# Residual income valuation

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Residual income valuation (RIV; also, residual income model and residual income method, RIM) is an approach to equity valuation that formally accounts for the cost of equity capital. Here, "residual" means in excess of any opportunity costs measured relative to the book value of shareholders' equity; residual income (RI) is then the income generated by a firm after accounting for the true cost of capital. The approach is largely analogous to the EVA/MVA based approach, with similar logic and advantages. Residual Income valuation has its origins in Edwards & Bell (1961), Peasnell (1982), and Ohlson (1995). [1]

In finance, the cost of equity is the return a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire capital from others to operate and grow. Individuals and organizations who are willing to provide their funds to others naturally desire to be rewarded. Just as landlords seek rents on their property, capital providers seek returns on their funds, which must be commensurate with the risk undertaken.

In microeconomic theory, the opportunity cost, or alternative cost, of making a particular choice is the value of the most valuable choice out of those that were not taken. In other words, opportunity that will require sacrifices.

In Economics and Accounting, the cost of capital is the cost of a company's funds, or, from an investor's point of view "the required rate of return on a portfolio company's existing securities". It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.

## Concept

The underlying idea is that investors require a rate of return from their resources – i.e. equity – under the control of the firm's management, compensating them for their opportunity cost and accounting for the level of risk resulting. This rate of return is the cost of equity, and a formal equity cost must be subtracted from net income. Consequently, to create shareholder value, management must generate returns at least as great as this cost. Thus, although a company may report a profit on its income statement, it may actually be economically unprofitable; see Economic profit. It is thus possible that a value deemed positive using a traditional discounted cash flow (DCF) approach may be negative here. RI-based valuation is therefore a valuable complement to more traditional techniques.

In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from the investment, such as interest payments or dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.

In accounting, equity is the difference between the value of the assets and the value of the liabilities of something owned. It is governed by the following equation:

Shareholder value is a business term, sometimes phrased as shareholder value maximization or as the shareholder value model, which implies that the ultimate measure of a company's success is the extent to which it enriches shareholders. It became popular during the 1980s, and is particularly associated with former CEO of General Electric, Jack Welch.

## Calculation of residual income

The cost of equity is typically calculated using the CAPM, although other approaches such as APT are also used. The currency charge to be subtracted is then simply

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.

In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. The theory was proposed by the economist Stephen Ross in 1976. The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.

Equity Charge = Equity Capital x Cost of Equity,

and

Residual income = Net Income − Equity Charge.

## Valuation formula

Using the residual income approach, the value of a company's stock can be calculated as the sum of its book value and the present value of its expected future residual income, discounted at the cost of equity, ${\displaystyle r}$, resulting in the general formula:

In accounting, book value is the value of an asset according to its balance sheet account balance. For assets, the value is based on the original cost of the asset less any depreciation, amortization or impairment costs made against the asset. Traditionally, a company's book value is its total assets minus intangible assets and liabilities. However, in practice, depending on the source of the calculation, book value may variably include goodwill, intangible assets, or both. The value inherent in its workforce, part of the intellectual capital of a company, is always ignored. When intangible assets and goodwill are explicitly excluded, the metric is often specified to be "tangible book value".

In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of the borrowed funds is less than the total amount of money paid to the lender.

${\displaystyle V_{0}=BV_{0}+\sum _{t=1}^{\infty }{RI_{t} \over (1+r)^{t}}}$

Here various adjustments to the balance sheet book value may be required; [2] see Clean surplus accounting.

In financial accounting, a balance sheet or statement of financial position or statement of financial condition is a summary of the financial balances of an individual or organization, whether it be a sole proprietorship, a business partnership, a corporation, private limited company or other organization such as Government or not-for-profit entity. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A balance sheet is often described as a "snapshot of a company's financial condition". Of the four basic financial statements, the balance sheet is the only statement which applies to a single point in time of a business' calendar year.

The clean surplus accounting method provides elements of a forecasting model that yields price as a function of earnings, expected returns, and change in book value. The theory's primary use is to estimate the value of a company’s shares. The secondary use is to estimate the cost of capital, as an alternative to e.g. the CAPM. The "clean surplus" is calculated by not including transactions with shareholders when calculating returns; whereas standard accounting for financial statements requires that the change in book value equal earnings minus dividends.

Typically, the above formula will be applied such that the company is assumed to achieve maturity, or "constant growth". (Note that the value will remain identical: the adjustment is a "telescoping" device). Here, analysts commonly employ the Perpetuity Growth Model to calculate the corresponding terminal value [3] (although various, more formal approaches are also applied [4] ). Then, assuming long-run, "constant", growth ${\displaystyle g}$ from year ${\displaystyle m}$, the terminal value is

In finance, the terminal value of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most often used in multi-stage discounted cash flow analysis, and allows for the limitation of cash flow projections to a several-year period. Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

${\displaystyle T_{m}={RI_{m} \over (r-g)}}$,

and the RI valuation would then be:

${\displaystyle V_{0}=BV_{0}+\sum _{t=1}^{m-1}{RI_{t} \over (1+r)^{t}}+{T_{m} \over (1+r)^{m-1}}}$.

## Comparison with other valuation methods

As can be seen, the residual income valuation formula is similar to the dividend discount model (DDM) (and to other discounted cash flow (DCF) valuation models), substituting future residual earnings for dividend (or free cash) payments (and the cost of equity for the weighted average cost of capital).

However, the RI-based approach is most appropriate when a firm is not paying dividends or exhibits an unpredictable dividend pattern, and / or when it has negative free cash flow many years out, but is expected to generate positive cash flow at some point in the future. Further, value is recognized earlier under the RI approach, since a large part of the stock's intrinsic value is recognized immediately – current book value per share – and residual income valuations are thus less sensitive to terminal value. [5]

At the same time, in addition to the accounting considerations mentioned above, the RI approach will not generally hold if there are expected changes in shares outstanding or if the firm plans to bring in "new" shareholders who derive a net benefit from their capital contributions. [6]

Although EVA is similar to residual income, there will be technical differences between EVA and RI, specifically Stern Stewart & Co, originators of EVA, recommend a fairly large number of adjustments to NOPAT before the methodology may be applied. [7] [8] See Economic value added § Comparison with other approaches.

## Notes

1. "8.10 Application IBM Step 1: Estimating Book Value". www.ftsmodules.com. Retrieved 2 October 2018.
2. Team, The AnalystNotes CFA. "December 2018 CFA Level 1: Study Session List". www.analystnotes.com. Retrieved 2 October 2018.
3. "Val22" (PDF). Retrieved 2018-10-02.
4. Martin, James R. "Management Accounting: Chapter 14". maaw.info. Retrieved 2 October 2018.
5. "EVA/Economic Profit Vs. Residual Income - AnalystForum". www.analystforum.com. Retrieved 2 October 2018.

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