Share Issuance Tutorial

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Introduction

In this tutorial we consider two scenarios for a company issuing new shares: Firstly new shares are issued in exchange for a cash payment, and secondly the cash is used to fund an investment whose return is uncertain. Whether the share issuance results in a gain or loss to the original and new shareholders depends on the company's current market-cap relative to its intrinsic value, which is also uncertain.

We can easily see what happens to the shareholder value when simulating the share issuance, so that thousands of valuations are calculated from probability distributions of the input values. You can view the full simulation reports here, 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.

We use the company Ulta Beauty as an example. We do not have any special insights into this company, 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 value of the company prior to the share issuance, as the present value of the future earnings that could be paid out as dividends. In this example, we assume high earnings growth for the next 5 years, and a terminal growth-rate around 5% per year. The input values are taken from the company's historical data as follows:

• Earnings Y1 = Net Profit Margin (2014-2023) x Sales (2023)
• Earnings Y2 = Earnings Y1 x Sales Growth (2009-2020)
• Earnings Y3 = Earnings Y2 x 1.15 (i.e. 15% growth)
• Earnings Y4 = Earnings Y3 x 1.15
• Earnings Y5 = Earnings Y4 x 1.15
• Terminal Growth-Rate = normal dist 5% mean, 0.5% std.dev.
• Discount Rate = normal dist 10% mean, 1% std.dev.

In this simple example, the funding required for the future growth has not been subtracted from the earnings, so the present value is likely over-estimated, because most companies cannot grow their sales and earnings without additional capital investment e.g. from retained earnings, so these should be subtracted in the calculation of the present value because they are no longer available for dividend payout, but that has been omitted here for simplicity.

It is also important that the dividend tax-rate is zero, otherwise it would distort the valuation of the share issuance.

Using these input values to simulate the present value results in the probability distribution shown in the plot below, which has an average present value of $26.9b.

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

Cash Payment

In the first scenario, the share issuance is made in exchange for a cash payment. We use the intrinsic value from above as input to a model that simulates the effect of a share issuance. 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 for the company's original shareholders, when making the share issuance.

The plot shows there is an 85% probability of loss with the average ROIV being around -1%. This is because the intrinsic value is likely greater than the current market-cap, so the original shareholders would give up more intrinsic value than they get back from the cash payment. It may seem like a small loss of only around -1% on average, but the share issuance is only $1b for a company with a $19b market-cap, and an intrinsic value that is about $27b on average. Had the share issuance been a greater amount, then the loss would also be greater.

The plot below is for the same simulation, but instead shows the so-called Return on Issuance (ROIS) for the company's 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. With these input assumptions, most ROIS ratios are between -200% and +50% with -40.7% on average. So the share issuance could result in a big gain to the original shareholders, but would more likely result in a very large loss, when compared to the amount of the share issuance.

The plot below is for the same simulation, but instead shows the Return on Issuance (ROIS) for the buyer of the newly issued shares, to measure the buyer's percentage gain/loss relative to the amount they paid for the newly issued shares. With these input assumptions, most ROIS ratios are between -50% and +200% with 38.7% on average, so the share issuance could result in a big loss for the buyer of the new shares, but would more likely result in a very large gain, when compared to the amount of money they paid for the newly issued shares. This is because the shares were likely under-valued relative to their intrinsic value.

Note in the two plots above, that the probability of loss does not sum to 100% for the company and the buyer of the newly issued shares. That is because this particular kind of share issuance is only a "zero-sum game" when the fees are zero.

The plot below varies the current share-price on the x-axis and shows the ROIV ratios on the y-axis. This lets us easily see how the ROIV ratios change with the current share-price. The plot for the ROIV ratio further 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. The full report also has similar plots for the two ROIS ratios.

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

Investment

In the second scenario, the cash raised by the company in the share issuance is used to make an investment whose return is also uncertain. We again use the intrinsic value from above as input to the simulation model. The issuance amount is again $1b and this should include all fees for the share issuance and investment. The present value of the return on the investment is normal distributed with mean $1.2b and std.dev. $100m, so the return on investment is 20% on average.

The plot below shows the Return on Issuance (ROIS) for the company's original shareholders, which measures the percentage gain/loss relative to the issuance amount. With these input assumptions, most ROIS ratios are between -200% and +100% with -19.8% on average. The probability of loss is 64%. This is because the company's current market-cap is likely lower than its intrinsic value, so the share issuance would likely result in a loss for the original shareholders, but that is partially offset by the average 20% return on investment. Compare this to the plot further above for a cash payment, whose ROIS ratios are roughly 20% lower than the plot below.

The plot below is for the same simulation, but instead shows the Return on Issuance (ROIS) from the perspective of the buyer of the newly issued shares, to measure the buyer's percentage gain/loss relative to the amount they paid for the newly issued shares. With these input assumptions, the range is around -50% to +200%, so the share issuance could result in a big loss for the buyer of the new shares, but would more likely result in a very large gain, when compared to the amount of money used for the share issuance.

Note in the two plots above, that the probability of loss does not sum to 100% for the original shareholders and the buyer of the newly issued shares. The average loss for the original shareholders is also -19.8%, while the average gain is +39.8% for the buyer of the newly issued shares. That is because this particular kind of share issuance is only a "zero-sum game" when the issuance amount exactly equals the return on the investment.

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