Residual Income Valuation

RESIDUAL INCOME (RI)

Residual income is the amount of net income above or below the expected return on equity.

Residual Income is calculated as follows:RIt = Et – rBt-1

RIt = Residual IncomeEt = Earnings (Net Income)r = Cost of EquityBt-1 = Book Value of Equity.rBt-1= Expected return on equity

A positive RI indicates that value has been created for shareholders. A negative RI means valued destruction for shareholders.

It measures the economic rather than accounting profit by a business after the cost of all financial resources has been taken into account.

Origin of Residual Income (RI)

Financial Statements are prepared to reflect earnings available to owners but not whether this earnings sufficient to meet their expectations.

Traditional accounting doesn´t show whether shareholder has earned what they expected, and leaves to the owners the determination as to whether the earnings are sufficient to meet their cost of equity.

An economic concept to whether the cost of equity capital is needed.

Residual Incomes provides information regarding the incremental value created by a firm or project. Note that it could also be a reduction in value in which case wealth is destroyed.

Residual Income

Remember that objective is to maximize shareholder´wealth. This can be achieved by maximizing Residual Income, and not maximizing return on investment (ROI). WHY?

Because if a manager is evaluated based on ROI will reject any project whose rate of return is below the division's current ROI even if the rate of return on the project is above the minimum rate of return for the entire company.

Any project whose rate of return is above the minimum required rate of return of the company will result in an increase in residual income.

An example of Residual IncomeAMC has total assets of €2,000,000 financed 50% with debt and 50% with equity capital. The cost of debt is 7%. Tax rate is 30% and the cost of equity is 12%. Net income for AMC can be determined as follows:

EBIT €200,000Less: Interest Expense 70,000Pre-Tax Income €130,000Income Tax Expense 39,000Net Income € 91,000

What is it’s residual income?

Expected Equity Return = Equity х Cost of Equity = €1,000,000 х 12% = € 120,000

Net Income € 91,000Expected Equity Return 120,000Residual Income €(29,000)

AMC did not earn enough to cover the cost of equity. As a result, it has negative residual income.

Residual Income / Economic Profits / Abnormal Earnings

Residual income has also been called economic profit and economic value added since it represents the economic profit of the firm after deducting the cost of all financial resources, debt and equity.

The term abnormal earnings is also used. Assuming that over the long term the firm is expected to earn its cost of capital (from all sources), any earnings in excess of the cost of capital can be termed abnormal earnings.

Economic Value Added is computed as:

NOPAT – WACC х (D+E)

NOPAT: Net Operating Profit After Taxes, WACC: Weighted Average Cost of Capital D: Debt E: Equity.

Residual Income Model (RIM)

Under Residual Income Model (RIM) of valuation, the intrinsic value of the firm has two components:

Book value of equity, plus Present value of future residual income

RIM can be expressed as:

B0 =Book value of equity at the beginning, Bt =Book value of equity at time t,RIt= Et – rBt-1 = Residual income in future periods, r = Required rate of return on equity,Et = Net Income during period t,

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Valuing a perpetuity with the RIM

A company will earn $1.00 per share forever, and the company also pays out all of this as dividends, $1.00 per share. The equity capital invested (book value) is $6.00 per share. Because the earnings and dividends will offset each other, the future book value of the stock will always stay at $6.00. The required rate of return on equity (or the percent cost of equity) is 10%.

1. Calculate the value of this stock using the dividend discount model.

2. What will be the residual income each year? Calculate the value of the stock using a residual income valuation model.

Perpetuity example

1) Since the dividend is a perpetuity,P0 = D / r = 1.00 / 0.10 = $10.00 per share.

2) The net income is $1.00 each year, the book value is always $6.00, and the required return is 10%, so the residual income in every year will be:

RIt = Et – rBt-1 = 1.00 – 0.10 (6.00) = 1.00 – 0.60 = $0.40.

