###### Implementation Shortfall

The implementation shortfall approach involves taking the difference between the prevailing price and... **Read More**

Residual income deducts a charge for equity capital to determine whether the company is earning a return above the opportunity costs for equity investors. Residual income is equivalent to economic profit. It is calculated as:

$$\begin{align*}\text{Residual income}&=\text{Net income}-\text{Equity charge}\\ \\ \text{Equity charge}&=\text{Cost of equity capital}\times\text{Equity capital}\end{align*}$$

Consider the following information:

- Total assets = $3,000,000
- Debt = 30%, Equity = 70%
- Cost of equity = 10%
- Cost of debt (before tax) = 7%
- EBIT = $400,000
- Tax rate = 30%

The residual income would be calculated as:

$$\small{\begin{array}{l|r}\text{EBIT} & 400,000 \\ \hline\text{Less: Interest expense} & (63,000) \\ \hline\text{Pre-tax income} & 337,000 \\ \hline\text{Less: Income tax expense} (30\%) & (101,100) \\ \hline\textbf{Net income} & \text{235,900}\\ \end{array}}$$

$$\begin{align*}\text{Debt}&=$3,000,000\times30\%\\&=$900,000\\ \\ \text{Interest expense}&=$900,000\times7\%\\&=$63,000\\ \\ \text{Equity capital}&=70\%\times$3,000,000\\&=$2,100,000\\ \\ \text{Equity charge}&=\text{Cost of equity capital}\times\text{Equity capital}\\&=10\%\times$2,100,000\\&=$210,000\\ \\ \text{Residual income}&=\text{Net income}-\text{Equity charge}\\&=$235,900-$210,000\\&=$25,900\end{align*}$$

A positive residual income indicates that the company earnings cover its cost of equity capital.

Economic value added (EVA) is calculated as:

$$\text{EVA}=\text{NOPAT}-(\text{C}\%\times\text{TC})$$

Where:

\(\text{NOPAT}\) = Net operating profit after tax

\(\text{C}\%\) = Cost of capital

\(\text{TC}\) = Total capital

NOPAT is calculated as:

$$\text{NOPAT}=\text{EBIT}-(\text{EBIT}\times\text{Taxes})$$

Where:

\(\text{EBIT}\) = Earnings before income and taxes

The following adjustments need to be made:

- R&D expenses are added back to earnings to compute NOPAT.
- For strategic investments that are not expected to generate an immediate return, a charge for capital is suspended until a later date
- Deferred taxes are eliminated. Only cash taxes are regarded as an expense.
- Any inventory LIFO reserve is added back to the capital, and any increase in the LIFO reserve is added in when computing NOPAT.
- Operating leases are regarded as capital leases, and nonrecurring items are adjusted.

A firm that generates positive economic profit should have its market value standing higher than the book value of its capital. MVA measures the value generated by management for the company’s investors by generating economic profits over the company’s life.

MVA is calculated as:

$$\text{MVA}=\text{Market value of the company}-\text{Book value of total capital}$$

Consider the following information:

$$\small{\begin{array}{l|r}\text{NOPAT} & \$1,650 \\ \hline\text{Total number of shares outstanding} & 550 \\ \hline\text{Market price per share} & \$35 \\ \hline\text{Market value of debt} & \$5,500 \\ \hline \text{Total invested capital} & \$19,250 \\ \hline\text{WACC} & 10\%\\ \end{array}}$$

The firm’s EVA and MVA are *closest to:*

$$\begin{align*}\text{EVA}&=\text{NOPAT}-(\text{C}\%\times\text{TC})\\&=1,650-(10\%\times19,250)\\&=-\$275\\ \text{Market value of the company}&=\text{Market value of equity} \\ & +\text{Market value of debt}\\&=(550\times35)+5.500\\&=$24,750\\ \text{MVA}&=\text{Market value of the company} \\ & -\text{Accounting book value of total capital}\\&=24,750-19,250\\&=$5,500\end{align*}$$

## Question

Given the following information:

- Total assets = $2,000,000
- Debt = 40%, Equity = 60%
- Cost of equity = 9%
- Cost of debt (before tax) = 5%
- EBIT = $200,000
- Tax rate = 20%
Residual income is

closest to:

- $4,000
- $40,000
- $108,000
## Solution

The correct answer is A.$$\small{\begin{array}{l|l}\text{EBIT} & \$200,000 \\ \hline\text{Less: Interest expense} & \$40,000 \\ \hline\text{Pre-tax income} & \$160,000 \\ \hline\text{Less: Income tax expense} (30\%) & \$48,000 \\ \hline \textbf{Net income} & \textbf{\$112,000}\\ \end{array}}$$

$$\begin{align*}\text{Debt}&=$2,000,000\times40\%\\&=$800,000\\ \\ \text{Interest expense}&=$800,000\times5\%\\&=$40,000\\ \\ \text{Equity capital}&=60\%\times$2,000,000\\&=$1,200,000\\ \\ \text{Equity charge}&=\text{Cost of equity capital}\times\text{Equity capital}\\&=9\%\times$1,200,000\\&=$108,000\\ \\ \text{Residual income}&=\text{Net income}-\text{Equity charge}\\&=$112,000-$108,000\\&=$4,000\end{align*}$$

*Reading 26: Residual Income Valuation*

*LOS 26 (a)** Calculate and interpret residual income, economic value-added, and market value-added.*