6. Application

Let us have a look at a few examples to practice the key relationships that we have discovered in this section. Please note that there is a separate module Leverage and the Cost of Capital which deals in great detail with the practical estimation of the cost of capital in virtually all valuation situations.

 

Application 1: Hershey's

Let us go back to the company Hershey's that we have analyzed at the beginning of this module. Now we want to estimate the firm's cost of equity. Let's assume the following:

  • The firm's overall cost of capital kA is 7%. 
  • The firm's cost of debt kD is 3%
  • The firm's debt-to-equity ratio (D/E, using market values) is 0.12

 

With this information, we can easily estimate the shareholders' required rate of return, kE:

 

\( k_E = k_A + (k_A - k_D) \times \frac{D}{E} = 0.07 + (0.07 - 0.03) \times 0.12 \) = 7.48%.

 

Interpretation: Because Hershey's leverage (in market values) is moderate, the firm's cost of equity (7.48%) is not much higher than the overall cost of capital (7%). 

How would the situation change if the firm decided to increase its debt-to-equity ratio to, say, 2 (that is, 66.7% of debt and 33.3% of equity)? Let's assume that this new financing policy would bring about a cost of debt of 4%. The result would be a considerable increase in the cost of equity to 13%:

 

\( k_E = k_A + (k_A - k_D) \times \frac{D}{E} = 0.07 + (0.07 - 0.04) \times 2 \) = 13%.

 

Application 2: The Financial Industry

The minimum equity requirements for banks are currently a very hot topic in the financial industry. Why is that? To understand parts of the discussion, let's consider a simplified case:

  • Let's assume that the average return a bank can generate with its operating activities is 1% (kA).
  • Moreover, let's assume that the typical debt-to-capital ratio in the industry is 0.95 and that banks can borrow money at a cost of 0.1% (kD).
  • Based on these numbers, the shareholders of a typical bank expect to earn an annual return of approximately 18%:

    \( k_E = k_A + (k_A - k_D) \times \frac{D}{E} = 0.01 + (0.01 - 0.001) \times \frac{0.95}{0.05} \) = 18.1%.
     
  • In words: by using substantial leverage, banks can translate a moderately profitable business into a high-return business for their shareholders.
  • Now suppose the regulator intervenes and limits the maximum debt-to-capital ratio to, say, 80%. Assuming the cost of borrowing (kD = 0.01) remains the same, these higher equity requirements drastically reduce the shareholders' expected rate of return:
     
    \( k_E = k_A + (k_A - k_D) \times \frac{D}{E} = 0.01 + (0.01 - 0.001) \times \frac{0.8}{0.2} \) = 4.6%.
     
  • The new regulation reduces the expected return on equity from 18.1% to 4.6%. Therefore, so the argument, stricter equity requirements are bad for business because it renders bank shares less attractive to investors.

 

With the knowledge from this section, we can easily see that this argument is incomplete. In principle, the expected return on equity drops because the firm's equity becomes less risky. However, the firm's underlying profitability (the cost of assets) remains the same across financing policies, and so should its ability to create value. Moreover, if shareholders have a preference for more risk (and returns), they can lever up their own portfolio. They do not need a (potentially systemic) bank to do that for them.

 

Application 3: Executive Compensation

Suppose a CEO's compensation depends on the firm's return on equity in a way that he receives a bonus if the return on equity exceeds 15%. The firm is fully equity financed and earns a return on assets of 10%. What can the CEO do to reach his bonus target?

In principle, there are two possible solutions:

  • He can work hard and improve the operating profitability (ROA) of the firm
  • He could initiate a share repurchase program in which the firm borrows money to repurchase shares from current shareholders.

 

Our CEO in question prefers borrowing over working hard. Let's assume the firm can borrow at 4%. Which fraction of the outstanding shares does he have to repurchase to reach a return on equity of 15%? Put differently, given the firm's kA and kD, at which debt-to-equity ratio will does the expected return on equity reach 15? We can solve the above equation for (D/E) to find an answer:

 

\( \frac{D}{E} = \frac{k_E-k_A}{k_A - k_D} = \frac{0.15-0.10}{0.10-0.04} \) = 0.833.

 

The firm's expected return on equity will increase to 15% if the debt-to-equity ratio increases to 0.833. Put differently, the CEO might have an incentive to move from a financing policy with zero debt to a financing policy with approximately 45% of debt and 55% of equity [0.45/0.55 ≈ 0.83].

 

This simple illustration raises a key concern of equity-based performance metrics such as the return on equity. The return on equity is not a pure measure of the firms operating profitability. Instead, it is a measure that blends operating profitability and financing policy. Therefore, it is not always easy to interpret. In particular, it is not directly clear whether an increase in ROE is the result of a better operating performance (which, one could argue, might be value enhancing) or a more aggressive financing policy (which, as we have seen, adds risk without affecting value). Therefore, it is actually not clear whether a higher ROE is indeed better for the shareholders. This raises doubt about the usefulness of ROE (and related metrics such as EPS) as a performance measure...

For a more comprensive discussion of ROE and its decomposition into various performance drivers from an accounting point of view, please refer to the module Financial Analysis.