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Internal Rate of Return

29 April, 2015 - 16:59

Another common yardstick of valuing projects is Internal Rate of Return, or IRR. IRR is the discount rate which, when applied to a project, will cause the NPV to be zero. Let us use a simple example:

Say you are going to lay out $100,000 for a project. This project will produce cash flows of $15,000 in year 1, and $50,000 in year 2, and $70,000 in year 3. What is the IRR?

In order to solve this problem, we must set up an equation for NPV and set it to zero:

0 = -100,000 + \frac{15,000}{1+r} + \frac{50,000}{(1+r)^2} + \frac{70,000}{(1+r)^3}

Then we simply solve for r. Of course, as there are 3 variables in this equation, we cannot solve it algebraically, and must use either a financial calculator, Excel, or some type of graphing program or calculator. Using a financial calculator, the answer can be found as 13.454%. So, if the company's cost of capital is 13%, then this project is good to take. However, if the company requires a 13.5% return, the project would not be wise.

There is one caveat to using IRR to evaluate projects. IRR is a rate, not an amount. So if your company must choose between two projects, one with an IRR of 8%, and another with an IRR of 11%, the 11% IRR project is not always the best choice.

Project A Project B
Initial Investment $100,000 $1,000
Return after 1 yr $108,000 $1,110
Total Profit $8,000 $110
IRR 8% 11%

So you see, the project with the higher IRR ends up netting the company far less money, as the projects are mutually exclusive. An example of resource allocation maybe that 70 project Bs can be undertaken, vs 1 project A. Project B has a higher IRR and would result in $7700 with an outlay of $70000 , not accounting for administrative costs, whereas 1 Project A would result in 8000 for $100000 outlay, and be likely less costly administratively. For the effort, work or taking on risk, the rate of return would be 7.7% or 8% on capital vs 3% from term deposit with no effort, (assuming tax deductions, e.g. for depreciation of capital plant/equipment/property , are already accounted for by reduction in tax payment cash outflow, which are included in annual cash flow calculations ).