[MUSIC] >> One more thing on, on this. And this is whether, remember when we calculated for Starbucks as 7.2%, at cost of capital, and when we used that 7.2% to evaluate whether we should invest in this coffee shop that was devel delivering cash flows for five years. When we did the discounting to calculate the NPV, remember that we used the same discount rate for year 1, year 2, year 3, year 4, and year 5. In other words, we assume that, that 7.2% was not changing over time. Now, of course, we know that discount rates change all the time. The easiest way to remember that is the following. Remember that a bonds yield to maturity is basically the cost of debt and the bonds yield to maturity was tied to the market price and that market price is going to be changing all the time. So strictly speaking, the cost of debt is changing all the time, therefore, the cost of capital is changing all the time. Remember how we calculated the cost of equity. We calculated that with a cap m and the starting point of the cap m was the race for rate. And that race for rate was the yield on ten year treasury notes. At least that's the way we calculated in the case of Starbucks. Well, guess what? That yield on ten year treasury notes is actually also changing all the time. So, the cost of equity is changing all the time and therefore the cost of capital is also going to be changing all the time. So if we have time changing, cost of debt, and cost of equity and therefore, cost of capital, then should ashu, actually use a cost of capital that changes over time? Or should we use as we've done in the Starbucks evaluation of that coffee shop. It cost them 7.2% overtime. Well this question it looks just as complicated as the other one but it's a little easier to solve from this point of view. First if you're going to use a time changing discount rate, that is a discount rate that changes over time, well that, first off, complicates quite a bit the calculation of the NPV. And the reason why it complicates the, the comp, the calculation of the NPV, is basically because remember what we did in year two when we actually evaluated the coffee shop. We basically discounted that by 1 plus 7.2% raised to the power of 2. Well, if you have a discount rate that changes over time, you can no longer do that. You have to do 1 plus the discount rate of the first period multiplied by 1 plus the discount rate of the second period. Right, now imagine what would happen in period five. If we had the ability, that's a huge if, and I'll get back to that in just a second, but if we had the ability of calculating the five discount rates, one for each of the five years for which we need to discount cashflow, notice that instead of doing what we did, 1 plus 7.2% raised to the power of 5, we couldn't do that. We would need to do 1 plus discount rate of the first period times 1 plus the discount rate of the second period over, and over, and over times 1 plus the discount rate of the fifth period. So we would get a huge denominator. Well imagine if you're evaluating a project that is going to deliver cash flows for 20, 30, 40 years. You would actually have this huge denominators as discount rates. You wouldn't have the very simple one plus the discount rate raised to the power of however many periods away that cash flow is, is coming. I don't want to over-complicate you with this, but I'm just trying to impress upon you the fact that if you're going to assume a change in discount rate then the NPVs going to be a little bit more complicated. It gets even worse with the IRR, because, you know, we can always let's suppose that we have a project in which we have no mathematical problems of those we discussed. We have a clean IRR and this IRR is 10%. All right? And now we have, you know, we, we estimate for year one a cost of capital of 7.2% and for year two a cost of capital of 12% and for year three a cost of capital of what have you, it doesn't really matter. But to which discount rate we're going to compare our 10% IRR? We don't know. It is that the one of the first period, the one of the second, the one of the third, the one of the last? That we don't know, so we cannot really use IRR if we have more than one discount rate. But here comes a more fundamental reason why you may not want to, and I, I might, I, I want to stress the word may. You may not want to calculate different discount rates for different periods. And, and the problem is we really have very little ability to foresee what those discount rates are going to be in the future. When we say, look we calculate the cost of capital Starbucks knowing everything we know about the company and building that into the cost of capital calculation today, we not really saying when we use this 7.2% over and over and over and over again, we're not really saying that we believe that discount rates are not going to change. We know that they're changing all the time. In fact, by the time we're done calculating the number, the number probably already changed because the market price of the debt might have changed. The return on debt might have changed. The ten year treasury bond might have cha, treasury bond yield might have changed. And the cost of equity might have changed, too. And all that implies that we know that this discount rate that we estimated is going to be changing all the time. What do we expect to get is we expect to get the