Financial Education

The single stage residual income model expresses the value of a stock as BV + BV{(ROE - r)/(r-g)} where

BV = the current book value of equity

ROE = return on equity or Net income divided by book value

r = the required return on an equity investment with risk characteristics similar to the firm in question

g = the growth rate

Algebraically, if an investor is confident that the book value and ROE are reliable, and that the estimate for required return is appropriate, the market price can be used to impute expected growth. Alternatively, for any given r, the amount of growth needed to justify the current market price can be calculated.

Consider Microsoft (MSFT). According to Yahoo! Finance it currently has a book value per share of $3.32 and an ROE of 39.52%. The share price is $29.00. How fast would Microsoft need to grow in order to justify the current share price given a required return of 10% per year?

$29.00 = $3.32 + $3.32((0.3952 - 0.10)/(0.10 - g))

Solving for g yields an implied growth rate of approximately 6.2% per year. This is below the growth rate of the last five years (8.1% per year) and below the consensus forecast growth rate for the next five years (11.5%). This could mean:

• the stock is undervalued
• growth will be lower than estimated
• the average investor requires more than a 10% annual return
• some combination of the above

As with implied growth rates based on the dividend discount model, using the market price to impute implicit assumptions can help investors narrow down possible discrepancies between market price and consensus forecasts.

For more information, see all articles on: Accounting, Financial Statement Analysis, Fundamental Analysis, Investing in Stocks, Valuation

See also:

Using the Market Price to Calculate Implicit Return in a Multi-Stage Dividend Discount Model

Multi-Stage Dividend Discount Models

Implied Growth Rates

A Two Stage Dividend Discount Model With Constant First-Stage Growth

The Residual Income Valuation Model