0:33

When we did the discounting to calculate the NPV, remember that we

Â used the same discount rate for year 1, year 2, year 3, year 4, and year 5.

Â In other words, we assume that, that 7.2% was not changing over time.

Â Now, of course, we know that discount rates change all the time.

Â The easiest way to remember that is the following.

Â Remember that a bonds yield to maturity is basically the cost of debt and

Â the bonds yield to maturity was tied to the market price and

Â that market price is going to be changing all the time.

Â So strictly speaking, the cost of debt is changing all the time,

Â therefore, the cost of capital is changing all the time.

Â Remember how we calculated the cost of equity.

Â We calculated that with a cap m and

Â the starting point of the cap m was the race for rate.

Â And that race for rate was the yield on ten year treasury notes.

Â At least that's the way we calculated in the case of Starbucks.

Â Well, guess what?

Â That yield on ten year treasury notes is actually also changing all the time.

Â So, the cost of equity is changing all the time and

Â therefore the cost of capital is also going to be changing all the time.

Â So if we have time changing, cost of debt, and cost of equity and therefore, cost

Â of capital, then should ashu, actually use a cost of capital that changes over time?

Â Or should we use as we've done in the Starbucks evaluation of that coffee shop.

Â It cost them 7.2% overtime.

Â Well this question it looks just as complicated as the other one but

Â it's a little easier to solve from this point of view.

Â 2:12

First if you're going to use a time changing discount rate,

Â that is a discount rate that changes over time, well that,

Â first off, complicates quite a bit the calculation of the NPV.

Â And the reason why it complicates the,

Â the comp, the calculation of the NPV, is basically because remember what we

Â did in year two when we actually evaluated the coffee shop.

Â We basically discounted that by 1 plus 7.2% raised to the power of 2.

Â Well, if you have a discount rate that changes over time,

Â you can no longer do that.

Â You have to do 1 plus the discount rate of

Â the first period multiplied by 1 plus the discount rate of the second period.

Â Right, now imagine what would happen in period five.

Â If we had the ability, that's a huge if, and

Â I'll get back to that in just a second, but if we had the ability of calculating

Â the five discount rates, one for each of the five years for

Â which we need to discount cashflow, notice that instead of doing what we did,

Â 1 plus 7.2% raised to the power of 5, we couldn't do that.

Â We would need to do 1 plus discount rate of the first period times 1

Â plus the discount rate of the second period over, and over, and

Â over times 1 plus the discount rate of the fifth period.

Â So we would get a huge denominator.

Â Well imagine if you're evaluating a project that is going to

Â deliver cash flows for 20, 30, 40 years.

Â You would actually have this huge denominators as discount rates.

Â You wouldn't have the very simple one plus the discount rate raised to

Â the power of however many periods away that cash flow is, is coming.

Â I don't want to over-complicate you with this, but

Â I'm just trying to impress upon you the fact that if you're going to assume

Â a change in discount rate then the NPVs going to be a little bit more complicated.

Â 4:05

It gets even worse with the IRR, because, you know,

Â we can always let's suppose that we have a project in which we

Â have no mathematical problems of those we discussed.

Â We have a clean IRR and this IRR is 10%.

Â All right? And now we have, you know,

Â we, we estimate for year one a cost of capital of 7.2% and for

Â year two a cost of capital of 12% and for

Â year three a cost of capital of what have you, it doesn't really matter.

Â But to which discount rate we're going to compare our 10% IRR?

Â We don't know.

Â It is that the one of the first period, the one of the second,

Â the one of the third, the one of the last?

Â That we don't know,

Â so we cannot really use IRR if we have more than one discount rate.

Â But here comes a more fundamental reason why you may not want to,

Â and I, I might, I, I want to stress the word may.

Â You may not want to calculate different discount rates for different periods.

Â And, and the problem is we really have very little ability to

Â foresee what those discount rates are going to be in the future.

Â When we say, look we calculate the cost of

Â capital Starbucks knowing everything we know about the company and

Â building that into the cost of capital calculation today, we not really saying

Â when we use this 7.2% over and over and over and over again, we're not

Â really saying that we believe that discount rates are not going to change.

Â We know that they're changing all the time.

Â In fact, by the time we're done calculating the number,

Â the number probably already changed because the market price of the debt

Â might have changed.

Â The return on debt might have changed.

Â The ten year treasury bond might have cha, treasury bond yield might have changed.

Â And the cost of equity might have changed, too.

Â And all that implies that we know that this discount rate that we

Â estimated is going to be changing all the time.

Â What do we expect to get is we expect to get the average rate.

