A technique that's closely related to net present value analysis is the internal rate of return. You'll recall that when CFOs were surveyed, in both the US and Australia - or I should say in surveys conducted around the world - we find time and time again that the internal rate of return method ranks just above the net present value technique in terms of popularity with managers, when assessing new projects. Actually, one point, just while we're on this slide, is that you'll see that if you sum up the percentages, they add up to more than 100%. And this highlights that chief financial officers will use many different techniques in project evaluation, quite often at the same time. So what is the technique? A project's internal rate of return is simply the discount rate that when applied to the project's expected cash flows yields an NVP equal to zero. So, if you recall from standard NPV analysis, the NPV of a project is simply the initial outlay on the project netted off against the present value of all the future expected cash flows that the project is promising. Well, we can adapt this formula for the internal rate of return of a project by simply setting the NPV=0. And then solving for the discount rate that when applied to the cash flows gives us that number. So there are four simple steps to the internal rate of return approach. Just as with NPV, we forecast the expected cash flows, both in terms of timing and the amount of those cash flows. The second step, though, has us selecting a discount rate that we then use to discount the promised cash flows. We then calculate the NPV of the project. And I put NPV in inverted commas to signify the fact that it's not the actual NPV of the project, but it's simply the sum of the discounted cash flows. We compare the calculated NPV with 0. And if the NPV is greater than 0, we increase the discount rate. We penalize those future cash flows by a higher amount per period. If the NPV is less than 0, we decrease the discount rate. So it's an iterative process. It's a process of trial and error. And we continue until we reach NPV=0. Now fortunately we can use a spread sheet or a program, or a financial calculator to calculate what that internal rate of return actually is. The final step as with MVP analysis is to apply the appropriate decision rule which will vary depending upon whether we're dealing with independent or mutually exclusive projects. So let's consider our earlier example from the previous video. We start with a outlay of $2 million, and the project promises $800,000 each and every year for the next four years. So our standard NPV calculation has us discounting those future cash flows by a discount rate of r%. So let's plug in 10% for our discount rate, discount those future cash flows, add up the discounted cash flows, net them off against the $2 million, and we end up with an NPV of $535,892. Pausing for a sec, you'll recall that that was the actual NPV of the project. So we know we're going to need to increase the discount rate to decrease the NPV. That is, we're increasing the penalty applied to those future expected cash flows. So when we use 25% per annum, we plug that in we discount the cash flows, we end up with an NPV of minus $110,720. So we've over penalized. Okay, remember our objective is to get to an NPV = 0. So back and forth we'll go. Then when we plug in 21.86% as our discount rate, low and behold, we end up with an NPV = 0. So the internal rate of return of this particular project is 21.86%. So looking at this graphically, the internal rate of return of a project is simply the horizontal intercept of the relationship between discount rates and NPVs. That is, that discount rate that implies an NPV=0. Now the next step is to apply the decision or the appropriate decision rule, and it depends once again on whether we're dealing with independent projects or projects that are mutually exclusive. So let's say we're dealing with independent projects. Well, now we simply compare the internal rate of return for the project with the appropriate discount rate, given the project's risk, opportunity cost, and the expectations about inflation, that is, the time value of money. So we compare the internal rate of return with that discount rate that we would use for standard NPV analysis. And if the internal rate of return exceeds that rate, then the project is deemed acceptable. If it's less than that rate, then we reject the project. And the reason for that is very simple to illustrate. Let's assume that the required rate of return from the project was 10%. We know that the internal rate of return is in excess of 21%, so this project is deemed acceptable. Why? Well, you'll see that where the internal rate of return exceeds the required rate of return, that also implies positive NPV. So the two techniques, internal rate of return and NPV, are telling you much the same thing. One is using a dollar value, the other, the internal rate of return, is using a percentage value, which managers quite often find easier to work with. Why is it easy to work with? It takes out the question of scale. Let's say that the appropriate required rate of return exceeded 21.86, our internal rate of return. In this case, the project is deemed unacceptable and we would reject the project. Why? Well, once again this implies a result that's consistent with standard NPV analysis, it implies a negative NPV. So, the project isn't acceptable to us. So, what about mutually exclusive projects? Well, the rule with mutually exclusive projects is to accept the project with the highest internal rate of return, provided it exceeds the minimum benchmark. So, once