Npv vs. Irr

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NPV Versus IRR W.L. Silber

I.

Our favorite project A has the following cash flows:

-1000 0

0 1

0 2

+300 3

+600 4

+900 5

We know that if the cost of capital is 18 percent we reject the project because the net present value is negative:
- 1000 + 300 600 900 + + = NPV 3 4 (1.18) (1.18) (1.18)5

- 1000 + 182.59 + 309.47 + 393.40 = -114.54

We also know that at a cost of capital of 8% we accept the project because the net present value is positive:
- 1000 +
300 600 900 + + = NPV 3 4 (1.08 ) (1.08 ) (1.08 )5

- 1000 + 238.15 + 441 .02 + 612 .52 = 291.69

II.

Thus, somewhere between 8% and 18% we change our evaluation of project A

from rejecting it (when NPV is negative) to accepting it (when NPV is
…show more content…
Indeed, the low cost of capital makes those “large but delayed” cash flows quite valuable.

VIII.

One way to understand the preference of NPV over IRR, more generally, is to

recognize that NPV uses the “correct” rate, i.e., the cost of capital, to discount the cash flows, rather than an “arbitrary” rate, i.e., the IRR, that makes NPV =0. Another way to understand the superiority of the NPV rule is that the discounting process inherent in both the IRR and NPV techniques implicitly assumes the reinvestment of the cash flows at whatever discount rate is used, either IRR or the cost of capital. When the IRR is very high relative to the cost of capital it is unrealistic to assume reinvestment at that high rate. This is especially damaging when comparing

two investments with very different timing of cash flows. We will revisit this reinvestment assumption later, under our discussion of yield to maturity on coupon bonds, where its meaning will become

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