Stock Swap – M&A Tutorial

Introduction Intrinsic Value Full Acquisition Partial Acquisition

Introduction

In this tutorial we consider two scenarios for a stock swap: (1) Company A issues new shares to fully acquire all the shares in company B, and (2) both companies issue new shares and swap them with each other, so they end up owning a part of each other. Whether the stock swap results in a gain or loss to the shareholders in the two companies, depends on how many shares are issued and swapped, relative to the intrinsic values of the two companies.

We can easily see what happens to the shareholder value when simulating the stock swap, so that thousands of valuations are calculated from probability distributions of the input values. You can view the simulation reports for the intrinsic values here and here, and for the stock swaps here and here, and clone the simulations to run them yourself with different input values. The valuation formulas used in the simulation models are described in the docs.

In this example we use Ulta Beauty (ULTA) as company A and Sally Beauty (SBH) as company B. We do not have any special insights into these companies, so we merely use historical data to estimate the probability distributions for the future earnings. We will not update this tutorial with new data in the future.

Intrinsic Value

We first simulate the intrinsic values of the two companies prior to the stock swap, as the present value of the future earnings that could be paid out as dividends.

In this example, we use the companies' historical Net Profit Margin and recent sales to estimate the next year's earnings. For both companies we assume zero real earnings growth in the future, and the discount rate is normal distributed with 10% mean and 1% std.dev. It could be argued that SBH should have a higher discount rate than ULTA, because SBH has more debt which makes it more risky, but we keep this example simple and you can run the simulations with other assumptions.

It is important that the dividend tax-rate is zero in these simulations of the present value, otherwise it would distort the valuation of the share issuance.

The simulated present values are shown in the two plots below. The left plot is for company A (ULTA) which has an average present value of $8.79b, compared to a market-cap of $18.9b. The right plot is for company B (SBH) which has an average present value of $2.1b, compared to a market-cap of $1.2b. So given these inputs for next year's earnings and zero future growth, ULTA is over-valued and SBH is under-valued.

Histogram of Present Value for the company Ulta Beauty when assuming zero earnings growth. Histogram of Present Value for the company Sally Beauty when assuming zero earnings growth.

You can view the full reports here and here and clone the simulations to run them yourself with different input values.

Full Acquisition

In the first scenario, the company A (ULTA) issues new shares to pay for a full acquisition of all the shares in company B (SBH). We use the intrinsic values from above as input to a model that simulates the effect of this stock swap. The present value of the earnings synergy between the two companies is normal-distributed with $100m mean and $10m std.dev. The transaction fees are set to $20m. We assume company A takes over the debt and liabilities of company B, otherwise company A would have to repay those when making the stock swap.

The so-called Swap Ratio is how many new shares are issued in company A (ULTA) for each share in company B (SBH). In this example we use a swap ratio of 0.03 because that corresponds to the current market-prices for the shares, which means company A is over-valued and company B is under-valued. In the video we change the swap ratio to around 0.11 so it is a more fair transaction for the two companies.

The model outputs several plots with the simulation results. The two plots below show histograms with the so-called Return on Intrinsic Value (ROIV) for the two companies, which is the percentage gain/loss to the intrinsic value for each company's original shareholders, when making the stock swap. The left plot shows there is nearly zero probability of loss for the shareholders of company A (ULTA), with the average ROIV being around 19.9%. The right plot shows there is nearly 100% probability of loss for the shareholders of company B (SBH), with the average ROIV being around -66.8%. This is again because the shares of company A (ULTA) are over-valued, and the shares of company B (SBH) are under-valued.

Histogram of simulated gain/loss for the original shareholders, when making a stock swap. Histogram of simulated gain/loss for the original shareholders, when making a stock swap.

The two plots below are for the same simulation, but instead show the so-called Return on Issuance (ROIS) for the two companies' original shareholders, which measures the percentage gain/loss relative to the issuance amount, so it may give a better sense of the magnitude of the gain/loss. The left plot shows the ROIS ratios for company A (ULTA) which are 123% on average. The right plot shows the ROIS ratios for company B (SBH) which are -117% on average. This is again because the shares of company A are over-valued and the shares of company B are under-valued, with the assumptions above. Note that this is only a "zero-sum game", so the loss of one company is exactly equal to the gain of the other company, when the fees equal the earnings synergy between the two companies.

Histogram of simulated gain/loss for the original shareholders, when making a stock swap. Histogram of simulated gain/loss for the original shareholders, when making a stock swap.

The two plots below vary the swap ratio on the x-axis and shows the ROIS ratios on the y-axis. This lets us easily see how the ROIS ratios change with the swap ratio. The two plots above for the ROIS ratios are actually the slices shown as the vertical dashed blue lines below. The shade of blue indicates the density of simulation results in a region of the plot, where darker blues indicate a higher density. In order for this to be a fair transaction where the shareholders of both companies have a roughly 50/50 chance of gain/loss, the swap ratio should be much higher around 0.11 as shown in the video above.

2D histogram of simulated gain/loss from making a stock swap, when also varying the swap ratio. 2D histogram of simulated gain/loss from making a stock swap, when also varying the swap ratio.

You can view the full report and clone the simulation to run it yourself with different input values.

Partial Acquisition

In the second scenario, the two companies both issue new shares and swap them with each other, so they end up owning a part of each other. We again use the above intrinsic value distributions for the two companies. Company B (SBH) issues 10m new shares in addition to its currently outstanding 110m shares. The swap ratio is again 0.03 so we use the current market-values for the shares, which means that company A (ULTA) should issue 0.3m new shares to swap with the 10m new shares in company B (SBH).

The two plots below show the Return on Intrinsic Value (ROIV) for the two companies, which is the percentage gain/loss to the intrinsic value for each company's original shareholders, when making the stock swap. These are quite similar to the plots above for a full acquisition, except that the magnitude is much smaller, because it is only a small part of the shares in the two companies that are swapped here. The left plot shows there is nearly zero probability of loss for the shareholders of company A (ULTA), with the average ROIV being around 1.67%. The right plot shows there is nearly 100% probability of loss for the shareholders of company B (SBH), with the average ROIV being around -5.92%. This is again because the shares of company A (ULTA) are over-valued, and the shares of company B (SBH) are under-valued.

Histogram of simulated gain/loss for the original shareholders, when making a stock swap. Histogram of simulated gain/loss for the original shareholders, when making a stock swap.

The two plots below are for the same simulation, but instead show the Return on Issuance (ROIS) for the two companies' original shareholders, which measures the percentage gain/loss relative to the issuance amount. That is why these plots are almost identical to the plots above for the full acquisition.

Histogram of simulated gain/loss for the original shareholders, when making a stock swap. Histogram of simulated gain/loss for the original shareholders, when making a stock swap.

The two plots below vary the swap ratio on the x-axis and shows the ROIS ratios on the y-axis. This lets us easily see how the ROIS ratios change with the swap ratio. The two plots above for the ROIS ratios are actually the slices shown as the vertical dashed blue lines below.

2D histogram of simulated gain/loss from making a stock swap, when also varying the swap ratio. 2D histogram of simulated gain/loss from making a stock swap, when also varying the swap ratio.

It is not a mistake that these two plots look quite different. It is because the new number of shares in company B is held constant at 10m, while the new number of shares in company A varies with the swap ratio. This means the issuance amount for company B is constant in the calculation of its ROIS ratio, while the issuance amount varies in the calculation of the ROIS ratio for company A. This tends to make the plot for company A (left) look more curved, while the plot for company B (right) looks more linear.

You can view the full report and clone the simulation to run it yourself with different input values.