Copper Kettle Co. currently has no debt. Its EBIT is $200,000, it is a zero-growth firm, its tax rate is 25%, and its current cost of equity is 12%. The firm is considering recapitalizing to a structure of 30% debt and 70% equity, based on market values. The new debt would carry an interest rate of 7.5%, and the added leverage would raise the cost of equity to 13.2%. If the plan is carried out, what would the firm's new value of operations be?

Question

BlackTom AI · Accepted Answer

Value of operations for a leveraged, zero-growth firm equals the after-tax EBIT divided by the firm’s weighted average cost of capital (WACC).

Relevant concepts:
- After-tax operating cash flow = EBIT × (1 − Tax rate).
- WACC with corporate taxes = wE × rE + wD × rD × (1 − Tax rate), where wE and wD are market-value weights.
- Value of operations = (after-tax EBIT) / WACC for a perpetual, zero-growth firm.

Step-by-step reasoning and calculations:
1. Compute after-tax operating cash flow:
   EBIT = $200,000; Tax rate = 25% → After-tax EBIT = 200,000 × (1 − 0.25) = 200,000 × 0.75 = $150,000.

2. Compute WACC using target capital structure:
   wD = 30% = 0.30, wE = 70% = 0.70.
   New cost of equity rE = 13.2% = 0.132.
   Cost of debt rD = 7.5% = 0.075.
   WACC = wE·rE + wD·rD·(1 − Tax rate)
        = 0.70·0.132 + 0.30·0.075·(1 − 0.25)
        = 0.0924 + 0.30·0.075·0.75
        = 0.0924 + 0.016875
        = 0.109275 (10.9275%).

3. Value of operations:
   Value = After-tax EBIT / WACC = 150,000 / 0.109275 ≈ 1,372,683.9 ≈ $1,372,684.

Why this answer is correct:
Using the firm’s new required returns (rE and rD) and the target market-value weights gives the appropriate WACC after recapitalization; dividing perpetual after-tax operating cash flow by that WACC yields the new value of operations.

Why other choices are incorrect (brief):
- $1,250,000: equals the unlevered value (150,000/0.12) before recapitalization, not after leverage.
- $1,153,846: equals 150,000/0.13 (incorrectly using rE alone).
- $1,305,483: results from using a different, incorrect discount rate.
- $1,830,245: equals 200,000/0.109275 (using pre-tax EBIT), which ignores taxes.

Conclusion: The firm’s new value of operations after recapitalizing is $1,372,684, matching the provided correct answer.

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