In my post on how to value stocks, I claimed that the growth in a company’s profits equals the company’s return on incremental equity investment multiplied by the percent of earnings that it reinvests.
g = ROE * reinvestment ratio = ROE * (1 - payout ratio)
In other words: growth in profits is determined by how much you reinvest in the business, and the return you get on the amount reinvested. Makes sense, right? However, that’s all still kind of abstract, so let’s look at an example: the proverbial lemonade stand.
Lemonade Stand
Pretend you have a lemonade stand business. You currently own 20 stands. Each one costs $10 to set it up and generates $2 in profit each year. You didn’t use any debt, so the ROE is 20% ($2 divided by $10).
A 20% return on investment is pretty good, so you consider expanding the lemonade stand business. However, you want to run through some scenarios.
Value with No Reinvestment
The status quo is no expansion. In this case, you reinvest none of the profit and pay it out completely as a dividend. However, as a result profits don’t grow.
g = 0% = 20% * (1 - 100%)
As explained in my post on how to value stocks, the value of the business equals the earnings multiplied by the payout ratio divided by the discount rate net of the growth rate.
P = E * payout ratio / (r - g)
At a discount rate of 10%, under the status quo the lemonade stand business is worth 10x earnings. Since earnings are then limited to $40 (20 stands multiplied by $2 per stand), in dollar terms the business is worth $400.
P = E * 100% / (10% - 0%) = E / 10% = E * 10 = $40 * 10 = $400
Value with Low Reinvestment
Since you generate $40 in profit each year and it costs $10 to set up a new stand, you can afford to build four new stands per year. However, you are considering only adding one additional lemonade to start, which would mean reinvesting a quarter of your profits.
Since each lemonade stand generates $2 in profits, that means profits will grow by $2, or 5% relative to the status quo profits of $40. Using the earnings growth formula, this checks out:
g = 20% * (1 - 75%) = 20% * 25% = 5%
As a thought experiment, you want to know what the business would be worth if you could reinvest 25% of the profits forever, which you think could be sustainable. Using the P/E-multiple formula, you find that the business would be worth 15x earnings with 25% sustainable reinvestment. So, continually reinvesting 25% of the profits would make your business 50% more valuable than the status quo with no reinvestment (15x P/E vs 10x P/E).
P = E * 75% / (10% - 5%) = E * 75% / 5% = 15*E = 15*40 = $600
Value with Medium Reinvestment
Let’s say you want to get a little more aggressive and reinvest half the profits. In this case, that means two additional lemonade stands per year, and additional profits of $4, or 10% growth relative to the status quo ($4 / $40). Again using the earnings growth formula, this checks out:
g = 10% * (1 - 50%) = 20% * 50% = 10%
However, you think you can only keep this up for five years, after which you’ll revert to the sustainable 25% reinvestment rate. At that point, the business will be generating about $64 in profits ($40*1.1^5) and will be worth 15x earnings, or $966 total. At a 10% discount rate, the $966 in five years is worth $600 today.
In addition, you’ll have paid out 50% of profits in each of the first year years. So $20 of dividends in the first year, $22 in the second year, $24.20 in the third year, $26.62 in the fourth year, and $29.28 in the fifth year, which summed up is worth $55 in present value. The total value of the business is therefore $655, or almost 64% more than the status quo.
Value with High Reinvestment
Finally, let’s say you want to get really aggressive and invest 100% of the profits for five years, after which you’ll return to a sustainable pace. Since each store cost $10, in the first year with $40 profits you’ll be able to build four more stores. Therefore, the additional profit in the first year is $8 (4 additional stores * $2 profit per store), or 20% growth relative to the status quo profits of $40. Using the earnings growth formula for the final time, again this checks out:
g = 20% * (1 - 0%) = 20%
Since you aren’t paying any dividends the first five year, the value of the business is completely in the value of dividends after year 5 when you return to the sustainable reinvestment rate of 25% and growth rate of 5%. At this point, earnings will be almost $100 ($40*1.2^5), which when multiplied by 15x P/E ratio means the value of future dividends at that point is almost $1,500. Discounting that back to today at 10% results in a present value of future dividends of $927, over 130% more than the status quo.
Takeaway
As shown in the examples above, when the return on incremental investment is good, reinvesting more will increase the present value of future dividends. Therefore, when you have a good return on incremental investment, it makes sense to reinvest as much as you can. And when valuing a business, estimating the company’s reinvestment runway is extremely important.