Suppose an Australian MNC wants to finance a project with an initial investment of USD 100 million. The long-term debt-to-equity ratio of the firm after this acquisition is set at 2. The current debt-to-equity ratio is 2.5. The beta of the firm is now at 1.2. Assume that the risk-free rate is 3%, the market premium is 10% (which means that the expected market return is 13%), and the marginal tax rate is 25%. Calculate the expected return the common equity holders will demand after the acquisition.

Question

BlackTom AI · Accepted Answer

Using Hamada’s equation to adjust beta for the change in leverage: βL = βU[1 + (1 − T)D/E]. Relevant knowledge points: (1) Hamada’s formula links levered (equity) beta to unlevered (asset) beta and debt/equity when corporate taxes exist; (2) CAPM gives required equity return: Re = Rf + βe × (market risk premium).

Step-by-step reasoning and calculations

1) Unlever the current equity beta (βL_current = 1.2) using current D/E = 2.5 and tax rate T = 25%:
- Factor = 1 + (1 − T) × (D/E) = 1 + 0.75 × 2.5 = 1 + 1.875 = 2.875
- βU = βL_current / Factor = 1.2 / 2.875 = 0.4173913 (approx)

2) Re-lever βU to the target long-term D/E = 2:
- New factor = 1 + (1 − T) × (D/E_new) = 1 + 0.75 × 2 = 1 + 1.5 = 2.5
- βL_new = βU × New factor = 0.4173913 × 2.5 = 1.0434783 (approx)

3) Apply CAPM with Rf = 3% and market risk premium = 10%:
- Re = Rf + βL_new × (market risk premium)
- Re = 3% + 1.0434783 × 10% = 3% + 10.434783% = 13.434783% ≈ 13.43%

Why this is correct: The firm’s observed beta reflects its current leverage; changing the capital structure changes equity risk. Hamada’s formula properly removes the effect of current leverage to get the asset (unlevered) beta and then re-applies the target leverage to find the new equity beta, which is then used in CAPM to find the required return.

Why the other choices are incorrect:
- b (7.17%) and c (7.80%) are far too low — they would correspond to either using an unlevered beta or misapplying the market return rather than the market risk premium.
- d (15.52%) is higher than the correct CAPM result and would arise from incorrectly using the current levered beta (1.2) or an incorrect premium scaling.

Conclusion: The expected return demanded by common equity holders after the acquisition is 13.43%, which matches answer (a).

类似问题

Use CAPM to find the cost of equity capital, if US Treasury rate is 2.6%, Stock Market risk is 11.6% and stock's Beta is 1.3.

If the risk-free rate is 3%, market risk is 11%, and the company's Beta is = 1.2, what is the cost of equity?

Calculate the company’s cost of equity if the company’s stock beta is 1.8, the risk-free rate is 5% and the expected market return is 13%. If the answer is 10.4567%, write 0.1046.

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