again, as an example, let's assume that the appropriate risk adjusted required rate of return was 10% prone. That's our discount rate that we would use for standard NPV analysis. NPV analysis would tell us to accept project one over project two because it implies a higher net present value at that discount rate. Similarly, the internal rate of return for project one exceeds the internal right of return for project two. Project one is about 22%, project two about 18%. So internal rate of return gives us exactly the same investment outcome, exactly the same ranking of mutually exclusive projects, as would be implied by standard NPV analysis. Or does it? Well let's think about some of the shortcomings of internal rate of return analysis. One of the first problems that you might have with internal rate of return is that some projects simply don't have a positive discount rate that when applied to a project's cash flows yields an NPV=0. So let's say we've got Project 3 and Project 4, and they look a little bit quirky. In fact they're the mirror image of each other. Project 4 involves borrowing. That is a cash in flow up front in return for a series of promise cash out flows. Project 3 looks a lot more like a standard project evaluation. Let's have a look. Project 3 is a very poor project. There is no discount rate that when applied to the cash flows for project three that will yield an NPV=0. Let's pause for a second. This of course implies that discount rates can only be positive, and that makes sense because money has a time value. Similarly, Project 4 is always going to be positive NPV no matter what discount rate you apply to it. So the takeaway from that is that you can't actually use internal rate of return on it's own to make a decision in this case because there is no internal rate of return. So what you would need to do is to calculate NPV. Another problem that you might come across is that projects might have multiple internal rates of return. Take Project 5, for example. Project 5 requires $10.2 million initial investment and promises $24 million at the end of the first year, but requires a cash outflow of $14 million at the end of the second year. Let's just pause for a second. This type of cash outflow at the end of a project is quite common, especially in the mining industry where you might have clean-up costs at the end of the project. Let's have a look at what happens when we plot the NPV of the project against alternative discount rates. And what you find here is that there are in fact two internal rates of return for the project. One at about 7%, the other at about 28%. So how do you know whether to accept this project or not? Let's assume that your risk-adjusted discount rate, your hurdle rate, is 15%. Well, one internal rate of return is less than the hurdle rate. The other internal rate of return is greater than the hurdle rate. You don't know whether you should accept the project until you calculate the NPV of the project. Well if you're going to calculate the NPV of the project anyway, why not just use that technique? So I guess the takeaway here is firstly, the internal rate of return method might give you mixed signals about the acceptability of the project. Secondly, you should always use the NPV technique just to double check your final answer. Another possible problem you might come across when dealing with the internal right of return method, is that you might get inconsistent rankings for mutually exclusive projects. Now, earlier we had a very simple case where one project clearly dominated the other in terms of both internal right of return, and the implied net present value of the project. Well what happens when that's not the case? Let's have a look. So, here we have Project 6 and Project 7. The first thing that you'll notice is that the timing of the cash flow and the amount of the cash flows are quite different between the two projects. Project 6 has a much more even flow of cash flows. Project 7, a lot of its cash flow's are weighted toward the end of its life. Now what this does is change the shape of those graphs from the previous slide. Let's have a look. So Project 6 clearly dominates in terms of the internal rate of return. Its internal rate of intern is far to the right of the internal rate of return of Project 7. So on the basis of internal rate of return, provided those rates exceed the required rate of return, we would always accept Project 6 over Project 7. But have a look at what happens at very low discount rates. At very low discount rates, Project 7 clearly dominates Project 6. It has a higher net present value. But the internal rate of intern technique is telling you to still accept Project 6. Alternatively, as discount rates increase, you'll move out of that area of inconsistency. Now the take away from this is that sometimes it might not be so simple as simply comparing the internal rate of return of two projects. You'll always need to go back and recalculate your NPVs. So, in summary, the internal rate of return technique is a popular discounted cash flow based approach to project evaluation. It represents a discount rate that when applied to a projects cash flows, yields NPV=0. There are four simple steps. Forecast cash flows, selected discount rate, and discount cash flows. Compare the NPV to zero and adjust the discount rate accordingly. Then we apply the decision rule. Finally, we need to exercise some caution. When using the technique, we need to be aware there might be missing internal rates of return, multiple internal rates of return, or inconsistent rankings for mutually exclusive projects on the basis of the technique.