4. ROE, EPS, and Equity Value

It is a misconception held by many practitioners that firms should take measures to improve Earnings per Share (EPS) because higher EPS will result in a higher stock price. This argument is often brought forward in the context of share repurchase programs, which tend to be EPS accretive. Often, managers are also willing to take great pain to avoid corporate actions that dilute EPS.

The purpose of this section is to quickly show that the world is not as simple as that. EPS and its changes are per se irrelevant for valuation. In fact, it is easy to fabricate transactions that increase EPS but destroy value.

 

ILLUSTRATION

To see that EPS is not directly value relevant, consider a very simple firm. This firm holds two assets:

  • 10'000 of Cash. For simplicity, let's assume that the firm earns no interest on this cash (this makes the analysis simpler without affecting the main conclusions).
  • Business-relevant assets with a market value of 9'000. 
  • By operating these assets, the firm generates a net income of 900. 
  • The firm is fully equity financed; there are no liabilities.
  • There are 10'000 shares of common stock outstanding.

 

With this information, we can describe the current financial situation of the firm as follows:

  • The market value of the firm is 10'000 (1'000 cash plus 9'000 business-relevant assets)
  • The market value of the firm's equity  is also 10'000 (because there is no debt outstanding)
  • The return on equity is 9% [= Net income / Equity = 900/10'000].
  • The theoretical share price is 1 [=Equity value / Number of shares = 10'000/10'000]
  • The firm's earnings per share (EPS) are 0.09 [= Net income / Number of shares = 900/10'000]

 

A SHARE REPURCHASE PROGRAM

Now let's assume that the firm decides to use it's cash of 1'000 to repurchase shares at the prevailing market price of 1. How will this transaction affect the ROE, EPS, and equity value of the company? 

  • At a share price of 1, the firm will be able to repurchase 1'000 shares. Hence, after the transaction, there will be 9'000 shares outstanding.
  • If net income remains at 900 (remember, the cash did not generate any interest income), EPS will increase from 0.09 to 0.1 [= 900/9'000]. Hence, the share repurchase program clearly increases EPS. The reason is quite obvious: The same amount of net income is shared among fewer shareholders.
  • As the firm pays ot the cash, the only remaining assets are the "business-relevant assets" with a value of 9'000. If the value of these assets is unaffected by the repurchase program (there is no obvious reason why it should be), the equity value after the transaction will be 9'000.
  • Hence, the firm's return on equity will be 10% [= Net income/Equity value = 900/9'000]. Clearly, the transaction therefore also improves the firm's return on equity (from 9% to 10%). Again, the reason is obvious: The firm disposes of the asset with the lowest return (and the lowest risk). If the return on the other assets does not change, thetotal return per invested dollar will go up. 
  • But what about value creation? Does the transaction also add value? The answer is NO. We can see this quite easily: Before, we have concluded that the equity value will be 9'000 after the repurchase program and that the firm will have 9'000 shares outstanding. Hence, the share price after the transaction will be 1 [= Equity value/Number of shares = 9'000/9'000]. The share price does not increase --- the transaction does not add any value.

 

INTERIM CONCLUSION

In sum, the above example has illustrated that there is no direct relation between ROE, EPS, and value creation. While the share repurchase program improves ROE and EPS, it leaves the share price unaffected. The reason is simple: In order to repurchase shares (reduce the numbers of shares outstanding), the firm has to liquidate its cash (reduce the value of its assets). In an efficient market, the two effects cancel each other out.

 

EXTENSION 1: BUT WHY DO SHARE PRICES GO UP?

In reality, the announcement of a share repurchase programs often brings about a slight increase in the share price. As many observers argue, the reason for this increase lies in the signal the management sends to the market when repurchasing shares. One interpretation of the repurchase decision could be that the firm believes its stock to be undervalued ("cheap"). With the repurchase program, the firm buys the shares "cheap," only to sell them later when the undervaluation has disappeared. 

 

Applied to our example, the share repurchase announcement could signal the market that the firm believes its "business relevant assets" to be more valuable that the 9'000 currently ascribed by the market. If the market thinks this signal is credible and reassesses the value of these assets to, say, 9'500, the share price might indeed increase---most likely by about 5% to approximately 1.05.

 

What is important to note, however, is that the increase in the share price is not caused by the higher earnings per share (EPS) the repurchase program brings about. The effect comes from the new information the market receives: "Our stock is undervalued." The firm could send another (credible) signal to the market to achieve the same outcome (for example, it could solicit a takeover bid).

 

EXTENSION 2: HIGHER EPS BUT LOWER STOCK PRICE

Note that it is not hard to fabricate a (realistic) situation where EPS goes up and value goes down. Try this for size: The announcement of the repurchase program could also send another signal to the market: "We return our cash because we ran out of good investment opportunities." If the market did not "know" that the firm has no more investment opportunities, it will most likely revise the valuation of the "business relevant assets" downwards to, say, 8'500. Presumably, there will be no direct impact on EPS, at least if the lack of investment opportunities applies to potential projects that would be realized only a few years down the road.

  • Upon the announcement, the share price will therefore drop to 0.95 [=(1'000 + 8'500)/10'000].
  • Assuming the firm repurchases shares at the new market price (0.95), it will repurchase 1'053 shares.
  • Assuming net income does not immediately change because of the negative signal, EPS will increase to approximately 0.1 [= 900/(10'000 - 1053)].

Hence, we have just fabricated a situation where EPS goes up and value goes down.

 

CONCLUSION

This brief discussion has illustrated that there is no direct relation between EPS, ROE, and shareholder value. In particular, EPS per se is irrelevant for valuation. 

It is very well possible that many transactions that increase EPS are good for shareholders. But these transactions are not good for shareholder because EPS goes up but because of another effect that takes place at the same time (for example, shareholders learn that the firm believes its stock to be undervalued). 

Similarly, it is possible that EPS accretive transactions go in hand with lower shareholder value. Again, the reason is an "other" effect that happens at the same time (for example, shareholders learn that the firm ran out of investment opportunities). 

So while EPS and shareholder value might be correlated in many instances, it is hard to make a case that changes in EPS cause changes in shareholder value. Therefore, we should always be critical when managers praise corporate actions because they increase EPS...