Question18 Cost of equity (CAPM): A stock has a beta of 1.25. The risk-free rate is 3% and themarket risk premium is 6%. Its cost of equity is:Select one alternative: 9.0% 10.5% 7.5% 11.25% ResetMaximum marks: 3 Flag question undefinedSingle choice
A
9.0%
B
10.5%
C
7.5%
D
11.25%

Question

Question18 Cost of equity (CAPM): A stock has a beta of 1.25. The risk-free rate is 3% and themarket risk premium is 6%. Its cost of equity is:Select one alternative: 9.0% 10.5% 7.5% 11.25% ResetMaximum marks: 3 Flag question undefinedSingle choice

A

9.0%

B

10.5%

C

7.5%

D

11.25%

BlackTom AI · Accepted Answer

Cost of equity (CAPM) uses: Cost of equity = rf + β × (market risk premium).

1. Relevant knowledge points and concepts
- Risk-free rate (rf): the return on a riskless asset; here rf = 3%.
- Beta (β): measures the stock’s sensitivity to market movements; here β = 1.25.
- Market risk premium (MRP): expected excess return of the market over the risk-free rate; here MRP = 6%.
- CAPM formula: Expected return (cost of equity) = rf + β × MRP.

2. Step-by-step reasoning
Apply the CAPM formula directly with the given numbers.

3. Intermediate calculations
- Convert percents to decimals for calculation: rf = 0.03, β = 1.25, MRP = 0.06.
- Compute β × MRP: 1.25 × 0.06 = 0.075 (7.5%).
- Add rf: 0.03 + 0.075 = 0.105.

4. Why the correct answer is correct
0.105 expressed as a percent is 10.5%. This follows exactly from CAPM: the stock’s systematic risk (β) magnifies the market risk premium, and the risk-free rate is then added to yield the required return. Thus the cost of equity = 10.5%.

5. Why the other options are incorrect
- 9.0%: would be rf + 1.00×MRP (3% + 6%), which assumes β = 1.0, not the given 1.25.
- 7.5%: equals β × MRP (1.25 × 6%) but omits the risk-free rate; CAPM requires adding rf.
- 11.25%: would correspond to rf + (β' × MRP) with β' = 1.375 (since 11.25% − 3% = 8.25% and 8.25%/6% = 1.375), which does not match the given β = 1.25.

6. Conclusion
The CAPM calculation gives a cost of equity of 10.5%, which matches the provided correct answer.

Question18 Cost of equity (CAPM): A stock has a beta of 1.25. The risk-free rate is 3% and themarket risk premium is 6%. Its cost of equity is:Select one alternative: 9.0% 10.5% 7.5% 11.25% ResetMaximum marks: 3 Flag question undefinedSingle choice

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