Residual Income Computation
What you'll learn
- LOS 21.cCalculate the intrinsic value of a common stock using the residual income model and compare value recognition in residual income and other present value models.
- LOS 21.dExplain fundamental determinants of residual income.
- LOS 21.eExplain the relation between residual income valuation and the justified price to book ratio based on forecasted fundamentals.
We can forecast residual income given some basic accounting information and an estimate of future earnings growth using the following formula:
Laura Kraft, CFA, was assigned the task of forecasting the residual income for Delilah Cosmetics, Inc., over the next two years. To accomplish this task, Kraft assembled the information provided in the following figure. Kraft used a required rate of return of 11%.
Forecast Delilah’s residual income for 2025 and 2026.
Delilah Data Forecast
Solution
Delilah Residual Income Forecast
The residual income valuation model breaks the intrinsic value of a stock into two elements: (1) current book value of equity and (2) present value of expected future residual income:
Don’t let this formula intimidate you! All the above expression really says is that a stock’s intrinsic value, , is equal to its current book value per share, , plus the present value of all its expected future residual income, which is the difference between end of period earnings and equity charges based on beginning of period book value.
The difficulty in implementing this model is that we have to make some assumptions about the pattern of residual income growth in the future because it’s difficult to take the present value of an infinite stream of residual incomes without more restrictive assumptions. In the following example, we make it easy by assuming the company ceases operations at the end of three years, so we only have three residual income forecasts to discount back.
Consolidated Pipe Products has a required rate of return of 14%. The current book value is C$6.50. Earnings forecasts for 2025, 2026, and 2027 are C$1.10, C$1.00, and C$0.95, respectively. Dividends in 2025 and 2026 are forecasted to be C$0.50 and C$0.60, respectively.
The dividend in 2027 is a liquidating dividend, which means that Consolidated will pay out its entire book value in dividends and cease doing business at the end of 2027. Calculate the value of Consolidated’s stock using the residual income model.
Solution
The residual income forecast is shown in the following table, with calculated values in blue.
Consolidated Pipe Residual Income Forecast
The intrinsic value of Consolidated Pipe Products is its current book value plus the present value of the future residual income forecasts:
We can also use the cash flow function on our calculators to solve this problem and save ourselves a little time. Here are the keystrokes:
Value tends to be recognized earlier in the RI approach than in other present value- based approaches. To see this, recall that with a dividend discount model (DDM) or free cash flow to equity (FCFE) model, a large portion of the estimated intrinsic value comes from the present value of the expected terminal value. Yet the uncertainty of the expected terminal value is usually greater than any of the other forecasted cash flows because it occurs several years in the future.
Valuation with residual income models, however, is relatively less sensitive to terminal value estimates, which reduces forecast error. This is because intrinsic values estimated with residual income models include the firm’s current book value (which is known and doesn’t need to be forecasted), and the current book value usually represents a substantial percentage of the estimated intrinsic value.
The general residual income models make no assumptions regarding the long term future earnings or dividend growth. However, if we make the simplifying assumption of a constant dividend and earnings growth rate, we can develop a residual income model that highlights the fundamental drivers of residual income. Value can be expressed in terms of book value:
This model is actually just another version of the Gordon growth model, so if you can use the same inputs, both models will give you the same value estimates.
This version of the residual income model is referred to as the single stage residual income valuation model. In this formulation (assuming constant earnings and dividend growth) the first term is the current book value, the value of the company’s assets net of liabilities. The second term in brackets is the present value of the expected future residual income.
We can use this relationship to identify the fundamental drivers of residual income:
- If return on equity (ROE) is equal to the required return on equity, the justified market value of a share of stock is equal to its book value. When ROE is higher than the required return on equity, the firm will have positive residual income and will be valued at more than book value.
is the additional value generated by the firm’s ability to produce returns in excess of the cost of equity and, consequently, is the present value of a firm’s expected economic profits (i.e., residual income).
Tobin’s Q is a related concept:
As with the DDM and FCFE models, residual income models can be used to estimate justified price multiples. Among the various market multiples, residual income models are most closely related to the price to book value (P/B) ratio because the justified P/B is directly linked to expected future residual income. This can be seen by observing the single stage model.
If ROE is greater than the required return on equity, the second term (the present value of residual income) will be positive, the market value will be greater than book value, and the justified P/B ratio will be greater than one.