Last week, I posted an article on a case scenario to estimate the price a business is worth. Unfortunately and disappointedly, there was only one reply. In my view, I think it is important for an investor to think about the price that he is willing to pay so that it matches the rate of return that he expects in the future. There’re a few ways to put a price to a marketable security. One is to determine the intrinsic value by estimating the present value of all future cash and one other is what I will describe here and it has nothing much (or nothing at all) to do with the intrinsic value of the business. Neither does this method examine the future viability and strength of the business. As an investor, determining the future existence of the business is the most important factor over any other factors because if it doesn’t exist or its business is not viable, it makes no sense to any value that you calculate. So essentially, this method is purely about numbers and nothing more, proper investing must constitute more than numbers, it must be a latticework of many mental models.

In order to put a purchase price based on one’s expectation future rate of return, we shall look at how the past business performance and market valuation contributed to the price of today of $44.

In order to put a purchase price based on one’s expectation future rate of return, we shall look at how the past business performance and market valuation contributed to the price of today of $44.

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**1) Inversion – Road to the current price of $44. (Refer to previous article for full picture)**

Let’s examine how did the stock price came to $44 from the year of 1980. The idea in this first step is to invert. Inversion is a great idea. It scrutinizes and examines all the contributing factors of an outcome. It is much like an investigative report into most things, like an accident report or something. We find out the source of the cause to predict into what will likely to happen in the future.

The stock price in 1980 was $0.12 and as of today, it is $44. The PE of the stock at $0.12 in 1982 is 11 and in 2007, at the price of $44, the PE is 16.3. The earning per share was 1.05cents in 1980 and in 2007, it was $2.71.

To understand how it spiraled from 12cents to 44 times on the dollar, there’re two major components that contributed to this phenomenal rise – 1) Fundamental return; 2) Speculative return, i.e. changes to the PE valuation.

In fundamental return, there’re two portions to be determined – 1) the compounded average EPS growth rate from 1980 to 2007; 2) the initial dividend’s yield based.

In this case, the EPS that moved from 1.05cents to $2.71 compounded at a rate of 22.85% for the past 27 years. The initial yield in dividend is 1.49%. Thus, giving a total fundamental return of 22.85% plus 1.49% that makes it 24.34%.

Now that we have determined the fundamental return, we shall determine the speculative return. As you can see for the past 27 years, investors in this business gradually value more of each dollar of the business earnings over time. It went from an earning multiple of 11 in 1980 to 16.3 in 2007. That means the PE translated to a compounded growth that averaged 1.45%.

Now let’s find out the average compounded growth of the stock price that went from 12cents to $44. It simply compounded at a rate of 24.6%.

Now if you add up both the fundamental return of 24.34% and the speculative return of 1.45%, it gives you a total real growth of 25.79%. Oh la la, now you may think that the return in stock price of 24.6% is pretty close to 25.79%, right? Well close, but not close enough. So, let’s make it even closer, since dividend is cash that is taken out from the business, it should be logically then deducted from the real growth of 25.79%, it will then gives you 24.3% after taking the dividend’s yield of 1.49%. Is it then a coincidence that 24.3% - the total of 1) average compounded return in EPS and 2) the return on the speculative component due to the changes in earnings valuation by the market – is so close to the actual average compounded stock price of 24.6%? That is something you have to think about based on what has been given so far – i.e. if what has been said thus far sounds logical to you.

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A word of caution before going further: It is important to understand the logic of how the price of $44 is derived from the past performance. It is only upon understanding it would you then able to figure out the manner or thought process I would go about in trying to determine the example that I have given in Case 1 in the article I posted last week. For the benefit of those who do not know, here is the case presented.

