Bondi Beachwear has an expected return of 12.9% and a beta of 1.21. The expected return on the market is 11.7%. What is the risk-free rate?

Question

BlackTom AI · Accepted Answer

To approach this question, we apply the CAPM formula: E(Ri) = Rf + βi [E(Rm) − Rf]. Here, the stock has E(Ri) = 12.9% (0.129), βi = 1.21, and the market return E(Rm) = 11.7% (0.117).

Option evaluation starts by plugging numbers into the CAPM equation and solving for Rf. 0.129 = Rf + 1.21(0.117 − Rf).

Distribute the terms: 0.129 = Rf + 0.14157 − 1.21Rf = 0.14157 − 0.21Rf.

Rearrange to isolate Rf: 0.129 − 0.14157 = −0.21Rf, which gives −0.01257 = −0.21Rf.

Divide both sides by −0.21: Rf = 0.01257 / 0.21 ≈ 0.059857… ≈ 5.99%.

Now, examine the answer options one by one.

Option 1: 5.38%. If Rf were 5.38%, compute E(Ri) = 0.0538 + 1.21(0.117 − 0.0538) = 0.0538 + 1.21(0.0632) ≈ 0.0538 + 0.0765 ≈ 0.1303, i.e., 13.03%. This is higher than the given 12.9%, so 5.38% is inconsistent with the provided data.

Option 2: 5.99%. Using Rf ≈ 5.99% in CAPM yields E(Ri) ≈ 0.0599 + 1.21(0.117 − 0.0599) = 0.0599 + 1.21(0.0571) ≈ 0.0599 + 0.0691 ≈ 0.1290, i.e., 12.90%. This aligns with the stated expected return, showing consistency with the given inputs.

Option 3: 4.24%. If Rf = 4.24%, then E(Ri) = 0.0424 + 1.21(0.117 − 0.0424) = 0.0424 + 1.21(0.0746) ≈ 0.0424 + 0.0902 ≈ 0.1326, or 13.26%, which is above the provided 12.9% and thus not consistent.

Option 4: 3.87%. With Rf = 3.87%, E(Ri) = 0.0387 + 1.21(0.117 − 0.0387) = 0.0387 + 1.21(0.0783) ≈ 0.0387 + 0.0948 ≈ 0.1335, i.e., 13.35%, again not matching 12.9%.

Option 5: 4.61%. If Rf = 4.61%, E(Ri) = 0.0461 + 1.21(0.117 − 0.0461) = 0.0461 + 1.21(0.0709) ≈ 0.0461 + 0.0859 ≈ 0.1320, or 13.20%, which does not equal 12.9%.

Across all alternatives, only 5.99% yields an expected return that matches the given data under CAPM, as shown in the computation for Option 2. The other options consistently produce an E(Ri) that diverges from 12.9%, highlighting the sensitivity of the result to the risk-free rate and the beta-multiplied market premium term.

Bondi Beachwear has an expected return of 12.9% and a beta of 1.21. The expected return on the market is 11.7%. What is the risk-free rate? 单项选择题

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