Question4 Assume a firm utilizes the security market line (CAPM) approach to determine its cost of equity. Grand Opal Ltd currently pays an annual dividend of $2.10 per share and has a beta of 1.30. All else constant, which of the following actions will decrease the firm’s cost of equity? Investors raise their expectations about the market rate of return. The firm increases its annual dividend to $2.40 per share. The firm restructures its operations so that its beta falls to 1.05. The market risk premium increases. ResetMaximum marks: 1 Flag question undefinedSingle choice
A
Investors raise their expectations about the market rate of return.
B
The firm increases its annual dividend to $2.40 per share.
C
The firm restructures its operations so that its beta falls to 1.05.
D
The market risk premium increases.

Question

Question4 Assume a firm utilizes the security market line (CAPM) approach to determine its cost of equity. Grand Opal Ltd currently pays an annual dividend of $2.10 per share and has a beta of 1.30. All else constant, which of the following actions will decrease the firm’s cost of equity? Investors raise their expectations about the market rate of return. The firm increases its annual dividend to $2.40 per share. The firm restructures its operations so that its beta falls to 1.05. The market risk premium increases. ResetMaximum marks: 1 Flag question undefinedSingle choice

A

Investors raise their expectations about the market rate of return.

B

The firm increases its annual dividend to $2.40 per share.

C

The firm restructures its operations so that its beta falls to 1.05.

D

The market risk premium increases.

BlackTom AI · Accepted Answer

CAPM: Re = Rf + β(Rm − Rf).

1. Relevant knowledge points and concepts
- The Capital Asset Pricing Model (CAPM) defines cost of equity (Re) as risk-free rate (Rf) plus beta (β) times the market risk premium (Rm − Rf).
- Beta measures systematic (market) risk; a lower beta reduces the sensitivity of the stock’s return to market movements, lowering Re under CAPM.
- Changes in Rm or the market risk premium directly alter Re. Dividend level does not enter the CAPM formula (though it matters in dividend-based models, not here).

2. Complete reasoning process step by step
- Start from the CAPM expression Re = Rf + β(Rm − Rf).
- Evaluate the effect of each listed action on the right-hand side:
  a) Investors raise expectations about Rm → Rm increases, so (Rm − Rf) increases ⇒ Re increases.
  b) Firm increases its dividend → no effect on Rf, β, or (Rm − Rf) in CAPM ⇒ Re unchanged.
  c) Firm reduces β from 1.30 to 1.05 → β decreases ⇒ β(Rm − Rf) decreases ⇒ Re decreases.
  d) Market risk premium increases directly → (Rm − Rf) increases ⇒ Re increases.

3. Calculations with intermediate steps (numeric example)
- Assume Rf = 3.0% and current Rm = 8.0% (market risk premium = 5.0%).
- Current Re = 3.0% + 1.30 × 5.0% = 3.0% + 6.5% = 9.5%.
- After β falls to 1.05: Re = 3.0% + 1.05 × 5.0% = 3.0% + 5.25% = 8.25%.
- Change: 9.5% → 8.25% (a decrease of 1.25 percentage points).

4. Why the correct answer is correct
- Lowering beta reduces the product β(Rm − Rf), directly reducing Re per the CAPM formula. The numerical example shows a clear decline in cost of equity when β falls from 1.30 to 1.05.

5. Why other options are incorrect
- Investors raising Rm: increases Rm − Rf, so Re rises (not decreases).
- Increasing the dividend to $2.40: CAPM does not use dividends; this action does not change Re under CAPM.
- Market risk premium increasing: directly increases Re, the opposite of decreasing.

6. Conclusion and confirmation
- Therefore, the action that will decrease the firm’s cost of equity under the CAPM approach is: "The firm restructures its operations so that its beta falls to 1.05." This matches the provided correct answer.