Math Problem Statement

You are currently working at a publicly traded company. The risk-free rate in the economy right now is 1.41%. You believe the market will average 7.05% per year over the long run. Your company's stock has a beta of 2.8. What is the required return for your company's stock?

Solution

This problem involves calculating the required return on a company's stock using the Capital Asset Pricing Model (CAPM) formula:

Required Return (R)=Rf+β(RmRf)\text{Required Return (R)} = R_f + \beta (R_m - R_f)

Where:

  • RfR_f = Risk-free rate = 1.41% (0.0141)
  • β\beta = Beta of the stock = 2.8
  • RmR_m = Expected market return = 7.05% (0.0705)

Step 1: Calculate the Market Risk Premium

RmRf=0.07050.0141=0.0564(5.64%)R_m - R_f = 0.0705 - 0.0141 = 0.0564 \, (5.64\%)

Step 2: Apply the CAPM Formula

R=0.0141+2.8×0.0564R = 0.0141 + 2.8 \times 0.0564

Step 3: Multiply and Add

R=0.0141+0.15792=0.17202(17.202%)R = 0.0141 + 0.15792 = 0.17202 \, (17.202\%)

Final Answer:

The required return for the company's stock is 17.20 (without the % symbol, as requested).

Would you like me to explain any specific step in more detail?


Related Questions:

  1. What does beta signify in the CAPM model, and why does a high beta imply higher risk?
  2. How does the risk-free rate affect the required return on a stock?
  3. What factors might cause the expected market return to change over time?
  4. How would the required return change if the beta were lower or higher?
  5. Why is CAPM widely used in finance, and what are its limitations?

Tip:

Always ensure the risk-free rate, beta, and market return are consistent in terms of time period (e.g., annualized) when using CAPM for calculations.

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Math Problem Analysis

Mathematical Concepts

Finance
Risk Analysis
Capital Asset Pricing Model (CAPM)

Formulas

Required Return = Risk-free rate + Beta * (Market Return - Risk-free rate)

Theorems

Capital Asset Pricing Model (CAPM)

Suitable Grade Level

Undergraduate Finance/Business