So in the previous clip, we talked about the IRR rule when we have an accept or reject decision. The conclusion we came to is that as long as we have an investing project, the IRR rule and the NPV rule agree. So that's fine, and that may give people who really like to compute IRR is some comfort because perhaps most of the time we're faced with investing projects. However, in practice, often the way the NPV rule and the IRR rule are used is not as an accept or reject decision, but to compare two different projects. Here we run into a host of other problems with the IRR. Let me just give you an example to show you what I'm talking about. So let's say we have the following two projects: project A and B, will make a chart. Project A starts with cash flow of negative 100. So the cost of project A is 100 and then the payoff is 400. Project B, starts with a cost of 250 and then a payoff of 650. Suppose that our discount rate is 10%, the NPV in each case we can compute in case for Project A is 264, for project B is 341. We can also compute the IRR. For example, for project A IRRA is equal to 400 over 100 minus one, which equals 300. That's a pretty good IRR, 300%. For B, we can do a similar calculation to show that the IRR is 160%. So these are both really good projects. In terms of accept or reject, the NPV rule and the IRR rule agree both projects should be accepted. But what if you can only do one of the two projects? You'd like to do both, but you only can do one. Maybe you only currently have the staff to do one. Maybe you only have the financing to do one. For whatever reason, you can only do one project. Maybe they compete with each other. Which one do you pick? You pick the one with a greater rate of return or do you pick the one with a greater NPV? Which one will increase the value of the company by more? The answer is clearly B. project B, will increase the value of the company by 341, whereas project A will increase the value of the company by 264. So we're comparing 341 and 264. 341 is bigger than 264, so we should choose B. But what about the fact that B has this lower IRR? It doesn't matter because B can be done at a larger scale. To summarize, based on the last example, we saw that IRR A is bigger than IRR B. IRR A being 300%, IRR B being 160%. But NPV B is bigger than NPV A. NPV B being 341, NPV A being 264. How is it possible that these two can disagree? In this case, B is operated at a larger scale. The problem with a rate of return measure like the IRR is it doesn't tell you about scale, and when we're talking about increasing the value of a company, you care about the scale because it's the eventual dollars that you ultimately care about. So scale matters and you should choose the project with the highest NPV. If you could scale up project A, that would clearly be the best, but you can't always do that. Now we're going to consider a different problem with IRR, one that has to do with timing rather than scale. So we have to projects, D and E, they cost the same, let's say $100. So they operate on the same scale. At time one, project D pays $100 but project E pays 10. Then at time two, project D pays 10 and project E pays 10, and at time three project D pays 10, but project E pays 120. Which of these projects is better? Well, that's going to depend on the discount rate. You can see that these projects differ in the timing of their cash flows. If we show the NPV of D and E on a plot, so NPV looks something like this. This is NPV E, and notice that when R is zero, by the way, the NPV of E is equal to 40. The NPV of D looks something like this. I'm exaggerating a bit, but you get the idea. When R is zero, the NPV of D is 20. So the IRR of E is about 13%. The IRR of D is higher, it's 16%. Note that IRR D is greater than IRR E. Does that mean that we should choose D? Not necessarily. Suppose your discount rate is 10%. So if R equals 10%, then the NPV of D is actually lower than the NPV of E. What's going on here? NPV of D is going to be less sensitive to the discount rate than the NPV of E. Because for the NPV of D, you get your money back sooner. Notice that this is a flatter line. E has a steeper line. The question is, do you care if you get your money back sooner? We're all else equal, of course, it's better to get your money back sooner because of the time value of money. But for project E, you get much more money in general than for project D. It really matters whether your discount rate is low or high. If your discount rate is less than the point at which these two cross, then project E is preferred. Notice that this is very closely related to something that was discussed earlier, namely the yield-to-maturity on a coupon bond. So remember that in our coupon bond discussion, we said that the yield to maturity is a flawed yardstick because to actually receive the yield to maturity as your return, you need to reinvest the coupons. The IRR is a similar concept to yield to maturity. In fact, it is exactly the same as yield to maturity if you define the project as purchase a bond. If the project is purchase a bond, then the IRR equals the yield to maturity, the price equals the present value of the payments. So the NPV of purchasing the bond is zero. Project D would clearly be better than Project E. If you could invest that wonderful, $100, you got a time one at the rate of return of 16%, the IRR for D. But there's no reason to think you've necessarily could. That's the danger here of thinking about IRR as a measure of return for these two projects. You can't necessarily re-invest. You don't necessarily have a new project D coming along at a time one. Another way to think about this as Project E is being unfairly penalized by being a long-term project. So if discount rates are 16%, yeah, this 120 way out here, that looks pretty bad. But if discount rates are only 10%, then you don't care. You're willing to wait. This is actually, I think, a very relevant problem to a lot of investors. If you talk to venture capital investors, they often use a IRR rule where they will say, "we're looking for IRRs that are bigger than 16%". The idea seems to be that they have an investment that has a 60% IRR, and so they're looking for investments with better IRRs. That rule penalizes long-term investments. Unless the actual discount rate in the economy is 16%, which it's not, you can actually make more money by choosing projects that have a lower IRR but increase value by more because those payoffs are weighted more to the future. That's something to think about. This is a tricky case, but one that I think we see all the time. It's a little counterintuitive, but it illustrates that rates of return when we apply them to investment decisions, real investment decisions aren't necessarily the way to go.
