# Jarrett Corp. Residual Income in Year 5 Let's solve for **Year 5 Residual Income** by step, with explanations after each stage. --- ## Step 1: Residual Income Formula Residual income (RI) for a given year is calculated as: \[ \text{RI}_t = \text{Net Income}_t - (\text{Equity at start of year} \times \text{Cost of Equity}) \] - **Net Income**: Projected after-tax earnings for the year. - **Equity at start of year**: Book value of common shareholders' equity at the beginning of the year. - **Cost of Equity**: Required rate of return by shareholders. --- ## Step 2: Find Equity at Start of Year 5 We start with equity at the end of Year , and add net income each year (since no dividends are paid and all earnings are retained): ### Calculating Equity Growth: | Year | Equity at Start | Net Income | Equity at End | |------|----------------|------------|---------------| | | $112,768 | - | $112,768 | | 1 | $112,768 | $20,856 | $133,624 | | 2 | $133,624 | $22,733 | $156,357 | | 3 | $156,357 | $24,552 | $180,909 | | 4 | $180,909 | $27,252 | $208,161 | | 5 | $208,161 | $29,978 | $238,139 | So, **Equity at the start of Year 5** is the ending equity of Year 4: \[ \text{Equity at start of Year 5} = \$208,161 \] --- ## Step 3: Net Income in Year 5 From the table: \[ \text{Year 5 Net Income} = \$29,978 \] --- ## Step 4: Cost of Equity Charge \[ \text{Equity Charge} = \text{Equity at start of Year 5} \times \text{Cost of Equity} \] \[ = \$208,161 \times .12 = \$24,979.32 \] --- ## Step 5: Calculate Residual Income for Year 5 \[ \text{RI}_5 = \text{Net Income}_5 - \text{Equity Charge} \] \[ = \$29,978 - \$24,979.32 = \$4,998.68 \] --- ## Step 6: Final Answer (Rounded) \[ \boxed{\$4,998} \] --- ## Explanation - **Residual income** measures the amount of income left after accounting for the cost of equity capital invested in the business. - Each year, we add net income to equity since no dividends are paid out. - In Year 5, the cost of equity capital is charged on the equity at the start of that year. - The residual income in Year 5 is **$4,998**, matching option **(b)**. --- **Conclusion:** Jarrett's residual income in Year 5 is **$4,998**, consistent with answer (b).