The value, using a residual income approach, is the current book value plus the present value of future residual income. The residual income is a perpetuity:

P0 = Book value + PV of Residual income = 6.00 + 0.40 / 0.10 = 6.00 + 4.00 = $10.00.

When to use RIM valuation

A Residual Income Model is most appropriate when:

A firm is not paying dividends of if it exhibits an unpredictable dividend pattern.

A firm has negative free cash flow many years out, but is expected to generate positive cash flow at some point in the future (for example, a young or rapidly growing firm where capital expenditures are being made to fuel future growth.

There is a great deal of uncertainty in forecasting terminal values.

Derivation of the RIM of valuation

Start with the DDM:

The relationship between earnings, dividends and book value is given by:

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Derivation of RIM

Then, Dt = Et – (Bt – Bt-1) = Et + Bt-1 – Bt

Substituting this into the DDM:

This equation can be simplified:

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Derivation of RIM of valuation

As ROE = Earnings/Book Value of Equity, this can also be expressed as:

This equation is logically equivalent to the one above since: RIt = (ROEt – r)×Bt-1.

Note that other than the “required rate of return”, the inputs to the residual income model are based upon accounting data.

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RIM of valuation example

SIT is expected to earn $4.00, $5.00, and $8.00 for the next three years. SIT will pay annual dividends of $2.00, $2.50, and $20.50 in each of these years. The last dividend includes the liquidating payment to shareholders at the end of year 3 when the firm will terminate operations. SIT’s book value is $8 per share and its required return on equity is 10%.

1. What is the current value per share of SIT according to the dividend discount model?

2. Calculate the book value and residual income for SIT for each of the next 3 years and use those results to find the stock’s value using the residual income model.

3. Calculate return on equity and use it as an input to the residual income model to calculate SIT’s value.

RIM of valuation example

1) P0 = Present Value of the future dividends

P0 = 2/1.10 + 2.50/(1.1)2 + 20.50/(1.1)3

P0 = $1.818 + $2.066 + $15.402 = 19.286

2) Book values and residual incomes for the next 3 years are:

Year 1 2 3Beginning Book Value of Equity 8.00 10.00 12.50Retained earnings (NI–DIV) 2.00 2.50(12.50)Ending Book Value of Equity 10.00 12.50 0.0Net income 4.00 5.00 8.00Less (r Book Value of Equity) 0.80 1.00 1.25Residual income 3.20 4.00 6.75

P0 = 8.00 + 3.20/1.1 + 4.00/(1.1)2 + 6.75/(1.1)3

P0 = 8.00 + 2.909 + 3.306 + 5.071 = 19.286

RIM of valuation example

3) Year 1 2 3Net income 4.00 5.00 8.00Beginning Book Value of Equity 8.00 10.00 12.50ROE (return on equity) 50% 50% 64%ROE – r 40% 40% 54%Residual income (ROE–r) BVE 3.20 4.00 6.75

P0 = 8.00 + 3.20/1.1 + 4.00/(1.1)2 + 6.75/(1.1)3

P0 = 8.00 + 2.909 + 3.306 + 5.071 = 19.286

Note: since the residual incomes for each year are necessarily the same in questions 1 & 2, the results for stock valuation are identical.

Constant growth RIM

A firm’s intrinsic value under a residual income can be expressed as:

B0 reflects the value of assets owned by the firm less its liabilities.

B0(ROE-r)/(r-g), represents additional value that is expected due to the firm’s ability to generate returns in excess of its cost of equity. It represents the value of the firm’s economic profits.

If a firm earns exactly the cost of equity the price should equal the book value per share.

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RIM, DDM and FCFE (SUMMARY)

Residual income models, dividend discount models, and free cash flow models are all theoretically sound.

DDM and FCFE models forecast future cash flows and find the value of stock by discounting them back to the present using the required return on equity.

RI model approaches this process differently. It starts with the book value of equity, and then makes adjustments to this value by adding the present values of future residual income (which can be positive or negative).

The recognition of value is different, but the total present value of these values (whether future dividends, future free cash flow, or book value plus future residual income) should be logically consistent.