Return on investment – ROI

Today I want to talk about return on investment and in particular, what I want to discuss is the strengths and weaknesses of the internal rate of return relative to the net present value rule. So let’s get started.

Today we are turning to a new topic, return on investment. But before diving in I actually want to spend a little bit of time recapping our last topic, discounted cash flow analysis. So what we did in our DCF topic is we began by introducing decision making. We showed some evidence, looked at some survey evidence of what people in practice were doing, CFOs of non-financial companies, private equity managers, and investment bankers. And we showed that they used a number of different criteria, DCF, or NPV, IRR and payback period.

Then we turned to looking at free cash flow, one of the key components of any DCF and we talked about the components that make up **free cash flow** and how to aggregate them.

Then we talked about forecast drivers, or the assumptions necessary to forecast each of the **components of free cash flow**, and we did it in the context of a capital budgeting example of a tablet.

We then applied our forecast drivers to forecast out each component of free cash flow and aggregate up to get a **free cash flow projection**.

We then looked at different decision criteria, that is, we figured out what to do with those cash flows, and ultimately what decision to make regarding the tablet. Specifically, we looked at MPV, IRR, and payback period. We talked about their strengths, some of their weaknesses, and then we closed out the topic with a discussion of sensitivity analysis, an integral element of any DCF.

Now I really want to continue on the theme set by DCF. And talk about return on an investment, and really emphasize IRR versus MPV, the two most commonly used decision metrics. So let’s get started.

So, recall that the internal rate of return of an asset is the one discount rate, such as the NPV of the asset’s free cash flows equals zero.

So, I have NPV. I have cash flow. We could have free cash flow. Do not let the convention confuse you. IRR is much broader than just free cash flow, as is cash flow. Anyway, IRR is just that one discount rate such that the NPV is equal to zero.

The IRR Decision Rule as you might recall says to accept all projects for which the IRR is greater than R, reject all projects for which the IRR is less than R, where R is our hurdle rate or opportunity cost of capital. The opportunity cost of capital.

And the intuition was simple, if it’s costing us R percent to raise money to fund investment, that investment should return something at least as big if not greater than R. Preferably greater. Now, I am going to spend some time here talking about IRR, a little bit of motivation here. Because rates of return are popular measures used for making decisions. Remember the survey evidence. The internal rate of return was the most popular decision criteria used by CFOs. It just edged out NPV. All right, and likewise for PE firms, private equity firms, internal rate of return is by far the dominant decision criterion used for evaluating investments. So it’s really important to understand this criterion.

So let’s compare it to NPV, and let’s do it by way of an example, shortly I should say. So first, the IRR is going to lead to the same decision, accept or reject, as the NPV rule if all negative cash flows precede all positive cash flows.

So here are some examples of cash flow sequences at least the sign of the cash flows where the IRR and NPV rules with coincide. Right? So I pay a bunch of money today and then I get nothing but positive cash flows. I pay money for the first three years. I do not like that. Let’s do this. For year one, two, and three and then years four, five and on are all positive. The key is that the negatives have to come before the positives, negative before positive then IRR and NPV lead to the same decision.

If that pattern of cash flow signs is violated, not only may IRR and NPV rules not coincide, not lead to the same decision, but you can get some pretty wacky stuff with IRR from multiple IRRs. In which case, which one do you choose? It is not obvious. Two imaginary IRRs and I mean mathematically, imaginary IRRs. You will get an IRR times some number times the square root of negative one, which is really hard to convey to a CEO. Trust me. So, let’s think about whether or not we can compare projects using IRR.

And here’s what I want to work in the context of a specific example. Imagine Wharton wants to upgrade its IT system and overhaul its network infrastructure. So it puts out a request for proposals in RFP and in comes a bid from Cisco. And the Cisco bid we evaluate to generate $60 million in cost savings over three years for an upfront cost to Wharton of $100 million. Now if Wharton’s cost of capital is 12%, what is our assessment of this bid?

First things first, write down the cash flows. Here they are. We are going to get, all right, bid one. It’s going to cost us $100 million today, then we’re going to experience cost savings of $60 million for the next three years. We can compute, let’s clear this up. We can compute the IRR by solving this equation, right? Just set the NPV for the project equal to zero and solve for IRR that gets us 36%.

**whats a good return on investment?**

Now because the IRR is greater than the discount rate, our hurdle rate, remember that was 12%.

And the cash flow signs are proper, that is, they follow right, negatives followed by positives, this project looks good.

If we compute the NPV, if we just discount future cash flows by the Wharton’s cost of capital, 12%, we’re going to get an NPV of $44.11 million.

Which is greater than zero, well that looks good, too.

So both IRR and NPV point in the same direction. This looks like a reasonable bid, Warton’s going to be better off.

By accepting it. But then Cisco comes back and they say, we’re going to give you the same cost savings, $60 million over three years, but now what we’re going to do instead of charging you $100 million up front, we’re going to spread the cost over time. $20 million today and then $35 million over three years.

So let’s try evaluating this bid. I mean it sounds somewhat attractive if we can avoid that huge upfront bill.

So for bid one a, here are the costs. It is going to cost us $20 million up front as opposed to 100 million, but we are going to have to pay 35 million over the next three years.

We still get the same costs savings so the net cash flows for this bid are -20, 25, 25, and 25.

