NPV Vs IRR

Water Cooler
#1

Can someone please inform me on why the reinvestment rate of the two indexes are different ?

#2

They’re not indices; they’re methods.

There’s a dichotomy amongst finance types

  • Group A believes that when you have an investment and you receive cash flows from that investment, those cash flows are still considered part of the investment until the investment ends.
  • Group B believes that when you have an investment and you receive cash flows from that investment, those cash flows are now your to do with as you please, and are no longer considered part of the investment.

I fall squarely into group B, so I have no reinvestment issue: the NPV or IRR is calculated only on the amount remaining in the investment, not on cash outflows from the investment.

Others fall into group A. For them, the reinvestment income from the cash outflows is part of the original investment, and will be counted in the total return on the investment when it finally ends. For these people, the only way they can earn the discount rate they use to compute the present value is to reinvest those cash flows at exactly that same discount rate.

For NPV, the discount rate is the cost of capital: the WACC, say.

For IRR, the discount rate is the IRR, which is likely different from the WACC.

Thus, for people in group A, the reinvestment rate in an NPV calculation is, say, WACC, while the reinvestment rate in an IRR calculation is IRR. This explains why NPV and IRR give different rankings of several projects: they have different reinvestment assumptions.

#3

S2000magician.

Thanks for the explanation. I have an additional question: Isn’t there a mathematical proof which of the 2 groups is correct? At least I never came across such proof. I was only aware of an explanation similar to yours above.

Thanks, Oscar

#4

huh? the proof is in the pudding.

#5

Both methods are correct.

#6

@magician thank you ,I am building a base in quants than moving to FRM later on.

#7

I don’ think there is any contradiction between Group A and Group B as long as you are clear on what the use of the IRR/YTM is. Clearly the calculation of either one incorporates no assumptions about reinvesting anything - you simply discount all cash flows at the time they are received. To repeat, no reinvestment assumption is ever, never ever, incorporated in the mathematical computation of the IRR/YTM. That’s what Group B is focused on, and they have formulas to show it.

But if you use IRR/YTM as a measure of the expected return on your initial investment, you need to be careful. Return over what period? For example, the very name “yield to maturity” may imply that you are earning that yield when you purchase a bond and hold it to maturity, while receiving (and spending!) some periodic coupons until the final principal payment. That would not be the case unless you reinvest all of your periodic coupons at the YTM, from the time you receive the coupon to the maturity date. Again, it is a very simple calculation to demonstrate that your terminal wealth would be different if you invest $X over N years at a rate YTM, vs. if you hold a coupon-paying bond with current price $X, and current yield YTM, maturing in N years. That’s what Group A is obsessed about.

There is no paradox or diverging philosophies, mostly semanitcs and Group A and Group B representatives talking over each other and not listening.