# GDP Growth and Terminal Growth Rate in DDM



## coolcup (27 September 2015)

Hi everyone

I am just trying to polish up my understanding of the dividend discount model when valuing companies. In essence, this entails:

1. Forecasting dividends from a company over say a 5 year period;
2. Estimating a terminal value of the company's shares at the end of the 5 year period
3. Discounting (1) and (2) back to a present value

My main interest is in part 2 of the above. In finance at uni (a long time ago) we were always advised that the terminal value for a share which was expected to last into perpetuity was calculated with reference to a long term cost of equity (k) and a terminal growth rate (g). We were advised that we shouldn't set "g" to be much higher than the long term GDP growth of an economy (usually 3% as a rule of thumb in Australia) as otherwise the terminal valuation would imply that the company would eventually grow larger than the whole economy, which was by definition impossible.

I am trying to think about "g" in the context of the above paragraph.

First, what does GDP measure? Is it total revenue or total profit in an economy? According to wikipedia it measures "the total dollar value of all goods and services produced over a specific time period". So, this implies to me that it is a total revenue measure. 

If this is correct, then why can't a company have a terminal growth rate that is higher than long term GDP growth? Most companies have a level of fixed costs and many employ a degree of financial leverage, which implies that if revenue is expected to grow in perpetuity over the long term in line with GDP, then their net profit should grow faster than this in perpetuity. If dividends are tied to net profit in some way (ie a payout ratio), then the terminal growth rate for many companies' dividends can be expected to grow at a faster rate than GDP as well. 

And so, in looking at the DDM and the terminal growth rate, if the above logic stands, I should be free to use a terminal growth rate in excess of expected long term GDP growth.

I am sure there are flaws in the above thought process, and would be very appreciative if people have views on the above.


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## luutzu (27 September 2015)

coolcup said:


> Hi everyone
> 
> I am just trying to polish up my understanding of the dividend discount model when valuing companies. In essence, this entails:
> 
> ...




Your thinking of it sounds about right (by what I can remember)... though it sounds illogical because it is somewhat insane... something hatched by people who need to put maths to some use and get a PhD and tenure.

I never really understand how these stuff could be logical. I mean I have worked them out and plug in the numbers and all that... but how does it work in real life?

Say you're estimating the value 5 years from now, discount it back to today at rates you've spent a lot of time estimating is the realistic figure over that five years.

Do you then hold on to your valuation for the next five years regardless? Of course not. You "update" it with changes each quarter or each year right? Then your 5 year valuation is no longer the same 5 years, but it's pushed further into the future. You're basically moving your goal post but make it out like you're adapting to news and development.

Then let say you're agile and adapt etc.... Why would you want to waste time valuing something so precisely for? Are you going to buy something at the price you think its value is at 5 years from now, discounted back at rates you think the RBA or the economy will go along with?

So these models asks you to be precise, yet it can't be, and further you shouldn't buy or sell based on such precision... but it's taught and done any way. Maybe somebody got to put MBAs to work at something.


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## skc (27 September 2015)

coolcup said:


> If this is correct, then why can't a company have a terminal growth rate that is higher than long term GDP growth? Most companies have a level of fixed costs and many employ a degree of financial leverage, which implies that if revenue is expected to grow in perpetuity over the long term in line with GDP, then their net profit should grow faster than this in perpetuity. If dividends are tied to net profit in some way (ie a payout ratio), then the terminal growth rate for many companies' dividends can be expected to grow at a faster rate than GDP as well.
> 
> And so, in looking at the DDM and the terminal growth rate, if the above logic stands, I should be free to use a terminal growth rate in excess of expected long term GDP growth.
> 
> I am sure there are flaws in the above thought process, and would be very appreciative if people have views on the above.




Just plug in some very large number for time period and you will find that the profit made by a company becomes greater than the entire GDP of the universe - which is simply impossible.

Quick example. GDP today = $100B. Terminal growth 3%. Company profit = $1B, terminal growth = 5%. You will find that by year ~240, the company's profit would be greater than the entire GDP.

And 240 years is well short of perpetuity, which is a very very long time.


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## coolcup (28 September 2015)

skc said:


> Just plug in some very large number for time period and you will find that the profit made by a company becomes greater than the entire GDP of the universe - which is simply impossible.
> 
> Quick example. GDP today = $100B. Terminal growth 3%. Company profit = $1B, terminal growth = 5%. You will find that by year ~240, the company's profit would be greater than the entire GDP.
> 
> And 240 years is well short of perpetuity, which is a very very long time.




Hi skc

Thanks for this. This is the exact concept I am struggling with. To me, GDP growth equates to total revenue growth in the economy. So by definition, profits should grow at least the same rate as GDP growth if not more (given leverage and fixed costs as explained in my note above). But then this leads to the farcical outcome described in your post... very strange.


