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Grow rate, multiple contraction or expansion during inflation


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So let's say interest rates are really low - and stock valuations are high because people pay a high multiple to earnings. Now, let's say growth rates vary by company - some can only do 5% per year others can do 15%. If inflation hits, some have said that value - or getting your profits out and in large amounts is key and that stock prices contract their multiples. So if I have even a high flying growth stock growing at 15% for 10 years and then the multipel shrinks from 40x to 20x, the result won't be too satisfactory. Likewise, if a cheap stock which only grows 5% has the same multiple, the result is perhaps a little better but not much. Since it isn't a fast grower, the multiple won't expand much. For example let's say IBM is trading at 12x FCF and grows 5%. The multiple may be the same and you get 5%. Or it might expand a little bit depending on what rates will be at the end of the 10 year period. I mean real growth rate here over inflation. Is this what they call the equity risk premium?


I found this study - https://www.franklintempleton.lu/downloadsServlet?docid=hmbg58za

But it only uses the average S&P P/E and doesn't have a formula for each individual stock and growth rate.


It seems that whether there is inflation or not, growth is STILL the most important unknown variable - as well as the ultimate rate of interest (how can one invest not knowing this?). A company that is priced below its ultimate growth rate can expand the multiple and those - like many today, priced above their growth rate may contract the multiple. In other words, is it really true that value beats growth in inflationary periods or is it in fact garp - growth at a reasonable price that  beats?


On top of this, inflation tends to reduce the growth rate of some businesses versus others, so it's not an independent input.

Does anyone know if there is a formula to determine how much contraction in multiple one should expect inputting these variables: ultimate interest rate, growth rate, current P/E ratio - or possibly expansion?


For example if bonds are yielding now a p/e of 33 and they go to 20 (5% 10 year bond), what should one expect the p/e ratio contraction/expansion of a stock to be at various rates of growth in earnings?



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