TB MC Qu. 103 Regulation Insurance has a beta of...

Regulation Insurance has a beta of .90, a dividend growth rate of 2.5 percent for the foreseeable future, a stock price of $47 per share, and an expected annual dividend of $.60 per share next year. The market rate of return is 13.9 percent, and the risk-free rate is 3.4 percent. What is the firm's average cost of equity?

Question

TB MC Qu. 103 Regulation Insurance has a beta of...

Regulation Insurance has a beta of .90, a dividend growth rate of 2.5 percent for the foreseeable future, a stock price of $47 per share, and an expected annual dividend of $.60 per share next year. The market rate of return is 13.9 percent, and the risk-free rate is 3.4 percent. What is the firm's average cost of equity?

BlackTom AI · Accepted Answer

Using both the CAPM and the Gordon (dividend growth) model produces two equity cost estimates; their simple average is used here as the firm's "average" cost of equity.

1) Relevant concepts
- CAPM: r_e = r_f + β (r_m − r_f). It prices equity using systematic risk (beta) and the market risk premium.
- Gordon (Dividend Growth) Model: r_e = D1/P0 + g, where D1 is next year’s expected dividend, P0 is current price, and g is the constant growth rate.
- Many practitioners average different model estimates to reduce reliance on any single set of inputs.

2) CAPM calculation (step-by-step)
- Risk-free rate r_f = 3.4%
- Market return r_m = 13.9% → market risk premium = r_m − r_f = 13.9% − 3.4% = 10.5%
- Beta β = 0.90 → β × (market risk premium) = 0.90 × 10.5% = 9.45%
- CAPM estimate r_CAPM = r_f + β(r_m − r_f) = 3.4% + 9.45% = 12.85%

3) Dividend growth model calculation (step-by-step)
- Expected dividend next year D1 = $0.60
- Current price P0 = $47 → D1/P0 = 0.60 / 47 = 0.01276596 = 1.2766%
- Dividend growth g = 2.5%
- DGM estimate r_DGM = D1/P0 + g = 1.2766% + 2.5% = 3.7766% ≈ 3.78%

4) Averaging the two estimates
- Average cost of equity = (r_CAPM + r_DGM) / 2 = (12.85% + 3.7766%) / 2 = 8.3133% ≈ 8.31%

5) Why the correct answer is correct and why other choices are incorrect
- The provided correct answer (8.31%) equals the arithmetic average of the CAPM and DGM estimates computed above. Other options (6.69%, 6.41%, 8.25%, 8.67%) do not equal this calculated average and do not match the CAPM or DGM estimates or their average.

Conclusion: The firm’s average cost of equity, obtained by averaging the CAPM (12.85%) and Gordon model (3.78%) estimates, is 8.31% — matching the provided answer.

类似问题

The cost of equity is ________.

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?

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