Calculate The Required Rate Of Return For Mudd Enterprises ✓ Solved

Calculate The Required Rate Of Return For Mudd Enterprises

Calculate the required rate of return for Mudd Enterprises assuming that investors expect a 3.3% rate of inflation in the future. The real risk-free rate is 2.0%, and the market risk premium is 6.0%. Mudd has a beta of 1.7, and its realized rate of return has averaged 10.0% over the past 5 years. Round your answer to two decimal places.

A stock has a required return of 15%, the risk-free rate is 4.5%, and the market risk premium is 5%. What is the stock's beta? Round your answer to two decimal places. If the market risk premium increased to 7%, what would happen to the stock's required rate of return? Assume that the risk-free rate and the beta remain unchanged. Do not round intermediate calculations. Round your answer to two decimal places.

Calculate Kish's required rate of return. The risk-free rate is 5%, and you believe the following probability distribution for future market returns is realistic: Probability Market Return 0.1-28% 0.2 0.4 30% 0.2 0.1 48%. What is the equation for the Security Market Line (SML)?

Calculate each stock's required rate of return. Round your answers to one decimal place. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Paper For Above Instructions

The required rate of return is a critical concept in finance, reflecting the minimum return an investor expects to earn while taking on the risk of an investment. For Mudd Enterprises, the calculation involves using data parameters such as inflation rates, risk-free rates, and market risk premiums. In this analysis, we focus on two primary components—expected return and beta—for Mudd Enterprises and another stock. The details of the calculations provide insight into assessing the investment's profitability and risk levels.

Calculating Required Rate of Return for Mudd Enterprises

To calculate the required rate of return for Mudd Enterprises, we can utilize the Capital Asset Pricing Model (CAPM), which is expressed as:

R = Rf + β * (Rm - Rf)

Where:

  • R = required rate of return
  • Rf = risk-free rate (2.0%)
  • β = beta of the stock (1.7)
  • Rm = expected market return

In this scenario, we know the market risk premium is 6.0%. Therefore, if we add the risk-free rate to the market risk premium, we find:

Rm = Rf + market risk premium = 2.0% + 6.0% = 8.0%

Substituting these values into the CAPM equation, we find:

R = 2.0% + 1.7 (8.0% - 2.0%) = 2.0% + 1.7 6.0% = 2.0% + 10.2% = 12.2%

Thus, the required rate of return for Mudd Enterprises is 12.2% when rounded to two decimal places.

Required Return for Another Stock

Next, we evaluate a stock with a required return of 15%, a risk-free rate of 4.5%, and a market risk premium of 5%. We can determine its beta using the following rearranged CAPM formula:

β = (R - Rf) / (Rm - Rf)

Here R is 15%, Rf is 4.5%, and Rm is:

Rm = Rf + market risk premium = 4.5% + 5% = 9.5%

Substituting these values into the beta formula results in:

β = (15% - 4.5%) / (9.5% - 4.5%) = 10.5% / 5% = 2.1

Hence, the stock’s beta is 2.1.

To examine what would happen if the market risk premium increased to 7%, we can plug the new value back into our required return formula, holding the risk-free rate and beta constant:

New Rm = 4.5% + 7% = 11.5%

Thus, the new required return would be:

R = Rf + β (New Rm - Rf) = 4.5% + 2.1 (11.5% - 4.5%) = 4.5% + 2.1 * 7% = 4.5% + 14.7% = 19.2%

Therefore, if the market risk premium increased to 7%, the stock's required rate of return would be 19.2%.

Kish's Required Rate of Return

Investing in stocks requires analyzing their expected returns against their risks. In the case of the Kish Hedge Fund, we need to calculate the overall beta of the fund, which is the weighted average of the betas of the stocks in the portfolio.

Investment composition shows:

  • Stock A: $160 million, Beta 0.3
  • Stock B: $120 million, Beta 1.5
  • Stock C: $80 million, Beta 1.8
  • Stock D: $80 million, Beta 1.0
  • Stock E: $60 million, Beta 1.5

The total capital is $500 million. Hence, the weighted average beta is calculated as follows:

Weighted Beta (β) = Σ(Investment_i * β_i) / Total Investment

Substituting values:

Weighted Beta = (0.3 160 + 1.5 120 + 1.8 80 + 1.0 80 + 1.5 * 60) / 500 = (48 + 180 + 144 + 80 + 90) / 500 = 542 / 500 = 1.084

With a calculated beta of 1.084, using the risk-free rate of 5% we can determine Kish's required rate of return:

R = 5% + 1.084 (6% - 5%) = 5% + 1.084 1% = 5% + 1.084% = 6.084%

The required rate of return for the Kish Hedge Fund, rounded to two decimal places, is 6.08%.

Conclusion

In summary, calculating the required rate of return using the CAPM provides invaluable insights for investors by quantifying the compensation expected for taking on increased risk. A clear understanding of returns adjusted for risk, using factors like market premiums and beta, aids in making confident investment decisions.

References

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