A company has a beta of 1.5. The expected return on the market is 15%, and the risk-free rate is 3.5%. Given this information, the company has a cost of equity that is ________.

Question

BlackTom AI · Accepted Answer

To evaluate the cost of equity, apply the CAPM formula: Re = Rf + beta × (Rm − Rf).

Option 1: 24.66%
If you try to back out the components, 24.66% would imply Re − Rf = 21.16%, which is far larger than beta × (Rm − Rf) with beta = 1.5 and (Rm − Rf) = 11.5%. Specifically, 1.5 × 11.5% = 17.25%, so this option overstates the equity cost.

Option 2: 21.55%
This value is closer to the CAPM result but still exceeds the 3.5% risk-free rate by 18.05% (21.55% − 3.5%). Since beta × (Rm − Rf) equals 17.25% in this scenario, it would require a slightly higher premium than CAPM provides, so this is inconsistent with the given beta and market premium.

Option 3: 19.50%
Here, Re − Rf would be 16.00% if we subtracted the risk-free rate, which is still below the beta × (Rm − Rf) value of 17.25% (the market premium component). This means the total would be too low given beta = 1.5 and the market premium of 11.5%. Therefore this option underestimates the cost of equity.

Option 4: 17.25%
Notice that 17.25% alone is exactly the product beta × (Rm − Rf) (1.5 × 11.5% = 17.25%). However, the full CAPM cost adds the risk-free rate of 3.5%, not just the premium. So this option omits the Rf term entirely, making it too low to represent Re.

Option 5: 20.75%
Compute Re = 3.5% + 1.5 × (15% − 3.5%). The market premium (Rm − Rf) is 11.5%. Multiplying by beta: 1.5 × 11.5% = 17.25%. Adding the risk-free rate: 3.5% + 17.25% = 20.75%. This aligns with the CAPM calculation for the given beta, market return, and risk-free rate.

MSB-250-300-002 Topic 9 Quiz

A company has a beta of 1.5. The expected return on the market is 15%, and the risk-free rate is 3.5%. Given this information, the company has a cost of equity that is ________.

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