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## coolcup (28 September 2015)

luutzu said:


> Why would you want to waste time valuing something so precisely for? Are you going to buy something at the price you think its value is at 5 years from now, discounted back at rates you think the RBA or the economy will go along with?




Thanks mate. I didn't want to have a debate about the efficacy of the DDM which, as you note, is very debatable! I just wanted to discuss more around the terminal growth rate vis a vis GDP growth.


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## craft (28 September 2015)

coolcup said:


> Hi everyone
> 
> I am just trying to polish up my understanding of the dividend discount model when valuing companies. In essence, this entails:
> 
> ...




Hi coolcup

3% you mention is approximately the long run “real” (inflation adjusted)  historical figure for AUS GDP.

Probably makes more sense for “Nominal”  (real + inflation) GDP to be the limit on growth.  

Gross National income (GNI or GNP) is probably a better measure than GDP for this purpose.

Historically aggregate market growth hasn’t grown as fast as GNI – some leakage out of the listed market to real estate / non- listed new enterprises etc etc. 

On the point of Profit vs Revenue. If profit is to grow more than revenue then at a national level you would have to have a redistribution of income from wages to capital. That’s been happening for quite a while in AUS but I suspect there’s a limit and it’s probably long term cyclical around a maybe slowly up sloping mean.


Terminal value calcs are so sensitive to small changes in assumptions that I prefer capitalisation multiples at the end of the cash flow estimations period, rather than trying to calculate a perpetual growth and discount rate.  But the line of thought of tying long term possibilities of a small part to the whole it exists within I think adds to the valuation process however you eventually apply the insight.


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## coolcup (28 September 2015)

craft said:


> On the point of Profit vs Revenue. If profit is to grow more than revenue then at a national level you would have to have a redistribution of income from wages to capital. That’s been happening for quite a while in AUS but I suspect there’s a limit and it’s probably long term cyclical around a maybe slowly up sloping mean.
> 
> 
> Terminal value calcs are so sensitive to small changes in assumptions that I prefer capitalisation multiples at the end of the cash flow estimations period, rather than trying to calculate a perpetual growth and discount rate.  But the line of thought of tying long term possibilities of a small part to the whole it exists within I think adds to the valuation process however you eventually apply the insight.




Hi craft,

As always, really appreciate your insights.

On the first paragraph above, could you elaborate on this a bit more? Particularly around the redistribution from wages to capital and how this might reverse over time? I didn't quite understand it, but I think it is important.

On the second paragraph, I didn't fully understand the difference between using a capitalisation multiple to calculate your terminal value vs using the perpetual growth / discount rate method. Isn't the capitalisation multiple simply (1/(k-g))? So, if for example, you used a 10x capitalisation multiple to calculate your terminal value, this would be the same as your discount rate being say 12% and a perpetual growth rate being say 2%? I see the discount rate / perpetual growth rate formula as a way of establishing more science around the capitalisation rate and breaking it into its component parts.

Interested in your further views if you have time.

Cheers


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## craft (28 September 2015)

coolcup said:


> On the first paragraph above, could you elaborate on this a bit more? Particularly around the redistribution from wages to capital and how this might reverse over time? I didn't quite understand it, but I think it is important.




I’m not educated in any of this just making it up to try and understand things myself.  – be warned.

Real GDP is made up of population growth (which is a volume increase) or productivity (which is increased profit) that profit either accrues to labour or to capital. If you are saying corporate profit can increase faster than GDP growth then you must be implying more profit will flow to capital than to labour.

This is total GOS /total compensation of employees. My guess is this is cyclical around an upward sloping mean as the country accumulates capital and invests for increased automation productivity.






coolcup said:


> On the second paragraph, I didn't fully understand the difference between using a capitalisation multiple to calculate your terminal value vs using the perpetual growth / discount rate method. Isn't the capitalisation multiple simply (1/(k-g))? So, if for example, you used a 10x capitalisation multiple to calculate your terminal value, this would be the same as your discount rate being say 12% and a perpetual growth rate being say 2%? I see the discount rate / perpetual growth rate formula as a way of establishing more science around the capitalisation rate and breaking it into its component parts.




Yep your right - I guess what I was trying to say is That I don't try to break it down to the components. 2% & 12% gives a big difference to a respective 4% and 10%.  Seeing there is no precision far into the future I prefer to just look at it from a macro cap multiple perspective rather than even try to guess the components. Nothing wrong with going to the component level, but I feel I tend to make errors that 'add' when I go to a component level that far into the future. Mind you my capitalisation multiples for different quality business have probably been formulated over the years by considering the components as you are doing now.

Cheers


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## Evolve (28 September 2015)

Hey Craft how do you decide on what capitalisation multiple to use?


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