Â You know, in the same way,

Â if you remember back in our very first session when we said, look,

Â if I invest in the world market, I'm going to get a mean annual return of 7.7%.

Â That doesn't mean that we expect to get 7.7, 7.7, 7.7, 7.7 over and over again.

Â The only thing that we are saying is that our mean annual rate is going to be 7%.

Â But if you remember, we were getting positive returns,

Â negative returns, low returns.

Â This is exactly the same thing.

Â In other words,

Â when we say we're going to discount these five year cash flows at 7.2%.

Â What we're really saying is that on average we expect to

Â get this number right.

Â We know that the number is going to be changing all the time over time but

Â if we are confident that it's a good estimate of the cost of

Â capital today maybe if the business doesn't change all

Â that much the appropriate discount rate shouldn't change all that all that much.

Â Let me finish this session with that.

Â this, what you're seeing.

Â This is the former CFO of Eli Lilly, large sophisticated company.

Â And you would think that you know this company had knowledgeable enough people to

Â implement any type of adjustments or any type of

Â little refinements that you need to implement in terms of the discount rate.

Â Well, the reason I like this example is because in this little

Â interview what the CFO says is the following, and

Â let me read that part to you that I'm highlighting there in, in blue.

Â It says to evaluate long term investment projects,

Â Lilly used a firm white cost of capital as [INAUDIBLE] rate.

Â Although we make other medical products,

Â we consider ourselves primarily a pharmaceutical company and so

Â we calculate one cost of capital for the whole company.

Â Let's stop there for just a second.

Â What this, this guy is saying is, look we are a large company.

Â We have many divisions.

Â We know that they're not identical and because we know they're not identical,

Â we know that they have somewhat different risk profiles, but

Â we don't think that they're all that different.

Â And therefore, instead of calculating a discount rate for

Â this division, we just calculate one discount rate for the whole

Â company that is the cost of capital and that we apply to all the divisions.

Â Is he saying that all the divisions are identical?

Â No, he's simply saying, going back to the word we used before,

Â that these divisions are not substantially different and

Â because they are not then we use the same cost of capital for all of them.

Â Let's keep reading.

Â And it says.

Â Currently, it's 15% and has been for about 20 years.

Â Now, of course, a discount rate doesn't remain constant for 20 years.

Â What he's saying is basically, look, we think that this is a proper discount rate.

Â For the type of risk that we bear, for the type of return that we need to deliver to

Â the capital providers, and, of course, this number is going to change over time.

Â But 15% seems to be the right number to discount to

Â make long term evaluations of investment projects.

Â In other words it's, it's it's a number that is sufficient for

Â us to make calculation.

Â It's sufficient to use across different divisions.

Â It's sufficient to use over time.

Â We know that neither these is going to be constant over time.

Â Now its going to be constant across divisions.

Â But neither one thing nor the other bothers us all that much.

Â So, you know, with a large sophisticated company we could do a lot better.

Â We don't think we need to bother.

Â So, we use 15% for all the divisions and we use 15% as a constant number over time.

Â So this is pretty much it for, for today.

Â Just backing up a little bit what we've done is discussing the two

Â main tools that we use to evaluate projects NPV.

Â An IRR, net present value, and internal rate of return.

Â The rules that we need to use for them are very straightforward.

Â A positive net present value says that we should invest,

Â a negative present value says that we shouldn't.

Â An internal rate of return higher than the discount rate says we should invest.

Â An internal rate of return lower than the discount rate said we shouldn't invest,

Â although, that second part remember it's a little tricky.

Â There may be circumstances in which IRR, the, the Internal Rate of Return,

Â the discount rate of that fancy equation that we've seen before,

Â may be problematic.

Â It may have more than one solution, it may have no solution at all.

Â It may suffer from the scale problem when we're comparing different projects.

Â So like any tool, handle with care.

Â So what we've done in this session is basically calculating an NPV,

Â calculating an IRR, and then having that data applying that to a project, and

Â then thinking a little bit further in terms of do we need more than that?

Â Do we need more than one discount rate?

Â Do we need more than one discount rate because we have different countries, we

Â have different divisions, or we think that this number is going to change over time?

Â There aren't extremely clear answers to those questions.

Â But at least we entertain arguments pro and

Â con in terms of whether we should go ahead with that or not.

Â So this is it for today.

Â We're done with the issue of product evaluation.

Â Remember there's a, a lecture there's a reading that compliments this session.

Â That actually deals with more problems of the IRR and

Â actually dealt goes a little bit deeper into this whole idea of present value.

Â We have only one more session to go.

Â We'll be talking about corporate value creation soon, so see you then.

Â [MUSIC]

Â