I know this is not how the real world works but theoretically speaking, assume a company is growing constantly at 10% and will probably do so in perpetuity. The multiple on this company hence should remain constant since its growth expectations are not changing , say p/E of 10x. So does the stock just keep on moving upwards every year as the numbers move up and the multiple remains the same ?? Thinking from another angle, the stock should jump to infinity becasue you are getting the company growing all the way to infinity ?? Makes sense ? Thoughts ?

yes. that’s why growth eventually falls inline with the real growth rate of the economy (as the company itself would eventually envelop and become the economy)

mar350 Wrote: ------------------------------------------------------- > yes. that’s why growth eventually falls inline > with the real growth rate of the economy (as the > company itself would eventually envelop and become > the economy) 1. reverts to the economy’s _nominal_, not real, growth rate 2. any study I’ve seen on this (and I haven’t seen very many) concludes that a firm usually reverts to its sector’s growth rate within 5 years. (which gives one pause when situations occur such as when google’s share price required 20y of consistent growth to justify) > Thinking from another angle, the stock should jump to infinity becasue you are getting the company growing all the way to infinity ?? No, because your discount rate is greater than your growth rate.

the answer is yes, the stock will increase uniformly each and every year, but if it were guaranteed to grow at 10% annually into infinity, the price would adjust such that it returned the risk-free rate, year after year. to adapt this to real life, a low risk, well-diversified stock is expected to return somewhere between the equity return and risk-free return for that time period as it is less risky than the rest of the market but it is not 100% guaranteed to ‘grow’/produce returns constantly and uniformly into perpetuity like a risk-free instrument.

MattLikesAnalysis Wrote: ------------------------------------------------------- > the answer is yes, the stock will increase > uniformly each and every year, but if it were > guaranteed to grow at 10% annually into infinity, > the price would adjust such that it returned the > risk-free rate, year after year. You guys are making this way too complicated. You’re creating a guaranteed risk-free asset that returns 10%. Therefore, the RFR itself would adjust, if 10% > RFR.

justin88 Wrote: ------------------------------------------------------- > MattLikesAnalysis Wrote: > -------------------------------------------------- > ----- > > the answer is yes, the stock will increase > > uniformly each and every year, but if it were > > guaranteed to grow at 10% annually into > infinity, > > the price would adjust such that it returned > the > > risk-free rate, year after year. > > You guys are making this way too complicated. > You’re creating a guaranteed risk-free asset that > returns 10%. Therefore, the RFR itself would > adjust, if 10% > RFR. incorrect. because there is limited quantity of this security, RFR would not adjust to 10%. the RFR would remain at whatever, 2-4%, and the security would be bid up to resemble a risk-free return. i suppose the fact that there is an asset that produces 10% growth risk free should force a slight adjustment to the RFR as it takes some of the demand for risk free assets but this would be dependent on the size of the company relative to the rest of the “risk free market”. but yes, it would eventually absorb the rest of risk assets and resemble a market return not the risk-free. but this is why it is a ‘philosophical’ question and not a real question because this scenario is impossible.

In the long run, the RFR -> 10% as the company becomes a larger and larger part of the economy.

MattLikesAnalysis Wrote: ------------------------------------------------------- > > incorrect. because there is limited quantity of > this security, RFR would not adjust to 10%. it might be limited quantity now, but it grows at 10% annually forever. just wait a little (or a while) - the adjustment may happen before perpetuity is over

the logical consequence of the assumptions (10% growth in perpetuity) is that the economy will grow at about 10% once the company becomes larger than the size of everything else in the economy. (longer post on its way)

Matt’s got the key point here. The “expected” return on a stock is really all about the riskiness of the stock, which is only indirectly related to its growth rate. The discount rate is supposed to adjust to account for this. If returns are guaranteed, then you should be able to replicate those returns with treasurys of that pay similar cash flows, and those treasurys will pay out the RFR. The cost of buying those treasurys today would be the proper price, and they would give the same yield. If returns are not guaranteed, then you discount those growing cash flows at a higher rate to reflect additional risk. That’s what the asset pricing models are for. If the earnings grow at faster than that discount rate, then the stock price should grow in this way: Assuming the stock is fairly priced today, it should give a total return (TR) equal to its discount rate. TR = cap gains + divs, so the stock *price* should grow at: discount rate - dividend yield If the stock’s long term earnings grow faster than the discount rate, then the stock price should grow even more to reflect the spread. Effectively, this is what alpha is. If this were constant earnings growth over the long term, then the additional growth over and above the discount rate: = Earnings growth - discount rate Putting these together, we see that the stock price growth is: stock LT capital growth = (disc. rate - div. yield + (Earn growth - disc rate) ) = Earnings Growth - Dividend Yield Which also implies that: Discount rate = Average LT Earnings Growth Rate for similarly risky companies Now you can start to see where asset pricing models come from. Basically, you are running a regression on number of factors that you think describe the stock’s risk, and it pops out a prediction based on the input data that tells you what the average company’s return is, given its score on those risks. Alpha is when you have an estimate of a stock’s return based on its risk and it diverges from another estimate of the stock’s return based on some other information (like financial statements, an analysis of changes in competitive structure, or whatever). Basically, alpha=(IRR of cash flows based on other information) - (return appropriate for a stock’s risk level) This is why asset pricing models don’t actually tell you what an asset’s price is. Instead, they just give you the discount rate (given some indicators about risk) that goes into telling you what an asset’s price should be. If you don’t have any information other than the asset pricing model, all you can do is assume that the stock is fairly priced and should grow, on average, at the rate of return predicted by the asset pricing mode.

Thanks for all the responses guys. One question though, the Treasuries have a finite time horizon while my hypothetical company is supposed to grow earnings at 10% in perpetuity. Doesn’t that make the stock jump to infinity assuming a perpetually growing cash flow ?

Just glanced through the discussion, REALLY interesting points from everyone. The conversation ended up being a lot more interesting / nuanced than I originally grasped when I glanced at it.