average rate. You know, in the same way, if you remember back in our very first session when we said, look, if I invest in the world market, I'm going to get a mean annual return of 7.7%. That doesn't mean that we expect to get 7.7, 7.7, 7.7, 7.7 over and over again. The only thing that we are saying is that our mean annual rate is going to be 7%. But if you remember, we were getting positive returns, negative returns, low returns. This is exactly the same thing. In other words, when we say we're going to discount these five year cash flows at 7.2%. What we're really saying is that on average we expect to get this number right. We know that the number is going to be changing all the time over time but if we are confident that it's a good estimate of the cost of capital today maybe if the business doesn't change all that much the appropriate discount rate shouldn't change all that all that much. Let me finish this session with that. this, what you're seeing. This is the former CFO of Eli Lilly, large sophisticated company. And you would think that you know this company had knowledgeable enough people to implement any type of adjustments or any type of little refinements that you need to implement in terms of the discount rate. Well, the reason I like this example is because in this little interview what the CFO says is the following, and let me read that part to you that I'm highlighting there in, in blue. It says to evaluate long term investment projects, Lilly used a firm white cost of capital as [INAUDIBLE] rate. Although we make other medical products, we consider ourselves primarily a pharmaceutical company and so we calculate one cost of capital for the whole company. Let's stop there for just a second. What this, this guy is saying is, look we are a large company. We have many divisions. We know that they're not identical and because we know they're not identical, we know that they have somewhat different risk profiles, but we don't think that they're all that different. And therefore, instead of calculating a discount rate for this division, we just calculate one discount rate for the whole company that is the cost of capital and that we apply to all the divisions. Is he saying that all the divisions are identical? No, he's simply saying, going back to the word we used before, that these divisions are not substantially different and because they are not then we use the same cost of capital for all of them. Let's keep reading. And it says. Currently, it's 15% and has been for about 20 years. Now, of course, a discount rate doesn't remain constant for 20 years. What he's saying is basically, look, we think that this is a proper discount rate. For the type of risk that we bear, for the type of return that we need to deliver to the capital providers, and, of course, this number is going to change over time. But 15% seems to be the right number to discount to make long term evaluations of investment projects. In other words it's, it's it's a number that is sufficient for us to make calculation. It's sufficient to use across different divisions. It's sufficient to use over time. We know that neither these is going to be constant over time. Now its going to be constant across divisions. But neither one thing nor the other bothers us all that much. So, you know, with a large sophisticated company we could do a lot better. We don't think we need to bother. So, we use 15% for all the divisions and we use 15% as a constant number over time. So this is pretty much it for, for today. Just backing up a little bit what we've done is discussing the two main tools that we use to evaluate projects NPV. An IRR, net present value, and internal rate of return. The rules that we need to use for them are very straightforward. A positive net present value says that we should invest, a negative present value says that we shouldn't. An internal rate of return higher than the discount rate says we should invest. An internal rate of return lower than the discount rate said we shouldn't invest, although, that second part remember it's a little tricky. There may be circumstances in which IRR, the, the Internal Rate of Return, the discount rate of that fancy equation that we've seen before, may be problematic. It may have more than one solution, it may have no solution at all. It may suffer from the scale problem when we're comparing different projects. So like any tool, handle with care. So what we've done in this session is basically calculating an NPV, calculating an IRR, and then having that data applying that to a project, and then thinking a little bit further in terms of do we need more than that? Do we need more than one discount rate? Do we need more than one discount rate because we have different countries, we have different divisions, or we think that this number is going to change over time? There aren't extremely clear answers to those questions. But at least we entertain arguments pro and con in terms of whether we should go ahead with that or not. So this is it for today. We're done with the issue of product evaluation. Remember there's a, a lecture there's a reading that compliments this session. That actually deals with more problems of the IRR and actually dealt goes a little bit deeper into this whole idea of present value. We have only one more session to go. We'll be talking about corporate value creation soon, so see you then. [MUSIC]