A research analyst calculates a risk-free rate (Rf) of 6.5%, a stock Beta of 1.20, and an Equity Market Risk Premium (Rm - Rf) of 7.0%. Under the Capital Asset Pricing Model (CAPM), what is the firm's Cost of Equity (Ke)?

[ A ]16.20% (Adding Rf to Rm before multiplying by Beta)

[ B ]8.40% (Market risk premium component alone)

[ C ]13.50%

[ D ]14.90% [ Rf + Beta * (Rm - Rf) = 6.5% + 1.20 * 7.0% ][ CORRECT ]

Takeaway

Option D is correct: 14.90% [ Rf + Beta * (Rm - Rf) = 6.5% + 1.20 * 7.0% ]

Derivation

CAPM builds Cost of Equity from a risk-free baseline plus compensation for the systematic risk the stock actually carries. The baseline is the risk-free rate itself, 6.5%. The risk premium the stock demands is its Beta multiplied by the market's overall equity risk premium: 1.20 × 7.0% = 8.40%, reflecting that this stock is 20% more volatile relative to the market than average and should be compensated accordingly. Adding the two: Ke = 6.5% + 8.40% = 14.90%. The formula's structure matters: Beta multiplies only the risk premium (Rm − Rf), not the risk-free rate plus the premium together, since the risk-free component is already compensation an investor earns without taking on any equity risk at all.

Why the others fail

A — 16.20% (Adding Rf to Rm before multiplying by Beta)

Adds the risk-free rate inside the parentheses before multiplying by Beta, which incorrectly scales the risk-free component by the stock's Beta as well.

B — 8.40% (Market risk premium component alone)

States only the Beta-scaled risk premium of 8.40% without adding back the baseline risk-free rate of 6.5% that CAPM requires as the starting point.

C — 13.50%

Does not correspond to the correct CAPM computation of risk-free rate plus Beta-scaled market risk premium using the figures given in the question.