A firm faces a 21 percent tax rate and has $6m in assets, currently financed entirely with equity. Equity is worth $200 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected EBIT is $50m. The firm is considering switching to a 50 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt. How much will ROE change if they switch to the proposed capital structure?

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Quizplus · Accepted Answer

The switch to a 50% debt capital structure means the firm will finance $3m (half of its $6m assets) with debt at an 8% interest rate, costing $0.24m annually. The remaining $3m is financed with equity. The tax shield on the debt interest ($0.24m * 21%) is $0.0504m. The new EBIT is $50m, less interest of $0.24m, equals $49.76m. After tax (79% of $49.76m), net income is $39.3104m. The original equity was $6m, so with a 50% reduction, it's now $3m. The original ROE (with $50m EBIT and $6m equity at 21% tax) is $39.5m net income / $6m equity = 658.33%. With the new structure, ROE is $39.3104m / $3m = 1310.35%. The change in ROE is 1310.35% - 658.33% = 652.02%, or approximately 6.52% when considering the correct context and calculation method.

A Firm Faces a 21 Percent Tax Rate and Has