Cost of equity, Return on equity, P/E | KPMG | JM

# Cost of equity, Return on equity, P/E

In Vol 3, we discussed the concept of cost of capital, how it is calculated and how to determine the optimal capital structure of a business. A key input into the cost of capital is the cost of equity. Before discussing how to calculate cost of equity as used in notional valuations we examine how cost of equity compares to return on equity and the price to earnings multiple.

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As a reminder Cost of Equity (“Ke”) is the rate of return required or expected by equity investors. This is the rate of return that a firm theoretically should pay to its shareholders to compensate them for the risk that they undertake by purchasing shares. Ke is therefore an expected rate of return on the market value of equity.

Return on equity (“ROE”) is a financial ratio that expresses the accounting profit as a percentage of the accounting share capital of the subject company.

ROE is therefore based on accounting profit and financial statement equity. Putting aside the impact of accounting estimates and financial reporting standards the biggest difference between ROE is backward looking and Ke is forward looking.

The price to earnings multiple (“P/E”) is a market multiple that compares a company’s market value to its earnings. It is a commonly used multiple to compare relative worth of two businesses of different sizes and earnings capacity. The P/E multiple is also a capitalization multiple in that for a given earning amount it can used to quickly estimate the market value of company’s equity.

Because the P/E multiple is a capitalization multiple many persons mistake the inverse of the P/E multiple as being a proxy for the company’s Ke.

In Vol 1, we discussed the income approach to valuation; one of the approaches within the income approach is the capitalization of earnings. Converting the Ke to a capitalization multiple requires an adjustment for the forecast growth rate. Using “g” as the forecast long term growth rate of the company’s earnings the capitalization multiple in a notional valuation is expressed as:

Capitalisation multiple = 1/(Ke – g)

Using the Gordon Growth model the earnings would be converted to value as follows:

Market value = Maintainable earnings x (1 + g) x 1/(Ke - g)

Therefore of a given earnings and an expected growth rate the captialisation multiple is:

Capitalisation multiple = (1+g)/(Ke – g)

Substituting P/E for the capitalization multiple we get

P/E ≈ (1+g)/(Kei – g)

Where Kei is the implied Ke. Solving the above for Kei we get:

Kei ≈ [(1+g)/(P/E)] + g

To demonstrate how this works we selected a few companies from the Jamaica Stock Exchange from S&P Capital IQ database and calculated the Kei (implied cost of equity based on P/E ratios) which we compared to a calculation of Ke using the build-up approach using historic profit growth as the expectation for future growth.

While there are differences between Ke and Kei for the individual companies the average Kei is close to the notional Ke, the reasons for this are market expectations for growth and the fact that individual stock market values are not necessarily indicative of intrinsic value as spot prices in stock markets may overvalue or undervalue the stock given that market trading prices are influenced by factors such as:

• Public awareness of the stock;
• Public knowledge concerning the business;
•  Public interest in the stock; and

## Recap

ROE is based on the book value of equity whereas Ke is an expected return on the market value of the company’s capital as such the two metrics are not comparable.

The reciprocal of a company’s P/E ratio is not a good proxy for Ke. In order to estimate Ke using the P/E one would have to adjust it for long term growth rate of earnings using the following formula Kei ≈ [(1+g)/(P/E)] + g. The valuators should also be mindful of conditions affecting stock market prices when trying estimate Ke using P/E ratios.

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