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The Economics Of Share Repurchases

One of the many great challenges of investing is properly evaluating the business economics of a share repurchase plan. The subject has left many of us scratching our heads. The intent of this article is to dispel the misconceptions and half-truths commonly associated with repurchases. The basic mechanics of repurchases are illustrated, as well as the economic consequences to the continuing long-term shareholder. In addition, the increasing marginal benefit of share repurchases will be discussed, as well as the benefit that arises when new investors acquire stock during a period of both undervaluation and ongoing share repurchases. Finally, the responsibility of a company's management to properly evaluate a repurchase opportunity is addressed.

The mechanics of a share repurchase are straight forward. Typically, the management of a company uses excess cash on the company's balance sheet to purchase outstanding shares of its own company. Often times, the shares are bought directly from the secondary market at the prevailing market price. These shares are effectively taken out of circulation, creating a greater concentration of equity ownership in the hands of the remaining shareholders. Although it's natural to assume that this will benefit shareholders in all instances, it's not always the case. The following examples will illustrate why this is;

Example1: Share Repurchases During a Period of Undervaluation

Company XYZ is a hypothetical company with a total of only 5 common shares outstanding. This simple company does not own any property, plant, or equipment, doesn't provide a service, has no debt, doesn't pay any salaries, and doesn't do much of anything for that matter. It does, however, hold two types of assets:

  1. The company keeps a total of $50 in a bank account. The money earns interest at the prevailing risk-free interest rate at all times.
  2. The company owns a perpetual security yielding $10/year. The cashflows (earnings) are paid out to the shareholders as an annual dividend.

Let's also assume that the tax rate on all company dividends and earnings is 0%, and the discount rate used to value the earnings is 10%. (These assumptions, although unrealistic, will affect only the company valuation, not the underlying principles discussed here).

Under these conditions, the $50 in the company's bank account should generate at least $50 dollar of intrinsic business value, or $10/share. The $10/year of perpetual interest payments would add a present value of $100, or $20/share (The value of a perpetuity = cashflow/discount rate). During "normal" times, the market value of the stock will most likely be aligned with the intrinsic value of the company. The shares will trade close to their fair value of $30/share. This scenario is illustrated below:

Each of the 5 shares of company XYZ have an equal claim on 1/5th of the $50 in the bank account, as well as 1/5th of the earnings value from the perpetuity. The different colors represent the two different types of assets, the green blocks being cash, and purple blocks, earnings power. The relative length of each block depicts the dollar amount of the asset's value.

Let's now assume that the entire stock market suddenly loses 1/3 of its value as the result of a large widespread market panic. The fundamentals of XYZ remain intact (and interest rates remain unchanged), but the share price of the stock plummets to $20/share from its original $30. Each share can now be acquired for a discount to its intrinsic value of $10/share. The situation is represented below;

Aware of this large undervaluation, management decides to repurchase its own stock. Since the company does not need the cash to make operating or capital expenditures, the management considers all of the $50.00 as "excess" capital, and is free to spend it buying back stock. The next trading day the company buys back a single share of XYZ (20% of the outstanding shares) for $20/share. The result of the share repurchase is shown below.

Since the company has one less shareholder after the repurchase, the $20 earnings value of the repurchased share has now been transferred equally to the remaining shareholders. This will materialize in an annual earnings increase of $0.50/share, or an increased present value of $5.00/share. It's critical to note that the EPS increase is only half of the story. Since the stock was repurchased with $20.00 from the company's balance sheet, the company's new cash position has decreased to $30.00, or $7.50/share. To properly evaluate the economic effect of the repurchase, both the benefit and the cost to remaining shareholders must be considered. In this example, each remaining shareholder paid 2.50/share in cash to receive $5.00/share in earnings value. The net effect of management's decision to buy back shares resulted in an increase per-share intrinsic value of $2.50, to $32.50, or 8.3% (relative to intrinsic value). Put another way, for every $1 the continuing shareholders gave up in cash, they received $2 in earnings value from the folks leaving. This example demonstrates a repurchase situation that created value for the remaining shareholders.

Example 2: Share Repurchases During a Period of Share Overvaluation

Now let's assume the share repurchase in Example 1 never happened and XYZ is back to 5 shares. This time, instead of a depression, the market surges into a period of euphoria. As a result, market values become detached from underlying business values and market prices skyrocket. Instead of the company selling in the market at a discount to intrinsic value, as in the previous example, it now sells for a $10 premium, or $40/share. XYZ's financial position is shown below;

Despite the share premium, the management decides to repurchase one share of the company's stock. XYZ's financial position after the repurchase is as follows;

This time the economic effect of the repurchase yields a quite different result. As in the last example, management's decision to repurchase shares has led to an increase in EPS of $0.50 per annum, or an added earnings value of $5/share. (The management team will always be quick to advertise this seemingly pleasant result). The unfortunate truth is that the economic benefit to the remaining shareholder did not outweigh the cost. As one can see, the company spent $7.50/share for only $5 of increased earnings value. The net result of the repurchase is a total per-share intrinsic value decrease of $2.50. In this case, the management effectively took $10.00 of cash from the balance sheet and donated it to the shareholders dumping the stock. So much for fiduciary duty!

It becomes clear that the increase in per-share intrinsic value resulting from share repurchases originates exclusively from the undervaluation of the repurchased stock. In Example 1, the $10.00/share discount was effectively transferred pro-rata from the single exiting shareholder to the four remaining shareholders. During a well executed share repurchase, capital is not so much returned to shareholders as it is transferred from active ones to the less active ones. (More on this later). In Example 2 however, that same $10.00 flowed out of the company to the selling shareholder.

