Meridian Corp is re-evaluating its debt level. Its current capital structure is 75% debt and 25% equity, its levered beta is 1.95, and its tax rate is 25%. The CFO is considering moving to a structure of 25% debt and 75% equity. The risk-free rate is 4.0% and the market risk premium is 6.0%. By how much would this change the firm's cost of equity?

Question

BlackTom AI · Accepted Answer

Applying Hamada’s equation and CAPM gives a direct path to the change in cost of equity when leverage changes.

1. Relevant knowledge points and concepts
- Hamada’s equation: βL = βU [1 + (1 − T)·(D/E)] links levered beta (βL) to unlevered beta (βU), tax rate T, and debt/equity ratio D/E.  
- CAPM: rE = rF + βE·(market risk premium) translates beta into cost of equity.  
- Changing capital structure changes βE via leverage, thus changing rE.

2. Step-by-step reasoning
- Use the given levered beta (1.95) and current D/E to solve for βU, then re-lever with the new D/E to get the new βL, and finally compute rE before and after.

3. Intermediate calculations
- Current D/E = 75% / 25% = 3.  
- Hamada to find βU: βU = βL / [1 + (1 − T)·(D/E)] = 1.95 / [1 + 0.75·3] = 1.95 / (1 + 2.25) = 1.95 / 3.25 = 0.60.  
- New D/E = 25% / 75% = 1/3 ≈ 0.3333.  
- New levered beta: βL_new = βU [1 + (1 − T)·(D/E)_new] = 0.60·[1 + 0.75·(1/3)] = 0.60·(1 + 0.25) = 0.60·1.25 = 0.75.  
- Initial cost of equity: rE_initial = 4.0% + 1.95·6.0% = 4.0% + 11.7% = 15.7%.  
- New cost of equity: rE_new = 4.0% + 0.75·6.0% = 4.0% + 4.5% = 8.5%.  
- Change in cost of equity = rE_new − rE_initial = 8.5% − 15.7% = −7.2% (a 7.20 percentage-point decrease).

4. Why the correct answer is correct
Reducing leverage lowers equity’s systematic risk (beta) because equity holders bear less debt-related risk; CAPM then yields a substantially lower rE. The numerical steps above derive this exact −7.20% change.

5. Why other options are incorrect
They do not match the computed change from the unlevering and re-levering process. The correct algebra and CAPM arithmetic produce −7.20%, not −8.40%, −6.60%, −5.40%, or −6.00%.

6. Conclusion
The firm’s cost of equity would decrease by 7.20 percentage points; the correct answer is −7.20%, matching the provided answer.

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