© 2000 John Petroff

2)- Calculation of IRR

An alternative capital budgeting approach is to calculate the total rate of return earned from the project, see Chapter 2 Section 2F-4b. This return is called internal rate of return (IRR). It is the same concept as yield to maturity of bonds. IRR is that specific discount rate for which the combined discounted benefits equal initial outlay; in other words, NPV is zero. The internal rate of return is then compared to the required rate of return (RRR) for this particular type of investment. RRR is the same as the discount rate used for NPV. A positive decision will be made if IRR is greater than RRR.

Example of calculation of IRR: We use spreadsheet formula calculation of IRR for the project of buying the printing press. It gives a value of 11%. Using the spreadsheet NPV formula calculation to verify that such a discount rate gives a zero NPV, we find that it gives a remainder of –1,603. This means that the IRR is too low (i.e. remember the inverse relationship between rate and value). Entering higher discount rates in the spreadsheet formula allows us to reduce the remainder to zero with a discount rate of 11.384%. We can now verify that 11.384 is indeed IRR: NPV = 47,000 x .897795 + 54,000 x .8060359 + 75,000 x .723655 – 140,000 = 42,196.37 + 43,525.94 + 54,274.13 – 140,000 = -3.57 There is still a remainder with a rate of 11.384%. But that should not be a problem because the precision is more than sufficient given the approximation in estimation of required rate of return. To obtain a more precise IRR, one should use a financial calculator. Actually, even 11% is quite acceptable. The rule for IRR is to choose a project if IRR is higher than RRR. Here 11% is clearly higher than 10%. Thus the project should be accepted on the basis of IRR.

Occasionally, there may be problems with IRR calculation when there are more than one outflow in the life of the project as illustrated in Appendix 3 to this chapter. The problem is explored in Section G-4 of this chapter, and methods for resolving such problem are looked at in Chapter 10 Section E.

See review questions Q-3G2.1 and Q-3G2.2.

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