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##### Subject 1. Calculating Residual Income
Residual income is net income less a charge for common shareholders' opportunity cost in generating net income. Unlike accounting income, residual income recognizes the cost of equity capital in the measurement of income. It attempts to measure economic profit: profits after accounting for all opportunity costs of capital.

Net income reported in financial statements includes a charge for the cost of debt capital in the form of interest expense but not the cost of equity capital. Shareholders run opportunity costs by foregoing other potentially profitable investments, having their capital tied up in the company's stock. A company can have positive net income but may still not be adding value for shareholders if it does not earn more than the cost of equity capital.

There are two ways to calculate residual income:

• Residual income is calculated as net income minus a deduction for the cost of capital. The deduction is called the equity charge which is the dollar amount of opportunity profits foregone by equity investors. The equity charge is equal to equity capital multiplied by the required rate of return on equity.
• Subtract total capital charge from after-tax operating income. Capital charge equals total assets times weighted average cost of capital (WACC). Since WACC reflects both cost of equity and after-tax cost of debt, multiplying it by total assets gives the total dollar cost of all sources of capital for the company.

Example

The Maisy Grain Company makes gourmet bread products.

• Assets = \$100.8 million.
• Debt = \$40.2 million.
• Equity = \$60.6 million.
• Pretax cost of debt = 7.1%.
• Cost of equity = 13.3%.
• Number of shares outstanding: 20 million.
• Tax rate = 40%.

First we calculate net income:

EBIT: \$7,560,000.
Less: interest expense: \$2,854,000 (\$40.2 million x 7.1%).
Pretax income: \$4,706,000.
Less: income tax expense: \$1,882,400 (4706000 x 0.4).
Net income: \$2,823,600.

1) Using the equity charge method, we calculate residual income:
Equity charge = equity capital x cost of equity = 60.6 x 13.3% = \$8,059,800.
Residual income = net income - equity charge = 2,823,600 - 8,059,800 = -\$5,236,200.

2) To use the capital charge method, we need to calculate WACC first.
WACC = Equity share x cost of equity + Debt share x cost of debt x (1 - Tax rate) = (\$60.6/\$100.8) x 0.133 + (\$40.2/\$100.8) x 0.071 x (1 - 0.4) = 9.69%.

Note that in the calculation of WACC we used after-tax cost of debt, since interest expense is tax-deductible.

After-tax operating income = EBIT x (1 - Tax rate) = \$7.56 x (1 - 0.4) = \$4,536 million.

Residual income = After-tax operating income - (Total Assets x WACC) = \$4.536 - (\$100.8 x 0.0969) = \$ (5.23) million.

As we can see, the capital charge and equity charge methods lead to the same residual income estimate.

Since the residual income is negative, the Maisy Grain Company is not earning enough to compensate its shareholders for the risk. If investors expect this situation to persist indefinitely, the demand of the company's stocks will go down and the stock will fall in price.

We can determine the price per share at which the company would be earning the required rate of return. Suppose the company is paying out all its earnings. We know that earnings per share equal net income/shares outstanding = \$2,823,600/20,000,000 = \$0.14118. The book value per share is 100.8/20 = \$5.04. Since the company is paying out all its earnings, its growth is zero and the earnings yield (E/P) equals its required rate of return (remember from Gordon constant growth model that if g=0, and b=1, we have P/E = 1/required rate of return).

Therefore, \$0.14118/P = 0.133 and P = \$1.06. As we see from this example, a company with negative residual income has its shares trading below the book value. At this market price per share, the company's stockholders can earn EPS/P = \$0.14118/\$1.06 = 0.133 or 13.3% which is equal to the cost of equity.

The two approaches will yield different results if the charge for debt capital differs from the interest expense used in net income, or the weights used in calculating the WACC are not based on the book value of the company's debt and equity.

User Comment
danlan2 Equity charge method and capital charge method give the same result, since the cost of debt equals the interest rate multiple by (1-tax rate).
bbadger How do they get EBIT in the example? Am I to assume it's given on a bullet point?
davcer the book value is based on total assets, should it be just equity?
davidt876 i'm fairly certain they just forgot to include EBIT in the list of info
TheCFAGuy @DAVCER agreed +1 ??

Also, if b=1, would that not make the PR (1-b) --> 0 ? 