A big retailer who has a past record of a far-above industry returns on invested capital and equity of over 20%. As such, its past performance in share price also compounded at a rate of over 20%. At its high two years ago in 2005, the stock price went to almost $60 and at this price the valuation then was 25 times earnings. However, in the past two years, the rate of growth on invested capital and equity slowed to a pace of slightly below 20% - a few percentage points drop. Similarly, the share price tracks the slight drop in return on capital and it is traded at $44 today at a valuation of about 16 times earnings. On the outlook, this would seems like a steal to most intelligent investors provided if the variables – return on capital, and valuation level – remain the same (into the foreseeable future).

However, every investor has a different take on a business. The question is if an should pay $44 today if he wants an average of 12% return on stock price for the next 20 years.

If Investor A thinks that the business economics will slow over time to 12% return on capital over the next 20 years on average, should he then pay $44 today if he expects an average of 12% return on stock price over the next 20 years?

If Investor B thinks that the business economics will maintain at about 18% to 20% return on capital over the next 20 years on average, is $44 today a steal and thus be able to gain him at least 12% return on stock price over the next 20 years?

Under both circumstances, if you stand in these investors’ position (what would you do?):

Under circumstance 1 (Investor A), a) what price would you pay if you want an average of 12% return on stock price for the next 20 years, and b) if you pay $44 today, do you think you would be able to achieve 12% return over the next 20 years, and if not, what return would you think you can gain if you pay $44 today?

Under circumstance 2 (Investor B), what price would you think the stock price will be in 20 years time?

A word of caution before going further: It is important to understand the logic of how the price of $44 is derived from the past performance. It is only upon understanding it would you then able to figure out the manner or thought process I would go about in trying to determine the example that I have given in Case 1 in the article I posted last week. For the benefit of those who do not know, here is the case presented.

A big retailer who has a past record of a far-above industry returns on invested capital and equity of over 20%. As such, its past performance in share price also compounded at a rate of over 20%. At its high two years ago in 2005, the stock price went to almost $60 and at this price the valuation then was 25 times earnings. However, in the past two years, the rate of growth on invested capital and equity slowed to a pace of slightly below 20% - a few percentage points drop. Similarly, the share price tracks the slight drop in return on capital and it is traded at $44 today at a valuation of about 16 times earnings. On the outlook, this would seems like a steal to most intelligent investors provided if the variables – return on capital, and valuation level – remain the same (into the foreseeable future).

However, every investor has a different take on a business. The question is if an should pay $44 today if he wants an average of 12% return on stock price for the next 20 years.

If Investor A thinks that the business economics will slow over time to 12% return on capital over the next 20 years on average, should he then pay $44 today if he expects an average of 12% return on stock price over the next 20 years?

If Investor B thinks that the business economics will maintain at about 18% to 20% return on capital over the next 20 years on average, is $44 today a steal and thus be able to gain him at least 12% return on stock price over the next 20 years?

Under both circumstances, if you stand in these investors’ position (what would you do?):

Under circumstance 1 (Investor A), a) what price would you pay if you want an average of 12% return on stock price for the next 20 years, and b) if you pay $44 today, do you think you would be able to achieve 12% return over the next 20 years, and if not, what return would you think you can gain if you pay $44 today?

Under circumstance 2 (Investor B), what price would you think the stock price will be in 20 years time?

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**2) Is $44 a correct price for a 12% return on stock price over the next 20 years (assuming return on capital falls to 12%)**Just to jot your memory, in the past, the historical return on capital is over 20% and with this performance, its earnings valuation is 16.3 times. So if return on capital is to drop to 12%, then logically, the valuation for each dollar of earning would also fall commensurately. So we shall assume, the final PE valuation would be 10 times at the end of the 20 years.

Since in the past return on capital of over 20% produces an almost similar return on EPS (22.85%), we shall then assume it to be the same in the future. That means we shall take the average compounded rate of EPS in the next 20 years to be 12%. With 12% compounded growth on EPS, the EPS of $2.71 in 2007 will be $26.14 in 2027. Since we have fixed the final value of PE at 10 at the end of 20 years, it means that the eventual stock price in 2027 will be $26.14 x 10 = $264.14.

