Imagine that you have two potential projects. You only have the resources to do one. Which project do you choose?
There are any number of reasons why a project should be chosen. If you not interested in making a profit (i.e. cold hard cash) on the project, then it may not matter which project gets completed.
If you do need to make a profit, then comparing the internal rate of return of both project will give help you decide which project to choose.
What is Internal Rate of Return?
The internal rate of return is “the discount rate at which the net present value of a project equal zero.”
I appreciate that 99% of people out there just thought, “Wow, that is useless to everybody except finance majors” (my MBA was in IT Management – so I understand how you feel).
In reality internal rate of return is easily understood, first we need to look at a few concepts.
Time Value of Money
The big concept is that $100 today is worth more that $100 next week. If you have the money in your hand you can do something with it (buy something, or invest it and earn a return). The “return” for the use of money is called “interest.”
Interest can be simple (paid once) or compound (interest is paid on the interest).
Future value is how much we will have if $X is invested at Y interest rate. The future value formula:
Future Value : Fn = P(1+r)n
We can also find out how much $X is worth today by finding the Present Value.
Present Value: P = Fn(1+r)n
In both formulas:
F = accumulation or future value
P = value today
r = interest rate per period
n = number of periods from today
Therefore, “net present value” is how much money we will make (or lose) on the project. When net present value is zero we find the internal rate of return.
Internal rate of return can be thought of as the interest rate we are going to receive on our investment.
Simple Example (no compound interest):
A project will cost $1,000 and will result in profits of $1,100 in one year.
Present Value is $1,000, the Future Value is $1,100, the term is for 1 year:
To find the Internal Rate of Return we solve for r (the interest rate).
r= (Future Value/Present Value) 1/n – 1
r = (1100/1000)1/1 -1 = 10% = Internal Rate of Return
note: In the above example n = 1 year
Gets ugly fast
As more returns and periods are added, the calculations quickly become more complex. Calculating internal rate of return by hand becomes a laborious process of trial and error: 1. guess at a internal rate of return, 2. calculate present value for all returns, 3. if present values equal zero then stop, 4. if present values are not equal to zero guess again.
Fortunately internal rate of return is easily calculated using a financial calculator (refer to your calculators user manual) or by using a computer spreadsheet (which is my preference).
Both Microsoft Excel and OpenOffice.org Calc have a built in function to calculate internal rate of return. In both spreadsheets the function is “IRR”.
Example:
We have two potential projects.
Project 1 requires an investment of $1,000 and will return $1,500 over three years (0 after the first year, $500 the second year, and $1,000 the third year).
Project 2 requires an investment of $1,000 and will return $1,500 over three years ($250 after the first year, $250 the second year, and $1,000 the third year).
Which project has the higher internal rate of return?
Open your spreadsheet of choice and enter -1,000 is the first row (e.g. “a1”) then enter 0 in a2, 500 in a3, and then 1,000 in a4. In a5 enter “=IRR(a1:a4)” (obviously, without the quotes) and you should find out that Project 1 has an internal rate of return of 16.54%.
Calculate the internal rate of return for Project 2 by entering the data into cells b1 through b4 (-1,000 in b1, 250 in b2, 250 in b3, and 1,000 in b4), and entering “=IRR(b1:b4)”. We find out that Project 2 has an internal rate of return of 18%.
Note that the first value is negative because we are spending/investing money at the start of the project. If you get 17% as your result you spreadsheet is probably rounding the result (you can change the “cell format” to allow numbers after decimal point).
Project 2 has a slightly higher internal rate of return and should be given preference over Project 1.
Threshold Test
Internal rate of return is also used as a risk “threshold” test. Obviously a project with a negative internal rate of return will be shelved. Just because a project has a positive return doesn’t mean that it is worth doing. A “threshold” internal rate of return level is set (which will be different for different companies/industries). Anything below that level won’t be considered/isn’t worth doing.
The threshold test becomes obvious when thought of as, “How much interest can we make if we just stick out money in a zero risk investment?” “Zero risk” is often set at the interest rate of U.S. treasury securities.
Conclusion
There you have internal rate of return in a nutshell. We’ve covered the concepts and avoided the math as much as possible (if you’re a finance nut then I apologize for butchering your subject – do you want to buy my Financial Accounting textbooks?). For all of the “non-finance” nuts out there I recommend “Financial Intelligence: A Manager’s Guide to Knowing What the Numbers Really Mean” by Berman, Knight, Case.
Good luck – and let me know if you want those text books.
