1:10

Take the example of a firm that expects to earn $3 million annually for

Â its 1 million stocks outstanding.

Â Dividing the two numbers gives us earnings per share, or

Â EPS, which in this case is $3.

Â The dividends per share, or DPS, of the firm would be exactly the same if

Â the firm decided to give all of its earnings back to the stockholders.

Â Many firms do exactly that because they do not have any new value-creating

Â projects to invest in or

Â because they are a subsidiary transferring earnings back to its parent company.

Â Either way, 100% dividend payout ratio, measured by DPS divided by EPS,

Â suggests an absence of any future growth opportunities.

Â 2:16

Rewriting the formula, the value of a stock is P subscript 0 for

Â the price today, which equals to the dividend in the numerator and

Â again r, which represent the share holders' required rate of return.

Â Let's assume that to be 15% in this example.

Â So what we'll have is the value of a share equal to $20 based on

Â the dividend of $3 divided by the discount rate of 15%.

Â Now, is this a fair price, meaning is it neither over or undervalued?

Â Well, Warren Buffett likely thinks that it is correctly

Â priced assuming the $3 dividend is more or

Â less certain and if the discount rate earns the time value of money.

Â Prices, however, are also influenced by a number of other factors

Â beside a rational model that is based on dividends and discount rates.

Â This is because the stock market is not insulated from changes in other markets

Â including the bond market, credit market, the commodity currency and

Â derivative markets.

Â Nor is it from unanticipated news that will inevitably influence market

Â perceptions about how attractive the stock really is.

Â 4:07

If our firm is in an industry that is able to sustain, let's say,

Â a 5% constant growth rate in the future, how does this change its price?

Â Again, it's easy to show that the stock price today will be based

Â on the next period's dividend, which would be divided by the difference between

Â the rate of return and the growth rate.

Â In other words, the price is going to be the next period's dividend,

Â which we're assuming to be $3 and the difference between the discount rate,

Â 15%, and our growth rate of 5%.

Â Remember, it's the next period's dividend that we look at,

Â which we've just assumed to remain at $3.

Â All right, let's pause here for just a moment.

Â First of all, it's worth emphasizing just how valuable growth opportunities are.

Â 5:01

The 5% growth gives the price a boost from $20 to $30, and that's a 50% increase.

Â Let's also look at the graph.

Â This reveals how price increases dramatically for growth-oriented stocks.

Â And if we add to this, the favorable tax treatment of price increases,

Â which is the treatment of capital gains versus the treatment of dividend income,

Â not to mention the management compensation schemes tied to growth.

Â Well, this might explain the temptation to manipulate financial statements

Â that artificially boost earnings per share and project fictitious growth.

Â 5:55

By rearranging the constant growth formula,

Â we can also see the two components of return.

Â The first component of return is simply the dividend divided by the price, and

Â this is known as the dividend yield.

Â The second component, which is denoted by g,

Â is the capital gain component, and that reflects the price appreciation.

Â All right, let's get back to our example.

Â So we started off with a pricing model for zero growth.

Â And the price was equal to the dividend divided by the required return

Â minus the growth rate.

Â 6:29

We can rearrange this formula and

Â see two very distinct components that are in fact very insightful.

Â So the first component is if we isolate r, it is going to be the dividend

Â divided by the price, and that gives us the dividend yield.

Â That's the first part.

Â And then, of course, the second part, which is g, the capital gains portion.

Â If we plug the number into the example that we had,

Â we have a dividend, expected dividend of $3.

Â We have a price today of $30, and we know that our

Â total return, the expected return, was 15%.

Â And since this is 10%, we also know that

Â the capital gains component, or g, is 5%.

Â All right, now let's look at the third case, and

Â in this case, we're going to look at growth rates that vary over time.

Â So we call this the non-constant growth model.

Â Suppose our firm is projecting growth rates of 5% for

Â the next two years that are going to be followed by 2% growth thereafter.

Â How do we price stocks in these cases of variable growth?

Â To find the answer, we'll start with our established method of plotting information

Â on a timeline and then we are going to use three particular steps to get the answer.

Â So what about that timeline?

Â If we draw a timeline, we can see that generally speaking, we have time zero.

Â And then in this case, we're going to have the next period's dividend,

Â the following period's dividend.

Â And until now, we have a growth rate of 5%, which was for the first two periods.

Â Following this, we had predicted the growth rate of 2% thereafter.

Â So all we need to do now is to make sure that we at least account for

Â the next period's dividend, which is D3.

Â And we also want to calculate the price at this point, which is going to be P2.

Â And remember, always the price refers to the next period's dividend,

Â D3, again divided by r minus g.

Â Right, so

Â then let's apply the information in the problem with the three step procedure.

Â Step one.

Â In step one we forecast the future dividends until they become constant,

Â as in this case, or zero growth.

Â So if we do the forecasting, notice for these three periods,

Â one, two, and three, we have a dividend that is forecasted

Â to be $3 in the first period that grows by 5%.

Â So this is going to be 3 times 1.05,

Â and that gives us $3.15.

