# Residual Income (RI) Valuation Model

## Introduction

• Residual income reflects net income minus a deduction for the required return on common equity.
• While a firm may show positive earnings, the company would not generate true economic profit in the event that its net profit margin is less than its cost of equity capital.

Basic RIt = Earningst - (rce * Book Value of Equity t-1)

Earnings is EPS when calculating a per share value for RI.

• Economic Value Added attempts to quantify the value management created for shareholders during a given period, usually one year.
• This concept was applied in Corporate Finance 1, under capital budgeting topics.

Economic Value Added = NOPAT - $WACC • NOPAT = [EBIT * (1 - tax rate)] •$WACC = WACC * invested capital

• When calculating Economic Value Added, the analyst would be expected to make standard adjustments to reported financials, as discussed in FRA part 3.

• MVA is the difference between the market value of a company's long-term debt and equity less the book value of capital supplied by investors.

• MVA attempts to measure the value created by management since the company started.

MVA = MV of debt and equity - book value of supplied capital

## Basic RI Model

Share Price0 = BVCE/Share0 + Σ RIt / (1 + rce)t

• This approach starts with the current book value per share of equity today and discounts the expected value of future residual incomes.
• Companies with positive residual incomes should have market share prices that exceed the book value per share.

## RI and Dividend Discount Modeling

• RI and DDM tend to produce a similar valuation, however there is a key difference - by starting with the current book value of equity, RI front loads value recognition in a multi-period model.
• Alternatively, a multi-stage DDM model will back load a large portion of value in the terminal value calculation (which is a much less certain value than the current book value).

## Fundamental Determinants of RI and the P/B Ratio

• In theory a stock's intrinsic value should exhibit a certain relationship among its ROE, its growth rate, and its cost of equity capital:

Value0 = BVCE0 + [((ROE - rce)/(rce - g)) × BVCE0]

• This relationship can be used to derive the price to book ratio and firms that generate a positive residual income should be valued with a price to book ratio greater than 1.0.

P0/B0 = (ROE - rce)/(rce - g)

• Note that if the other variables are known, the implied growth rate of a company can be determined using the RI model.

## RI and Accounting Issues

Because residual income valuation relies heavily on reported financial data, analysts must proceed with certain cautions in mind:

• Is the company in question applying aggressive accounting assumptions and estimates in order to drive an artificially high net income?

• Does the company violate a clean surplus relationship?

• Clean surplus refers to the allowance of certain items to bypass the income statement and move directly to equity. In U.S. GAAP, this includes specific items related to pensions, foreign exchange translations, and the valuation of financial instruments (these are direct to equity adjustments that fall under Other Comprehensive Income).

• When clean surplus is violated the book value of equity may be accurate, net income is absent of certain value drivers; therefore adjustments are required.

• Does the analyst need to revalue certain balance sheet items to their current market value and/or add in off balance sheet items?

• Are intangible assets, such as goodwill, large enough that they require balance sheet and income statement adjustment?

## Single Stage RI Model

Value0 = BVE0 + [((ROE - rce)/(rce - g)) × BVE0]

• Values would be on a per share basis.
• Keep in mind that the RI model (like the Gordon Growth Model) can be used to derive a growth rate, when current and expected share prices are given.

## Multi-Stage RI Model

• Just as the dividend discount model and the free cash flow discounting models can have multiple stages, so can the residual income model.

• This requires calculation of a terminal value of the residual income at the end of the abnormal growth phase.

• In contrast to the terminal value in a multi-stage DDM, the terminal value in a multi-stage RI model will be much smaller, as it will only capture the terminal value of residual income following the high growth period and not the terminal value of the share price.

• In the RI model, much of the value is front-loaded because the model uses the book value of equity as a starting point.

• Advantages of the RI Model

• Because terminal value is not as significant in the RI model when compared to other models, there may be greater certainty in the valuation.

• The model is driven by publicly available accounting data.

• The model does not require a dividend payment.

• The model is not impacted by near term negative or unpredictable cash flows.

• The model captures economic profit.

• Disadvantages of the RI Model

• The model is vulnerable to accounting manipulation by company management.

• The model requires that the analyst have sophisticated understanding of public financial reporting, as large adjustments to reported financials may be required.

• Similar to the previous point, the model requires a clean surplus relationship.

• Appropriateness of RI Model

• The RI model can be utilized when: the company does not pay dividends; free cash flows are expected to be negative; or when there exists a high level of uncertainty around the terminal value.