So does $264.14 in 2007 gives you an average of 12% return on stock price? If you pay $44 today and you expect 12% return for the next 20 years, it means you want the stock to be worth $424 in 2007. So obviously, $264.14 falls way short of 12% that you have expected – 38% short.

So if you pay $44 today, and the eventual stock price is $264 in 2027, that translates to an average compounded growth on stock price of 9.3%. It falls short by 2.7% of your expectation.

So now you may again ask how is it possible that it falls shorter than the growth in EPS of 12%? Well, again, the stock price is determined by two factors – the fundamental return (only take in account EPS growth, ignore dividend here) and the speculative component.

We know the fundamental return is 12% for EPS. And now we have earlier assumed that the PE of 16.3 in 2007 will fall almost commensurately because of the deterioration of the return on capital. So the PE falls from 16.3 to 10 in 2027 eventually. And this fall in PE over the next 20 years resulted in a negative compounded return of –2.4%. So 12% minus 2.4% equals to 9.6% and this is very close to the 9.3% as calculated.

So by paying $44 today and if you expect the business’s return on capital to falls to 12%, the likelihood is that you’d be disappointed if you are looking for a 12% return on stock price.

So the next question, you may be asking is “Then how much should I pay for if I want a 12% return?” Simple, if you think the eventual PE is 10 because the average return on EPS or capital falls to 12%, then you should only pay $27 today (divide $264 by a factor of 1.12 back by 20 times).

Since in the past return on capital of over 20% produces an almost similar return on EPS (22.85%), we shall then assume it to be the same in the future. That means we shall take the average compounded rate of EPS in the next 20 years to be 12%. With 12% compounded growth on EPS, the EPS of $2.71 in 2007 will be $26.14 in 2027. Since we have fixed the final value of PE at 10 at the end of 20 years, it means that the eventual stock price in 2027 will be $26.14 x 10 = $264.14.

So does $264.14 in 2007 gives you an average of 12% return on stock price? If you pay $44 today and you expect 12% return for the next 20 years, it means you want the stock to be worth $424 in 2007. So obviously, $264.14 falls way short of 12% that you have expected – 38% short.

So if you pay $44 today, and the eventual stock price is $264 in 2027, that translates to an average compounded growth on stock price of 9.3%. It falls short by 2.7% of your expectation.

So now you may again ask how is it possible that it falls shorter than the growth in EPS of 12%? Well, again, the stock price is determined by two factors – the fundamental return (only take in account EPS growth, ignore dividend here) and the speculative component.

We know the fundamental return is 12% for EPS. And now we have earlier assumed that the PE of 16.3 in 2007 will fall almost commensurately because of the deterioration of the return on capital. So the PE falls from 16.3 to 10 in 2027 eventually. And this fall in PE over the next 20 years resulted in a negative compounded return of –2.4%. So 12% minus 2.4% equals to 9.6% and this is very close to the 9.3% as calculated.

So by paying $44 today and if you expect the business’s return on capital to falls to 12%, the likelihood is that you’d be disappointed if you are looking for a 12% return on stock price.

So the next question, you may be asking is “Then how much should I pay for if I want a 12% return?” Simple, if you think the eventual PE is 10 because the average return on EPS or capital falls to 12%, then you should only pay $27 today (divide $264 by a factor of 1.12 back by 20 times).

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Anyway, I’ll not do the example on the second circumstance because it is quite obvious that the investor would easily fulfill the hurdle rate he sets for himself. This is because if the return on capital in the future is about the same as it is now, the return on EPS will be close to 18% and the drop in eventual PE will be minimal. So it will be quite easy.

Anyway, I’ll not do the example on the second circumstance because it is quite obvious that the investor would easily fulfill the hurdle rate he sets for himself. This is because if the return on capital in the future is about the same as it is now, the return on EPS will be close to 18% and the drop in eventual PE will be minimal. So it will be quite easy.

