Session 15: Investment Returns II - Getting to Time Weighted Cash Flows

In this session 15 of a 36 session corporate finance class, I'd like to talk about the process by which we go from earnings to cash flows. From cash flows to incremental cash flows, and from incremental cash flows to time weighted incremental cash flow returns. We're now in the midst of talking about measuring investment returns on a project. So let's see where we are in this process. The last session we talked about why cash flows are better than accounting earnings, but we spent the bulk of the session talking about an accounting measure of return. Return on investment capital, or its variant, return on equity. In this session, I want to talk about moving from accounting earnings to cash flows, from cash flows to incremental cash flows, and then from incremental cash flows to time weighted incremental cash flows. To do this, I'm going to return to the accounting earnings that I estimated for this particular theme park, and go through the three step process for going from earnings to cash flows. So this is the accounting earnings page for the project. Let's see if we can convert these accounting earnings into cash flows. Remember again, add depreciation amortization, subtract out capital expenditures, subtract out change in working capital. Magic, I've got the cash flows in the project. Notice now that in year zero, you get a big negative number. That makes sense. You're spending a lot of money in year zero, but it was capital expenditures. Wasn't showing up in your accounting earnings statement, but it does show up now. So that's the first item you see, is capital expenditures across the board. I've added back depreciation and amortization, right? And if you remember, I subtracted it out to get to accounting earnings. That might make it seem like depreciation amortization is getting canceled out, but it isn't. Here's why. It leaves its imprint on the cash flows because it saves you taxes. In fact, we know exactly how much taxes we save because of depreciation amortization. Take year one, have depreciation of 50 million, right? With a 36% tax rate, I'm going to save myself $18 million in taxes every year. The change in working capital converts my accrual earnings into cash earnings. And each year, I take the total working capital, I compute the change in each year, and that affects my cash flows. So we've gone from earnings to cash flows by adding back depreciation, subtracting our capex, subtracting our change in working capital. Now, you ready? Let's talk about incremental cash flows. There are two big adjustments I want to make here. First, in year zero, remember there was a half a billion dollars of that two and a half billion that you've already spent? You're not going to get that money back if you reject this investment. In finance, we call that a sunk cost. And one of the first principles in decision making is that you ignore sunk cost. I know it's easier said than done because as human beings, we chase after sunk costs. It's very difficult psychologically to ignore what's already happened, but you should. So I'm going to take the half a billion dollars out of the initial investment saying, hey, I'm not going to get that money back if I reject this investment. No point loading it into the decision making process. So that's the first item I'm adjusting for. The second is notice that I'm adding back a portion of the allocated GNA. That's a two thirds of the GNA that's going to be there anyway. And because it's going to be there anyway, it's not incremental. Here's a very simple way to test to see whether something is incremental. Ask yourself two questions. What will happen if I take this investment? What will happen if I don't take this investment? If your answer is the same to both questions, that item is not incremental. Think about the half a billion you've already spent. What will happen if you take this investment? You've spent a half a billion. What will happen if you don't take this investment? You've spent a half a billion. This particular investment makes no decision, no effect on that sunk cost, on that cost. That's why we treat it as a sunk cost. We take it out of the process. Same reasoning with the allocated GNA. What will happen if I take this project? Well, two thirds of the GNA will get allocated to the project. What will happen if I don't take this project? Well, that expense will just get allocated somewhere else. The company will still bear the expense, so it's a non-incremental expense. The one adjustment I have to make is because I got a tax benefit from that allocated GNA, when I add it back, I'm going to add back the after tax amount, which is the allocated GNA, the two thirds of it, times one minus the tax rate. So with those adjustments, I've gone from cash flows to incremental cash flows. These are the cash flows I should be focusing on when I look at this investment. There's one final step to take, right? I want to time wait these cash flows. That's just a fancy way of saying I want to discount these cash flows, because that's exactly what discounting is. When I talk about discounting a cash flow in the future, I'm going to discount it more, the further into the future that cash flow is, and the riskier that cash flow is. So discounting is effectively time waiting cash flows. So if I can figure out a way to discount these cash flows, I've time waited them. So I'm going to spend a page listing out some very simple present value equations. Don't read too much into this page, because much of this is built into your financial calculators now. I just prefer to see the equations behind those present value buttons. So fundamentally, there are only five types of cash flows you're ever going to face in finance. First is a simple cash flow, $100 five years out, $10 million, 10 years out. Discounting it is simple. Just take the cash flow, divide it by 1 plus the discount rate raised to whenever you get that cash flow. The second type of cash flow you might run into is an annuity. An annuity is a constant cash flow that occurs at regular