Some of this is good and pretty insightful. It is a good reminder to see just how extreme expectations need to be to support a multiple of almost 70.
However, a few things. First of all, this is a bit of a nitpick, but I can't stand seeing numbers to 4 or 5 significant figures when for all we know they could be 20% or 30% off. It conveys a sense of accuracy we really don't have.
Second, you need to account for what they do with the cash they don't reinvest when you do the total rate of return calculation. If they didn't reinvest any, the rate of return would not be zero. It would be the equal to the dividend yield, which is 1/PE * (1-reinvestment rate) = 1/65 * 0.33 = 0.5%, which we would add onto that 12.4% to get 12.9%. So in this case not too impactful, but always worth considering. A business that can grow 10% YOY while investing 100% of profits is a lot less valuable than one that can do so while investing only 20% of profits, and paying the rest out in dividends or buybacks.
Third, you use a linear model for the number of locations to calculate how long they can keep expanding, but then use an exponential model for earnings, which implicitly assumes an exponential number of locations. That's quite a convoluted way of saying it, so I'll try to explain another way. If they keep building 120 restaurants per year, right now their restaurant count would be increasing by about 4% YOY, but by the time they're at 7000 restaurants, 120 per year is only 1.7% growth in store count. Therefore, their reinvestment rate will drop significantly.
If you need another clue that your model is fundamentally flawed, notice that the further you reduce the number of stores built per year, the more their apparent intrinsic value goes up, because their earnings can keep compounding at the rate you calculated for longer. What's going on here? The issue is you're using separate models of store count and earnings/cash flow, with no feedback between them. You need one iterative model where the number of restos influences earnings, and potentially earnings also influence the number of restaurants. You can project that forwards in time and get much more sensible numbers, as long as you account for how return on incremental capital will decrease as the market becomes saturated, and their reinvestment rate will also decrease as they begin to find it harder to find places to put a larger amount of earnings.
In any case though, I don't think you need any kind of model to realise that buying an already-large restaurant chain for 65x earnings is incredibly risky and daft.
Some of this is good and pretty insightful. It is a good reminder to see just how extreme expectations need to be to support a multiple of almost 70.
However, a few things. First of all, this is a bit of a nitpick, but I can't stand seeing numbers to 4 or 5 significant figures when for all we know they could be 20% or 30% off. It conveys a sense of accuracy we really don't have.
Second, you need to account for what they do with the cash they don't reinvest when you do the total rate of return calculation. If they didn't reinvest any, the rate of return would not be zero. It would be the equal to the dividend yield, which is 1/PE * (1-reinvestment rate) = 1/65 * 0.33 = 0.5%, which we would add onto that 12.4% to get 12.9%. So in this case not too impactful, but always worth considering. A business that can grow 10% YOY while investing 100% of profits is a lot less valuable than one that can do so while investing only 20% of profits, and paying the rest out in dividends or buybacks.
Third, you use a linear model for the number of locations to calculate how long they can keep expanding, but then use an exponential model for earnings, which implicitly assumes an exponential number of locations. That's quite a convoluted way of saying it, so I'll try to explain another way. If they keep building 120 restaurants per year, right now their restaurant count would be increasing by about 4% YOY, but by the time they're at 7000 restaurants, 120 per year is only 1.7% growth in store count. Therefore, their reinvestment rate will drop significantly.
If you need another clue that your model is fundamentally flawed, notice that the further you reduce the number of stores built per year, the more their apparent intrinsic value goes up, because their earnings can keep compounding at the rate you calculated for longer. What's going on here? The issue is you're using separate models of store count and earnings/cash flow, with no feedback between them. You need one iterative model where the number of restos influences earnings, and potentially earnings also influence the number of restaurants. You can project that forwards in time and get much more sensible numbers, as long as you account for how return on incremental capital will decrease as the market becomes saturated, and their reinvestment rate will also decrease as they begin to find it harder to find places to put a larger amount of earnings.
In any case though, I don't think you need any kind of model to realise that buying an already-large restaurant chain for 65x earnings is incredibly risky and daft.