Constant Growth Model for RI

Equity Valuation 2 min readModule 3 of 5Save

What you'll learn

LOS 21.f
Calculate and interpret the intrinsic value of a common stock using single stage (constant growth) and multistage residual income models.
LOS 21.g
Calculate the implied growth rate in residual income, given the market price to book ratio and an estimate of the required rate of return on equity.

Worked example: Calculating value with a single stage residual income model

Western Atlantic Railroad has a book value of $23.00 per share. The company’s return on new investments (ROE) is 14%, and its required return on equity is 12%. The dividend payout ratio is 60%.

Calculate the value of the shares using a single stage residual income model and the present value of expected economic profits.

Solution

First, calculate the growth rate:

g = retention ratio \times ROE = (1 - 0.6) \times 0.14 = 0.056 = 5.6%

Then, calculate intrinsic value using the single stage model:

The present value of the firm’s expected economic profits is $7.19.

Worked example: Western Atlantic Railroad valuation with Gordon growth model

Use the information in the previous example to calculate the value of Western Atlantic common stock using the Gordon growth model.

Solution

Earnings in Year 1 ( $E_{1}$ ) is equal to beginning book value multiplied by ROE: $E_{1}$ = $23.00 × 0.14 = $3.22. With a dividend payout ratio of 60%, $D_{1}$ = $3.22 (0.6) = $1.932. Then, using the Gordon growth model:

Notice that this is the same estimate as in the previous example where we used the single stage residual income model.

We can rearrange the single stage residual income valuation model and solve for the growth rate in terms of the other variables:

This expression can now be used to directly compute the market’s expectations of residual income growth implied by the current market price under the assumption that intrinsic value is equal to market price.

Worked example: Calculating implied growth rate

You are considering the purchase of Tellis Telecommunications, Inc., which has a P/B ratio of 2.50. ROE is expected to be 13%, current book value per share is €8.00, and the cost of equity is 11%. Calculate the growth rate implied by the current P/B ratio.

Solution

The P/B ratio of 2.50 and the current book value per share of €8.00 imply a current market price of €20.00(8 × 2.50). This implies a growth rate of:

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