Calculating Property Value Using CAPM

Problem:

You are considering the purchase of real estate that will provide perpetual income that should average $50,000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolio’s? The T-bill rate is 5%, and the expected market return is 12.5%.

Solution:

To determine the price you should pay for the property, we’ll use the perpetuity valuation formula:

$$\text{Value} = \frac{\text{Cash Flow}}{\text{Required Return}}$$

Since the property has the same market risk as the market portfolio, its beta = 1. So, we’ll use the Capital Asset Pricing Model (CAPM) to find the required return:

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Step 1: Calculate required return using CAPM

$$R = R_f + \beta(R_m - R_f)$$
$$R = 5\% + 1 \times (12.5\% - 5\%) = 5\% + 7.5\% = \boxed{12.5\%}$$

Step 2: Calculate the value of the property

$$\text{Value} = \frac{50,000}{0.125} = \boxed{400,000}$$

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✅ Final Answer:

You should be willing to pay $400,000 for the property.

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 Mutual Fund Return Analysis And Assessment

Problem:

A mutual fund manager expects her portfolio to earn a rate of return of 11% this year. The beta of her portfolio is .8.  

a. If the rate of return available on risk-free assets is 4% and you expect the rate of return on the market portfolio to be 14%, what expected rate of return would you demand before you would be willing to invest in this mutual fund? 

 b. Is this fund attractive?

Solution:

We’ll use the Capital Asset Pricing Model (CAPM) to determine whether the mutual fund offers a return that justifies its risk level.

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CAPM Formula:

$$R_i = R_f + \beta_i (R_m - R_f)$$

Where:

• $R_i$: required return on the investment
• $R_f$: risk-free rate
• $\beta_i$: beta of the investment
• $R_m$: expected return on the market

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Given:

• Fund’s expected return = 11%
• Fund’s beta = 0.8
• Risk-free rate = 4%
• Market return = 14%

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(a) Required Return Using CAPM:

$$R_i = 4\% + 0.8 \times (14\% - 4\%) = 4\% + 0.8 \times 10\% = 4\% + 8\% = \boxed{12\%}$$

So, you would demand a return of 12% to invest in a portfolio with a beta of 0.8.

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(b) