IBM expects to pay a dividend of $4 next year and expects these dividends to grow at 7% a year. The price of IBM is $90 per share. Your estimate of the market risk premium is 6%. The risk-free rate of return is 5% and IBM has a beta of 1.2.What is IBM's cost of equity capital using the two methodologies, discounted growth model (DGM) and capital asset pricing model (CAPM) respectively?

Question

BlackTom AI · Accepted Answer

Gordon growth model (DGM): r_e = D1 / P0 + g. With D1 = $4, P0 = $90, g = 7%:
D1 / P0 = 4 / 90 = 0.044444... = 4.4444%
r_e (DGM) = 4.4444% + 7.0000% = 11.4444% ≈ 11.44%.

Capital Asset Pricing Model (CAPM): r_e = r_f + β × (market risk premium).
Given r_f = 5%, β = 1.2, market risk premium = 6%:
β × MRP = 1.2 × 6% = 7.2%
r_e (CAPM) = 5% + 7.2% = 12.2%.

Step-by-step intermediate calculations:
- DGM numerator: 4 / 90 = 0.044444...
- Add growth: 0.044444... + 0.07 = 0.114444... → 11.4444% → round to 11.44%.
- CAPM: 1.2 × 0.06 = 0.072 → add 0.05 → 0.122 → 12.2%.

Why these are correct:
- DGM uses the next expected dividend (D1) divided by current price, plus the perpetual growth rate; that directly yields the implied required return consistent with a Gordon-growth valuation.
- CAPM uses the risk-free rate plus beta times the market risk premium to estimate the expected return given systematic risk.

Why the other answer choices are incorrect:
- Any choice whose DGM value is not 11.44% misapplies the DGM formula or uses an incorrect dividend or price.
- Any choice whose CAPM value is not 12.2% miscalculates β × MRP or the addition of the risk-free rate.
- Specifically, the remaining options present numbers (9.65%/10.2%, 10.89%/11.2%, 10.23%/10.8%) that do not match the straightforward algebra above.

Conclusion: The cost of equity is 11.44% by DGM and 12.2% by CAPM, matching the provided answer.

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.

Calculate the company’s cost of equity if the company’s stock beta is 1.8, the risk-free rate is 2% and the expected market risk premium is 6%. If the answer is 10.4567%, write 0.1046.

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