Â And then from thereon to D3, which is going to grow at 2%.

Â So we're going to take $3.15, and

Â that will grow at 2%, which gives us a value of $3.21.

Â That's step one.

Â Let's move on to step number two.

Â 9:41

Once we forecasted the dividends, step number two is to calculate that price.

Â So, we compute the price at the point where the growth rate

Â either becomes constant or zero growth.

Â In this example we just have to plug the numbers in.

Â Step two, we calculate the price, in this case P2,

Â which is going to be 3 over r minus g.

Â And as we can see, the numbers we forecasted, D3 is 3.21.

Â The discount rate we already know is 15%,

Â and the growth rate from this point on is 2%.

Â And if we do this calculation, we get the price of

Â $24.72, and that takes care of step two.

Â Do notice, however, that this price takes into account

Â the next period's dividend and all other dividends in the future.

Â And that takes us to the final step, and that final step we simply present value

Â 10:42

all of the dividends in step one and the price in step two.

Â So generally speaking, what we're doing now is

Â simply present valuing the dividend and the price.

Â If we apply to a problem here, we have a dividend of $3

Â that we need to bring back for one year at 15%.

Â And we have the dividend for year two, which is $3.15.

Â So we've taken care of this dividend, we've taken care of the next dividend.

Â Now we need to take care of all the future dividends,

Â which is reflected in this price here.

Â So we're going to add to this the price 24.72, and

Â then simply bring these two amounts back into today's dollars at 15%.

Â And that gives us a present value of $23.67.

Â That should be the price of the stock with variable growth.

Â [COUGH] Now, if you're wondering what do you do in the case

Â when the stocks are not paying any dividends at all.

Â And the answer here is typically to use another approach.

Â This approach is known as the multiple approach.

Â And the most common multiple to use in this approach is

Â the price earnings multiple or the PE multiple.

Â Let's apply this to our example here.

Â So we have in this case multiples, and

Â we mentioned the first approach is the price earnings multiple.

Â And what do we have in this example?

Â The price E is denoting earnings per share.

Â So we know the price is 30, we know the earnings per share is 3,

Â and therefore the multiple is 10 times.

Â So using this $30 price, this suggests that

Â this value is worth ten times its earnings.

Â 12:51

And the multiple could be benchmarked against, let's say,

Â the firm's historical multiple.

Â Or it could be based on some average or

Â median value of a sample of say comparable competitors' multiples.

Â If we did that and we assume that the competitors have

Â a benchmark multiple of 8 times, then what this suggests

Â is that 8 times our earnings of 3 gives us a value of 24.

Â And the value of 24 is suggesting that the current price,

Â if the current price is going to be $30, which we computed right in the beginning,

Â well then, we can see our shares are actually overvalued.

Â Whereas if we used the calculation earlier of 23,

Â we can see that the shares are undervalued.

Â And accordingly, we would buy or we would sell.

Â 14:01

We looked at several variations that consider assumptions about future growth,

Â and we came up with a number of formulas.

Â So if I have to summarize these formulas for you with the space that I have left on

Â this lightboard, I will start with the zero growth mode.

Â Zero growth model said the price is simply equal to the dividends divided by

Â the discount rate r.

Â [COUGH] We then move to the next case of constant growth.

Â And in the constant growth case, we said the price is going to be

Â equal to the next period's dividend divided by r minus g.

Â And finally, we look at the third variation of the growth model,

Â which is non-constant.

Â And in this case, we compute the price as simply equal to the present value of those

Â future dividends and the price in the future when dividends become constant or

Â zero growth.

Â We can denote that by forecasting those dividends, D1, D2 right up til Dt.

Â And not to forget that at this point when the growth rate becomes constant or

Â zero, we also calculate the price at that point t.

Â And then we have to bring all of these values back, so

Â we would bring back D1 at the appropriate discount rate for

Â one period, bring back D2, discount rate for

Â two periods right down to the period where the growth rate changes.

Â And then our price, and this price at the point t

Â is going to equal to the next period's dividend,

Â t+1, over r minus g.

Â And this too is going to be brought back at 1 + r raised to the power t,

Â which is what we did right here in the calculation.

Â [COUGH] So, while we know that the stockholders' expected rate of return,

Â the r that we've been using throughout these examples,

Â they include two components, which are the dividend yield and the capital

Â gains component, obtaining that rate of return is easier said than done.

Â This is because the valuation models have to account for risk.

Â And given our formulas, risks can be either imputed in two places.

Â So if we look at the formula where we started for the price,

Â we can have the risk imputed either in the numerator or imputed in the denominator.

Â There's only two places to go.

Â [COUGH] So conventionally what we do is we either adjust the cash

Â flows to take care of risk or we adjust more conventionally in

Â the discount rate, which includes both inflation and risk.

Â So really,

Â when it comes down to it, valuation is more of an art than a science.

Â And as mentioned right at the beginning of the segment,

Â if you are Warren Buffet, you probably want to keep everything simple and

Â you're going to account for risk in the numerator.

Â But as we're going to see in course number three,

Â conventional financial wisdom opts to include risk in the denominator.

Â