Calculation Explanation

Step 1: Calculate the after-tax cost of debt

• Cost of debt before tax: 6%
• Tax rate: 25%
• After-tax cost of debt = 6% × (1 - 0.25) = 4.5%

Step 2: Calculate the weighted average cost of capital (WACC)

• Total capital = $4,000,000 + $6,000,000 = $10,000,000
• Weight of debt = $4,000,000 / $10,000,000 = 0.4
• Weight of equity = $6,000,000 / $10,000,000 = 0.6
• WACC = (0.4 × 4.5%) + (0.6 × 10%) = 1.8% + 6% = 7.8%

Step 3: Calculate the required return

• Required return = Total capital × WACC = $10,000,000 × 7.8% = $780,000

Step 4: Calculate residual income

• Residual income = Net operating profit after tax - Required return
• Residual income = $750,000 - $780,000 = -$30,000

The company's residual income is -$30,000, indicating it is not covering its cost of capital.