### 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 expected rate of return that a company must offer its investors to purchase its shares in the primary market and to maintain its price in the secondary market. The cost of equity is often found using CAPM:

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

but could also be calculated using other models, which we will see in the section Equity Valuation: Concepts and Basic Tools.

## Return on Equity (ROE)

Return on Equity is the primary measure that equity investors use to determine whether the management of a company is effectively and efficiently using the capital that the owners have provided to generate profits. Return on equity is calculated by taking net income and dividing it 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 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 during 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?

A. Greater than 15%

B. Less than 15%

C. 15%

Solution

The correct answer is A.

Since return on equity is being based on the average book value of equity, the full 15% increase in the book value of equity is not being accounted for in the denominator. Because the beginning and ending book values are averaged together, the average book value used in the calculation would only be 7.5% higher than the same figure in 2017.

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 so therefore 2018 ROE is greater than 15%.

Reading 47 LOS 47h:

Compare a company’s cost of equity, its (accounting) return on equity, and investors’ required rates of return

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