© 2000 John Petroff
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© 2000 John Petroff |
5)- Further comparison of NPV and IRR
Conflicts between NPV and IRR can arise in numerous circumstances: different lives, different sizes, different risk factors, or different timing of cash flows. The underlying cause of the conflict resides in the assumption of cash flow reinvestment. The process of discounting and time value of money is predicated on interest compounding and discounting (defined in Chapter 2) is predicated on what discount rate is chosen. In IRR calculation, the implied interest rate of reinvestment of cash flows is IRR itself. In NPV calculation, it is the discount rate. Which of the two methods is correct depends on the choice of what is a more realistic rate of reinvestment of cash flows: IRR or discount rate. Most often the reinvestment opportunities that a company has are those that can earn its weighted average cost of capital, because it is what its projects earn on average. Relying on an assumption of weight average cost of capital as the reinvestment opportunity is also more conservative. Thus, NPV is most often the safest basis for decision.
But that may not be always the case. For instance, choosing projects that have positive NPV implies that they earn a higher return than risk adjusted cost of capital. This implies that we expect opportunities for reinvestment of cash flows at higher rates. Higher rates of return can also be required when future inflation is anticipated. To investigate the impact of cash flow reinvestment opportunity, advanced textbooks in financial management recommend calculating an adjusted NPV and an adjusted IRR. These are obtained by first calculating a terminal value which is the future value of cash flows compounded at the opportunity rate of reinvestment (see Chapter 2 for calculation of future value). Then the terminal value is discounted to the present using the weighted average cost of capital. Thus the adjusted NPV is given by
Adjusted NPV = - I0 + S (Ct(1+k0)t ) * ((1 + kc )n – 1) / kc
Likewise, the adjusted IRR is given by
Adjusted IRR = x where I0 = S (Ct(1+k0)t ) * ((1 + x )n – 1) / x
By using the same rate of reinvestment of cash flows for NPV and IRR removes the conflict between NPV and IRR. The additional steps required in the calculation of adjusted NPV and IRR are not intuitively appealing. The complexity of the procedure makes it rather unpopular, and as long as conservative rates of reinvestment are used the results merely confirm the conclusion reached with the unadjusted NPV. This gives even more reason to rely on ordinary NPV. Also keep in mind the rough estimates often used in cash flow projections: the theoretical complexity seems somewhat remote from reality.
To illustrate the conflict between NPV and IRR, two projects, 10 and 11, are presented in Table T-10.11 below. Since conflicts between NPV and IRR for reasons of different lives, risk and sizes were already covered in previous paragraphs, in this example they were removed, and the only remaining cause is the timing of cash flows.
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| IRR |
18% |
15% |
| NPV |
$304.71 |
$386.53 |
| PI |
$1.62 |
$1.80 |
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1 |
-500 |
-500 |
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2 |
120 |
5 |
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3 |
150 |
15 |
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4 |
150 |
50 |
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5 |
150 |
100 |
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6 |
150 |
300 |
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7 |
150 |
580 |
Table T-10.11 shows that project 10 has a higher NPV but lower IRR. To study the complete range of possible conflict, Graph G-10.4 represents all the NPV values for discount rates from 0.01 to 0.20.
Graph G-10.4 shows that project 10 has a superior NPV up to 0.11, then with higher discount rates project 11 has a higher NPV, as well as IRR. This implies that if the rate of reinvestment of cash flows is above 11% there is no conflict. The conflict only arises when the rate of reinvestment of cash flows is below 11%. But in that case, IRR is precisely unrealistically high. This leads once again to the conclusion that NPV is the better basis for decisions. It also reinforces the importance of the choice of an appropriate discount rate that reflects the risk present in a project as well as the opportunity to reinvest cash flows.
See review questions Q-10E5.1 through Q-10E5.6.
See research assignment R-10E5.1.
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