intervals. $10 million every year for the next 20 years is an annuity. The equation that you see there is the present value of an annuity. Incidentally, this is exactly what happens in the background when you hit the payment, the N, the R, and the PV button on a financial calculator. It goes through this equation and comes up with the present value. Try it out if you don't believe me. The third is a growing annuity. Let me explain what a growing annuity is. $100 growing at 5% a year for the next 25 years is a growing annuity. You can compute the present value of a growing annuity two ways. The long way is to get the cash flow each year, discount each cash flow back to the present, add up the present value. That'll always work. The other is to use the equation that you see listed here. That'll give you the present value of a growing annuity. A very useful equation to use when you have an annuity stretching out over 25 or 30 years and there's a fixed growth rate over that period. The fourth cash flow is a perpetuity. That's a constant cash flow every year forever. The present value of a perpetuity is just the cash flow divided by the discount rate. And the final and the most dangerous cash flow is a growing perpetuity. That's a cash flow growing at a constant rate forever. The present value of a growing perpetuity is the expected cash flow one year out, it's always one year out, divided by the difference between the discount rate and the growth rate. Now you can see why it's so dangerous because if you look at the denominator, if you let the growth rate get out of control, this number can move towards infinity. Those are the five types of cash flows you will face and the present value equations are listed there. Now let me get back to the project because I'd like to bring this into the process to compute a time-weighted incremental cash flow return. There are two basic time-weighted incremental cash flow measures of return. The first is called a net present value and here's what you do in the net present value. You take the present value of each cash flow on a project, you add up those present values and you come up with a sum. The sum of the present values of all of your cash flows is the net present value. How do you use it? Very simple. If that net present value is greater than zero, even if it's one dollar, it's a good project. That sounds weird, right? Five million dollar project, you're saying a net present value of a dollar is still good. Remember the net present value is over and above your cost of capital. So you're earning what you need to make plus an extra dollar. Would you rather make a billion? Sure, but if you have a choice between taking a project with a net present value of one dollar and doing nothing, I'd suggest you take the project with a net present value of a dollar. The second measure of incremental cash flow returns is called the internal rate of return. It's that discount rate that makes the present value of your cash flows and the net present value of your cash flows equal to zero. It's a time-weighted incremental cash flow analog to the accounting return on capital. How do you use it? You compute the internal rate of return on a project. You compare it to the cost of capital. The internal rate of return is greater than your required return. You have a good investment. So you either do an NPV, which is a dollar value or an absolute value, and compare it to zero, or you compute the IRR, or the internal rate of return, and you compare it to your hurdle rate. Either way, you've computed an incremental cash flow measure of return. Let's try this for our project. Before we do that, though, there's one loose end I want to tie up. In the last session, I talked about cutting this project off after 10 years and why it was so unfair given that it was a theme park with potentially a lifetime of 50, 60, or even 100 years. Not much you can do about it with an accounting return, but with cash flows, there's something I can try to do. Here's what I'm going to try to do. I'm going to assume that the cash flows beyond year 10 will continue to grow at the inflation rate. Put differently, I'm assuming that Disney will be able to raise ticket prices for the theme park at the inflation rate after year 10, but that the number of tours will level off in year 10. Do you see why I'm making this assumption? If I let the number of tours continue to grow after year 10, my theme park is going to get really crowded, and I'll have to make fresh investments to expand it. This way, the theme park stays fixed, but the cash flows continue to grow at 2% a year forever. I know the forever scares you, and I'll come back to that in a minute, but if you make that assumption of cash flows growing at 2% a year forever, you have a growing perpetuity, right? The present value is expected cash flow one year out, which in this case is the cash flow in year 11. And that's basically what you see in the numerator here is the $715 million is your cash flow in year 10 grown out one extra year at 2%. That's a US dollar inflation rate because I'm doing everything in US dollars. Divided by the cost of capital, we came up with a theme park of 8.46% minus the 2% growth rate and perpetuity. The $11,275 million here is what I'm estimating the value of the theme park to be at the end of year 10. This is called a terminal value, as opposed to what? As opposed to a salvage value. There are some projects where at the end of the project life, you shut the project down, you sell off the assets for whatever you can get for them, and you collect that money. That's called salvage value. This is a going concern value or a terminal value. And that terminal value is my rough estimate of what I think I can sell this theme park for at the end of year 10. Lock, stock, barrel, and Mickey included. Everything's got to be included in the theme park if somebody's going to be willing to pay you $11,275 million. But what I've done by doing this computation is broaden what happens after year 10 into my cash flows without explicitly having to estimate year 11, year 12, year 13, etc. I'm now ready