Let’s compute the IRR and NPV. IRR first. Well, the IRR, we set the NPV of these cash flows equal to 0. Solve for the IRR. And we get, whoa! 112%. That is impressive.

That is very impressive. And we see that the IRR for bid 1a, this bid, is 112% is greater, much greater, I’m going to put much greater, than the bid one, the first bid from Cisco which had an IRR of 36%.

We can also compute the NPV by just discounting by the cost of capital 12%. Warten’s cost of capital. That gets us a NPV of $40.05 million. So bid 1 had an NPV of 44.11 million, bid 1a has a NPV of 45.05 million. Which, according to the NPV rule, means Bid #1 is better than Bid #1a. What is going on here, right? NPV says Bid #1 is better, right? 44.1 is bigger than the 40.05.

IRR says Bid #1a is better because 112% returns better than 36% return.

What do we do? Well, let’s take a closer look. That is the first thing we do. And we see, let’s look. Here is Bid #1, Cisco’s costs are $100 million, all upfront.

For bid 1a, sorry Cisco’s cost. Wharton’s cost is $100 million up front. Bid 1a, Wharton’s cost are only $20 million up front but then $35 million every year thereafter. And so what bid 1a is doing is, is it’s inserting a loan. Cisco’s lending us money. In particular, they are lending us $80 million today in exchanged for $35 million over the next three years. Here is a question, what is the interest rate on the loan?

We can figure that out. Right, I can figure out what the interest rate on this loan is. How? Just compute the IRR.

And if we do that, we see that the interest rate is 15%, and again, this is just the IRR, I want to emphasize. I want to clean that up. If I move this over here, this will be zero and this equals – 80. So that is just the IRR, it is 15%. It is also the Yield to Maturity.

Which we have discussed in the past. Well, is the 15% high or low? Is it good or bad?

Well, it’s terrible. Cisco’s charging us a higher interest rate than our cost of capital. In other words, we can go to the capital markets and raise the money for a loan at 12%, as opposed to implicitly borrow from Cisco at 15.

See, what happened is the IRR increased because the initial investment fell more than the future cash flows, right? Small payoffs on a small investment can generate very large returns. We are dividing by small numbers here, but the NPV rightfully fell because Cisco is lending us money at an interest rate that is greater than our cost of capital. So the IRR spiked because we have this smaller upfront investment. That is very misleading. The NPV fell; it accurately captured the bad loan Cisco was inserting into the deal. Therefore, the lesson here is that IRR projects can mislead when we are deciding among projects. Whereas NPV will not mislead in comparisons. The larger the NPV, the greater the value.

Now let’s briefly talk about a couple of additional bids just to hammer home the point. We also heard from Juniper and Huawei who had costs and cost savings for us as laid out in this, table, and how would we rank these bids according to the IRR and NPV? Well, we know how to compute the IRR and NPV; we just replicate or repeat, what we did for Cisco, or what we have done in past lectures. And you get this set of IRRs and this set of NPVs. And what you quickly see is that the IRR ranking is that the Huawei #3 bid is better than the #2 bid from Juniper, which is better than the #1 bid from Cisco, the exact opposite ranking relative to what NPV tells us.

And here’s a picture of what’s going on. I’ve got the discount rate. We have seen a picture like this before. I’ve got the discount rate on the horizontal axis and I’ve got NPV on the vertical axis, and each line graphs the relation between NPV as a function of the discount rate. So at our cost of capital here, if we go up to each line we can see the NPVs of each of the bids. And quite clearly the Cisco bid on the green line is better than the Juniper bid on the red line, which is better than the Huawei bid which is on the blue line.

When we go over here, where the lines cross the x-axis, right? These are the IRRs. By definition, the IRRs is the discount rate where the MPV equals zero. Here are the IRRs. In this case, we see that the IRR for Huawei is much bigger than the IRR for Juniper, which is bigger than the IRR for Cisco. The exact opposite ranking according to the IRR rule or relative to the MPV rule. What is going on? Well if you look more closely at the cash flow streams, you can see that Huawei has small upfront cost. That increases the IRR relatively speaking and Juniper has front-loaded cash flows, which is going to increase the IRR relative to the Cisco bid.

So one lesson is the IRR does not address differences in scale and there is no better way to emphasize this point than would you rather earn 100% on a $1 investment or 10% on $1 million of investment. Well quite clearly, the latter you are going to wind up with a lot more money.

Some more intuition, Juniper’s bid is actually like Cisco’s with an embedded loan and you can see that here where Cisco charges 100 million then you get the cost savings. What Huawei is doing is it’s giving you an $80 million loan and then charging you 40 every period as opposed to the 35 million that Cisco’s 1a bid was charging you.

And if we ask what the loan is for this interest rate, what the interest rate is on this loan, we see it’s 23%. The IRR to this loan is just 23%. Which is much bigger than the 12% cost of capital that Wharton faces. Okay, let’s summarize this. What are the lessons here? Look, internal rate of return is useful. It is a way to convey the attractiveness of a project or an investment in a manner that investors get returns, okay? The problem with the IRR Decision Rule is that it only works or overlaps with NPV in certain situations. When we are not comparing projects and when the cash flow signs are, all negative cash flows preceding all positive cash flows. So I think the end message here is that use IRR in your investment analysis, your capital budget. But be cognizant of the limitation, know when to use it. Know when not to use it. That is what is critical.