Consider the following information and calculate the required rate of return for the Winkler Investment Fund. The total investment fund is $2 million.
Stock Investment Beta
----- ---------- ----
A $ 200,000 1.50
B 300,000 -0.50
C 500,000 1.25
D 1,000,000 0.75
The market required rate of return is 15% and the risk-free rate is 7 percent.
To calculate the required rate of return for the Winkler Investment Fund, we will use the Capital Asset Pricing Model (CAPM) formula:
Required rate of return = Risk-free rate + Beta * (Market required rate of return - Risk-free rate)
Let's calculate the required rate of return for each stock step-by-step:
For Stock A:
Required rate of return for Stock A = 7% + 1.50 * (15% - 7%)
Required rate of return for Stock A = 7% + 1.50 * 8%
Required rate of return for Stock A = 7% + 12%
Required rate of return for Stock A = 19%
For Stock B:
Required rate of return for Stock B = 7% + (-0.50) * (15% - 7%)
Required rate of return for Stock B = 7% + (-0.50) * 8%
Required rate of return for Stock B = 7% - 4%
Required rate of return for Stock B = 3%
For Stock C:
Required rate of return for Stock C = 7% + 1.25 * (15% - 7%)
Required rate of return for Stock C = 7% + 1.25 * 8%
Required rate of return for Stock C = 7% + 10%
Required rate of return for Stock C = 17%
For Stock D:
Required rate of return for Stock D = 7% + 0.75 * (15% - 7%)
Required rate of return for Stock D = 7% + 0.75 * 8%
Required rate of return for Stock D = 7% + 6%
Required rate of return for Stock D = 13%
Therefore, the required rate of return for the Winkler Investment Fund is as follows:
- Stock A: 19%
- Stock B: 3%
- Stock C: 17%
- Stock D: 13%
To calculate the required rate of return for the Winkler Investment Fund, we need to use the Capital Asset Pricing Model (CAPM) formula. The CAPM formula is as follows:
Required Rate of Return = Risk-free rate + Beta * (Market Rate of Return - Risk-free rate)
Given that the risk-free rate is 7% and the market rate of return is 15%, we can now calculate the required rate of return for each stock in the Winkler Investment Fund.
1. Stock A:
Investment: $200,000
Beta: 1.50
Required Rate of Return for Stock A = 7% + 1.50 * (15% - 7%)
= 7% + 1.50 * 8%
= 7% + 12%
= 19%
2. Stock B:
Investment: $300,000
Beta: -0.50
Required Rate of Return for Stock B = 7% + (-0.50) * (15% - 7%)
= 7% + (-0.50) * 8%
= 7% - 4%
= 3%
3. Stock C:
Investment: $500,000
Beta: 1.25
Required Rate of Return for Stock C = 7% + 1.25 * (15% - 7%)
= 7% + 1.25 * 8%
= 7% + 10%
= 17%
4. Stock D:
Investment: $1,000,000
Beta: 0.75
Required Rate of Return for Stock D = 7% + 0.75 * (15% - 7%)
= 7% + 0.75 * 8%
= 7% + 6%
= 13%
Therefore, the required rate of return for the Winkler Investment Fund is as follows:
Stock A: 19%
Stock B: 3%
Stock C: 17%
Stock D: 13%