Share Buyback Simulation
How to simulate the value of a share buyback to long-term shareholders.
Introduction
There are a lot of myths and disagreements about share buybacks. Academia does not have a proper framework for valuing share buybacks, because finance professors have believed for half a century, that stock-markets are “efficient” so share-prices always equal the “risk-adjusted value” to long-term investors. From this belief they concluded that there was no difference between share buybacks and dividends, possibly with the exception of taxes. But their arguments are pseudo-science.
The reality is that a share buyback has two immediate effects: It reduces the company’s cash holdings, and it reduces the number of shares outstanding. So a share buyback is a kind of investment the company is making in itself, on behalf of the remaining shareholders. It obviously matters a great deal whether the shares are priced high or low compared to the future earnings of the company.
SimSim.Run makes it very quick and easy to simulate share buybacks (among other things), so you can see how it impacts the shareholder value. Once you learn how to use it, you can make a simulation in just a few minutes, and you can also share it with others. We recommend you watch the tutorial video and study the paper as well.
Simulate Earnings
It seems obvious that a share buyback should only be made when it benefits the remaining shareholders. From this statement it can be argued, that there is no need to consider a share buyback’s impact on future share-prices, because we are always valuing the share buyback from the perspective of an “eternal” shareholder who will never sell their shares, so the valuation should only consider the future earnings that could be paid out as dividends. We will do that here, but we will also simulate the share-prices further below.
We use the company Foot Locker in this example. The future earnings are simulated from the company’s historical Net Profit Margin and recent sales. We assume zero real earnings growth to make a conservative valuation, that is, we assume the earnings merely grow the same as the inflation. We use a fixed discount rate of 9% here, which is the historical average real return on the S&P 500 stock-index, plus a 5% risk-premium.
The model outputs several plots with the simulation results. The plot below shows a histogram with the so-called Return on Intrinsic Value (ROIV), which is the percentage gain/loss to the intrinsic value per-share, when making a share buyback instead of a dividend payout now. Most of the values are between 1–3%. This may seem small, but the share buyback is only $100m for a company with a $2.5b market-cap, and an intrinsic value that is likely somewhere between $2–9b. If the buyback amount is $500m instead, then the ROIV is mostly between 10–20%, which would be a very significant gain in shareholder value, achieved simply by repurchasing the shares at a significantly lower price than their intrinsic value.
The plot below is for the same simulation, but shows the so-called Return on Buyback (ROB) instead, which measures the percentage gain/loss relative to the buyback amount. With these input assumptions, the range is around -100% to +400%, so the share buyback could result in a big loss, but would more likely result in a very large gain, when compared to the amount of money used for the share buyback.
The plot below varies the current share-price on the x-axis and shows the ROB ratios on the y-axis. This lets us easily see how the ROB ratios change with the current share-price. The histogram above is actually the slice shown as the vertical dashed blue line. The shade of blue indicates the density of simulation results in a region of the plot, where darker blues indicate a higher density.
You can view the full report and clone the simulation to run it yourself with different input values.
Simulate Share-Prices
A common argument in favor of companies making share buybacks instead of dividend payouts, is when capital gains taxes are lower than dividend taxes. In this tutorial we have set all tax-rates to zero, but you can clone the simulation to experiment with different tax-rates. You will find that different tax-rates do affect the value of share buybacks, but the share-price relative to the intrinsic value is far more important.
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In addition to the future earnings, we now also simulate the company’s future share-prices by splitting the price into two components: A valuation metric such as P/E or P/S ratio, and the earnings or sales. We simulate these independently of each other and multiply the values together to get the share-price. We personally prefer using historical P/S ratios because they are usually much more stable than P/E ratios, which are also ill-defined when the earnings are negative or zero.
Below is a so-called violin-plot which shows the distributions vertically with simulation results for each future year (these sometimes resemble violins). This plot shows the ROIV for each of the 10 future years, that is, if the company makes a share buyback at the current price, and you sell your shares in one of the future 10 years, then how much has the intrinsic value of the shares gained or lost from making the share buyback today, compared to the company making a dividend payout instead.
The plot below varies the current share-price on the x-axis and shows the ROIV ratios on the y-axis. This shows that if the current share-price is lower, then the ROIV ratios are higher, and vice versa. So a share buyback becomes increasingly beneficial to the remaining shareholders, as the share-price becomes lower relative to the stock’s intrinsic value, and vice versa. That is also common sense.
You can view the full report and clone the simulation to run it yourself with different input values.
Video Tutorial
It is recommended that you also watch the full video tutorial, which shows and explains many more details.
Caution
This is an example that should not be considered investment advice for a specific stock or valuation methodology. We do not have any special insights into the stocks used in these examples, and we merely use historical data to generate the probability distributions. We may buy and sell these stocks at any time due to changing share-prices and assumptions about the company’s future, but we will not update these examples.
Although simulation models are far more useful than point-estimates, the accuracy of the simulation still depends on how accurately you have estimated the probability distributions.
