Question5 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

Question5 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

Under the CAPM, the cost of equity (ke) is given by ke = Rf + β(Rm − Rf), where Rf is the risk-free rate, β is the stock’s beta, and (Rm − Rf) is the market risk premium.

1) Relevant concepts
- CAPM formula determines required return on equity from three inputs: risk-free rate, beta, and market risk premium.
- Changes in dividends do not enter the CAPM formula directly; dividend policy does not change ke under CAPM.
- Increasing beta or the market risk premium raises ke; decreasing beta lowers ke.

2) Step-by-step reasoning (algebraic)
- Initial cost of equity: ke1 = Rf + 1.30 × (Rm − Rf).
- After restructuring: ke2 = Rf + 1.05 × (Rm − Rf).
- Difference: ke2 − ke1 = [Rf + 1.05(MRP)] − [Rf + 1.30(MRP)] = (1.05 − 1.30)×MRP = −0.25×MRP.
- Because MRP > 0, −0.25×MRP is negative, so ke2 < ke1. Thus lowering beta decreases ke.

3) Numerical example (intermediate steps)
- Assume Rf = 2% and MRP = 6% (example values).
- ke1 = 2% + 1.30×6% = 2% + 7.8% = 9.8%.
- ke2 = 2% + 1.05×6% = 2% + 6.3% = 8.3%.
- Change = 8.3% − 9.8% = −1.5 percentage points (a decrease).

4) Why the correct answer is correct
- Restructuring that reduces beta directly reduces the β(Rm − Rf) term, lowering the required return (ke) per the CAPM expression. All else constant, this is the only choice that reduces ke.

5) Why the other options are incorrect
- Investors raise expectations about market return: that increases Rm (or MRP), raising ke.
- Firm increases its dividend: CAPM ke does not depend on dividend level, so no change in ke.
- Market risk premium increases: directly increases β(MRP) and thus raises ke.

Conclusion: The firm restructuring to reduce beta to 1.05 will decrease the cost of equity. This matches the provided correct answer: "The firm restructures its operations so that its beta falls to 1.05."