to compute the net present value of this theme park. What you see on this table are my incremental cash flows every year for the next 10 years that came from the previous table, the $11,275 million, which is my estimate of this theme park as a going concern after year 10, and the present value at the cost of capital of 8.46%. The net present value that I get for this theme park is roughly $3.3 billion. Now, before I go further, let me go back and clarify on this forever assumption. I know you're saying nothing lasts forever, even the very best theme park. You're absolutely right. But here's why I went with the forever. If I'd used a 50-year life after year 10, the net present value that I'd have got would have been very close to $3.3 billion. In fact, my value for this theme park, if I use a 50-year life instead of forever, is about $11 billion. So by using a perpetuity, I got a much simpler equation. It didn't change the value very much. What I'm arguing for is we have very long-term projects. There's nothing wrong with using a perpetuity assumption, even though you know that the project will not last forever. And based on the net present value, here's what I see as my conclusion. This is a good project. By taking this project, Disney will increase its value as a company by $3.3 billion. That is one of the most useful properties of a net present value. When you take a project with a positive net present value, your value as a business increases by that amount. Conversely, if you take a project with a negative net present value, your value as a business will decrease by that amount. You might wonder why you would ever take a project with a negative net present value, but that's exactly what you're doing when you overpay for another company in an acquisition, for instance. That's why many bidding companies, when you see them win an acquisition battle, will often see their stock prices go down after they win the battle. So the net present value says that this project is a good project. And let's try the IRR. Now, the way in which most people compute internal rate of return or IRR is they use the function on Excel or in the calculator. I actually prefer to draw what's called a net present value profile. Sounds fancy, right? But it's really not that complicated. What I do is I compute the net present value at different discount rates, and I plot it out. So you see the graph there. You're saying, what does it tell me? First, see the point at which it crosses the axis? That's where the net present value is zero. That's my internal rate of return for this particular project. In this case, this theme park's IRR is 12.6%. That's higher than my cost of capital. Here's the other thing I learned when I do a net present value profile. It tells me how sensitive my project is to changes in my discount rate. If you're familiar with the concept of bond duration, bond duration measures how sensitive a bond price is to changes in interest rates. This is the analogous measure for a project. This is a measure of project duration. It measures how sensitive the net present value of my project is to changes in my discount rate. Now, the 12.6% IRR, is it a good project? That's simple. Compare it to your cost of capital. When you compare it to the cost of capital, which is 8.46%, it confirms a conclusion that we got from the net present value. This is a good project. Now, before we go any further, there's one final byline I want to talk about. A lot of corporate finance classes, a lot of time is spent talking about NPV versus IRR. We often talk about why and when they're different. There are three cases where you can get differences. The first is when there are differences in scale and you're comparing two projects with very different scales. What I mean by that is you compare a million-dollar project to a billion-dollar project, NPV is going to tilt you towards a larger project because it's a measure of absolute value. IRR is going to tilt you towards smaller projects. We know that. The second issue where there might be a difference is you can get only one NPV for a project, but you can get multiple IRRs. In fact, any time there's a change in sign in your cash flows, when you look at a project, there's another internal rate of return waiting to be found out. That, again, is an issue sometimes when you have projects with changing cash flows. One, you might have a negative to positive. You might see another switch in year seven and again in year 15. The third and final issue, and this is an issue that's worth thinking about, is these rules make slightly different assumptions about what you do with cash flows you get in year one, two, and three. If you have a 10-year project, what do you do with those earlier cash flows? The NPV assumes you can reinvest those cash flows at the hurdle rate, the cost of capital if you're doing a cash flow analysis to the entire business or the cost of equity if you're doing an equity analysis. The IRR assumes you can make the IRR. In the context of this theme park, when I use the NPV, I'm assuming that the cash flows I get in the theme park will get reinvested at the cost of capital. But if I use the IRR of 12.6%, I'm assuming Disney is going to be able to invest those cash flows that it gets in the earlier years at a 12.6% return, which might be a little dangerous because this might be a once-in-a-lifetime investment. The IRR is a little more dangerous than the assumption it makes about reinvestment. But here's the bottom line. If you're looking at an individual project as we are, 95 times out of 100, when the NPV is positive, the IRR is going to be greater than the cost of capital. We're fighting about the small change here. So if your choice is IRR or return on capital, I'd rather that you use the internal rate of return than the return on capital. If it's between NPV and IRR, I'm not going to make as much of an issue about which one to use because they're both time-weighted incremental cash flow returns. That's about it for this particular session. In the next session, we'll tie up the loose ends on measuring investment returns.