Company’s Cost of Equity

Required rates of return describe the reward investors expect from taking on a given level of risk.

Cost of Equity

The cost of equity is the minimum return a company must offer to attract investors and keep its share price stable. This cost is commonly calculated using the Capital Asset Pricing Model (CAPM), as illustrated below.

$$ E(R_i) = R_f + \beta_i[E(R_m) – R_f] $$

However, you can also compute it using different models, as we’ll explore in the “Equity Valuation: Concepts and Basic Tools” section.

Return on Equity (ROE)

Return on Equity (ROE) is the key metric for equity investors assessing how effectively a company’s management uses the capital provided by owners to generate profits. ROE is computed by dividing net income by the average book value of equity.

$$ ROE = \frac{NI_1}{(BV_1 + BV_0)/2} $$

Where:

NI₁ = Net income at year-end.

BV₁ = Ending book value.

BV₀ = Beginning book value.

The average book value of equity is used in cases where a company’s book value tends to be volatile from year to year or when it is the industry standard. Otherwise, basing ROE on the beginning book value of equity can also be appropriate.

Required Rate of Return

Investors’ required rate of return on debt securities is simply the interest rate on the company’s bonds. Thus, the cost of debt is equal to the debt investors’ minimum required rate of return.

Investors’ required rate of return on equity securities is more difficult to pin down. An equity investor’s minimum required rate of return is based on the future cash flows they expect to receive, which are uncertain and must be estimated. The minimum required return may differ across investors, resulting in a cost of equity that differs from the minimum required return of some investors.

Question

ABC Corp generated a 15% return on equity in 2017. The 2017 beginning and ending book values of equity were the same. In 2018, ABC Corp reported a 15% increase in net income and a 15% increase in the book value of equity from one year prior. Using the average book value of equity approach, what was ABC’s 2018 return on equity?

1. Exactly 15%.
2. Less than 15%.
3. Greater than 15%.

Solution

The correct answer is C.

The problem with the return on equity calculation is that it only considers the average book value of equity, not the full 15% increase. Since it averages the beginning and ending book values, it results in an average book value that’s only 7.5% higher than the 2017 figure.

Net income, however, increases exactly 15%. The 2017 return on equity was 15%, and 2018 net income increased more than the average book value of equity; therefore 2018 ROE is greater than 15%.