Implied Growth Rate in Residual Income

Implied Growth Rate in Residual Income

The single-stage residual income equation can be rearranged to calculate the growth implied by the current market price. The current market price would be assumed to equal the stock’s intrinsic value. The intrinsic value is assumed to be the market price.

$$\text{g}=\text{r}-\bigg[\frac{(\text{ROE}-\text{r})\times\text{B}_{0}}{\text{V}_{0}-\text{B}_{0}}\bigg]$$

Example

Assuming a company has the following information:

  • Current book value per share = $8
  • Expected long-term ROE = 15%
  • Required rate of return on equity = 8%

If the current market price is $32, the implied growth rate can be calculated as:

$$\begin{align*}\text{g}&=\text{r}-\bigg[\frac{(\text{ROE}-\text{r})\times\text{B}_{0}}{\text{V}_{0}-\text{B}_{0}}\bigg]\\&=0.08-\bigg[\frac{(0.15-0.08)\times8}{32-8}\bigg]\\&=5.7\%\end{align*}$$

Question

Assuming a company has the following information:

  • Current book value per share = $12
  • Expected long-term ROE = 14%
  • Required rate of return on equity = 9%
  • Current market price = $42

The implied growth rate is closest to?

  1. 6%
  2. 7%
  3. 8%

Solution

The correct answer is B.

$$\begin{align*}\text{g}&=\text{r}-\bigg[\frac{(\text{ROE}-\text{r})\times\text{B}_{0}}{\text{V}_{0}-\text{B}_{0}}\bigg]\\&=9\%-\bigg[\frac{(14\%-9\%)\times12}{42-12}\bigg]\\&=7\%\end{align*}$$

Reading 26: Residual Income Valuation

LOS 26 (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.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.