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MGT215 Fundamentals of Financial Management

Fundamentals of Financial ManagementTU Board 2082

A stock has required rate of return 12 percent, a beta of 1.5 and the expected return on the market is 10 percent. What must the risk free rate be?

2

Answer

Padhai · Based on the official syllabus and past papers
Updated 10 Oct 2026

The Capital Asset Pricing Model (CAPM) relates the expected return of a stock to its risk (beta) and the market’s risk premium. The formula is:

$E (R_{i}) = R_{f} + β_{i} [E (R_{m}) - R_{f}]$

Where:

$E (R_{i}) = 12%$ (required return of the stock)
$β_{i} = 1.5$ (beta of the stock)
$E (R_{m}) = 10%$ (expected market return)
$R_{f} = ?$ (risk-free rate)

Rearranging to solve for $R_{f}$ :

$12% = R_{f} + 1.5 [10% - R_{f}]$

$12% = R_{f} + 15% - 1.5 R_{f}$

$12% - 15% = - 0.5 R_{f}$

$- 3% = - 0.5 R_{f}$

$R_{f} = \frac{- 3%}{- 0.5} = 6%$

The risk-free rate must be 6%.

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