflows x PVAF(13% , 3 ) + Sale price of building x (PVF13% , 3 )
= 25,000 x 2.361 + 450,000 x 0.693
= 59,025 + 311,850
= $370,875
NPV (at 13%) = Present value of cash inflows - Present value of cash outflows
= 370,875 - 375,000
= - $4,125
Since at 10%, NPV is positive and at 13%, NPV is negative, hence the IRR of the project must lie between 10% to 13%. Exact IRR can be calculated as under:
IRR = Lower rate + {NPV at lower rate/(NPV at lower rate - NPV at higher rate)} x (Higher rate - lower rate)
= 10% + {25,125/(25,125 + 4,125)} x (13% - 10%)
= 10% + (25,125/29,250) x 3
= 10% + 2.58%
= 12.58%
Hence, IRR of the project is 12.58%(Approx.)
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