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In case you miss out, you think that 12% and 9.3% do not give much difference, or you think “so what if I get 9.3% or 12%, it is small difference.” Then this example will show you that the eventual net worth is large in magnitude and wide in disappointment. Because if a stock is to compound at 12% return, it’d be worth $424 in 20 years, and if it did at a rate of 9.3%, then it is about $264 – a difference of $160 (almost 4 times your original principal). Imagine that this investment is a house that you buy, it means you have 4 less houses in 20 years than you could have had – now it probably sounds very huge to you for this difference in 2.7% in performance.

In case you miss out, you think that 12% and 9.3% do not give much difference, or you think “so what if I get 9.3% or 12%, it is small difference.” Then this example will show you that the eventual net worth is large in magnitude and wide in disappointment. Because if a stock is to compound at 12% return, it’d be worth $424 in 20 years, and if it did at a rate of 9.3%, then it is about $264 – a difference of $160 (almost 4 times your original principal). Imagine that this investment is a house that you buy, it means you have 4 less houses in 20 years than you could have had – now it probably sounds very huge to you for this difference in 2.7% in performance.

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Maybe you are thinking that one single calculation may not be true for all the rest. In fact, I have did quite a few others and all shows similar result. In addition, I pick a random stock on SGX now just for this article – Singtel – to show what causes the price if an investor had bought in 2001 at $1.75 results in if he is still holding it as at today which trades at $3.78.

In 2001, the EPS was 13cents and the EPS in 2007 is 23.25cents which translates to a fundamental compounded growth of 10.2% on EPS. At the price of $1.75 which an investor had gotten in 2001, he was paying at a multiple of 13.46 for each dollar of earnings. As at today, the earning multiple is 16.26. This increase in PE from 13.46 to 16.26 represents a compounded growth of 3.2%.

So when you add the EPS fundamental growth and the speculative growth, you have a total growth of 13.4%. So how did the stock perform? Singtel went from $1.75 in 2001 to $3.78 as of today which represents a compounded growth of 13.7%.

Maybe you are thinking that one single calculation may not be true for all the rest. In fact, I have did quite a few others and all shows similar result. In addition, I pick a random stock on SGX now just for this article – Singtel – to show what causes the price if an investor had bought in 2001 at $1.75 results in if he is still holding it as at today which trades at $3.78.

In 2001, the EPS was 13cents and the EPS in 2007 is 23.25cents which translates to a fundamental compounded growth of 10.2% on EPS. At the price of $1.75 which an investor had gotten in 2001, he was paying at a multiple of 13.46 for each dollar of earnings. As at today, the earning multiple is 16.26. This increase in PE from 13.46 to 16.26 represents a compounded growth of 3.2%.

So when you add the EPS fundamental growth and the speculative growth, you have a total growth of 13.4%. So how did the stock perform? Singtel went from $1.75 in 2001 to $3.78 as of today which represents a compounded growth of 13.7%.

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Hopefully, the article makes some sense to you or it do helps you to think a little bit more. Maybe the thought process or idea may not be perfect but this is the first time I’m thinking it through in this manner – if you have some ideas to improve on, do drop a note.

All in all, I think fundamental growth is much easier to predict for the future, but not speculative. So it is always better to based an investor calculation more on fundamental growth rather than to bank on the market to value each dollar of earning of a business more.

In any case, there’re a lot of numbers involved here and it may confuse you. And if need be, you may request for the excel file which I did to arrive at the conclusion.

## 2 comments:

I believe that the main reason most investors are not more successful is simply because when theirs and kind of panic they are unable to control their impluse to sell. Panicing is the worst quality an investor can possible have.

It was a very nice idea! Just wanna say thank you for the information you have shared. Just continue writing this kind of post. I will be your loyal reader. Thanks again.

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