A Bit of Math

We can mathematically express the value added (or lost) as a result of the repurchases. The following formula shows the economic per-share value gain or loss (in dollars) as a result of repurchases in a given period;

The formula simply expresses what was already observed in the previous examples. It shows that the per-share value created (or destroyed) as a result of share repurchases is simply the average per-share discount to intrinsic value (Vi-Pavg), times the number of shares repurchased Srp, distributed evenly across the remaining shareholder base So.

It's just as useful to express this result as a percentage of intrinsic value;

Close investigation into these formulas yields the following conclusions;

  1. The per-share value created, Vc, is proportional to the discount to intrinsic value, Davg. The more the market discount to intrinsic value widens, the greater the economic benefit to remaining shareholders. Conversely, if share repurchases are executed when the company is selling at a premium to intrinsic value, Davg will be negative, and the result is a transfer of business value from the continuing shareholder to the exiting shareholder. When the stock is fairly valued, average market price and business value are equal (Davg is zero), and nobody benefits.
  2. In addition to the market discount, the per-share value created, Vc, is also proportional to the number of shares repurchased during the period, Srp, and inversely proportional to the amount of shares remaining after the repurchase, So. As the numerator increases, the denominator decreases (excluding the effects of executed options, warrants, share issuance, etc.) This effect, taken alone, creates an increasing marginal benefit to the remaining shareholder. Figure 1 illustrates this pleasant result under different market discounts;

Figure 1- Economic Benefit of Repurchases at Different Market Discounts

The graph uses Equation 1c to plot the value added per-share as a result of repurchases, Vc/Vi, against the percentage of the company repurchased in a given period, Srp/Stot. Each curve represents a different discount to intrinsic value. As discussed above, a greater discount will result in a proportionally greater added value. In this undervalued condition, the value added to each share increases exponentially as more if the company is repurchased.

In practice, the amount of shares repurchased will be limited by the amount of excess cash on a company's balance sheet. A greater market discount will not only magnify the repurchase benefit, but will also allow for a greater number of shares to be repurchased in a given period. This will thus maximize the increasing marginal benefit effect of the repurchase. The benefit to shareholders becomes self-reinforcing the more the stock price falls relative to value. The dotted lines in Figure 1 represent the maximum amount of shares available for repurchase with a given amount of excess cash. The excess cash is represented as a proportion of intrinsic value. It's clear that the optimum benefit to shareholders will result from the repurchase of the maximum amount of shares possible during a period of maximum undervaluation. In the case of share repurchases, an opportunistic management is the friend of the long term investor.

Example 3: Entering Shareholders

So far, the discussion has focused on the benefits of share repurchases to existing shareholders. However, shareholders buying into a company during a period of both undervaluation and share repurchases can receive substantially more value than the existing shareholders of that same company. Both groups receive the benefit of the share repurchase previously discussed, but the new shareholder also receives the value of the current market discount. This is because the initial investment is made at the depressed market price. The outcome can be illustrated using the post-repurchase results of Example 1 presented earlier;

Since a new shareholder can buy a share at the depressed market price of $20.00, the total benefit from this well timed share acquisition is $2.50/share due to the repurchase, plus $10/share from the market discount. The savvy investor can buy $32.50 of value for only $20.00. This "dual benefit" for the new shareholder is expressed mathematically below;

Equation 2b is also presented below as a percent of intrinsic value;

The expression sums both the value created from the ongoing repurchase and value obtained from the initial purchase of the undervalued share. It also assumes that the average purchase price of the entering investor is the same price the management is paying for their shares. If the company is indeed undervalued, the total economic benefit received by the new shareholder will be, at a minimum, equal to the discount to intrinsic value. The benefit will multiply as the company repurchases greater amounts of stock.

Management Responsibility and the Return of Capital Myth

Managements that choose to repurchase shares must first acknowledge that, unlike a dividend, their judgment alone determines the benefit to shareholders. As shown above, the optimum benefit arises when repurchases are executed shrewdly. Thus, it is managements' responsibility to perform the following tasks when confronted with the decision of share repurchases;

  1. Formulate a proper valuation of the company before shares are repurchased. (An outside opinion by one or more independent parties may be better for shareholders than the "instinct" of an optimistic CEO.)
  2. Compare the conservatively estimated share repurchase benefit to all other capital allocation alternatives and execute the best option.
  3. Act at all times in the best interest of the long term shareholder. This includes displaying restraint during periods of fair or overvaluation, even when the exercise of performance stock options start to dilute the EPS figure.

Incidentally, these guidelines are nearly identical to the due diligence performed before any typical business investment or acquisition. The main difference for a repurchase evaluation is that management already knows everything there is to know about their potential target. Although share repurchases are often labeled as a "return" of capital, and can be shown as mathematically equivalent under certain circumstances, it may be more appropriate to classify them as a reinvestment of capital. Beware of managements that hide behind the pretext of the former definition to avoid the accountability inherent in the latter. Whether investing in whole companies, real estate, oil wells, or the earnings of exiting shareholders, the benefit to long term shareholders originates from management paying less for an asset than what that asset is intrinsically worth. As in any investment, it's management's judgment and skill, or lack of, that will be the deciding factor. When evaluating companies that regularly repurchases their own stock, choosing a company with the right management will be just as important as choosing the right company. Be sure to choose wisely.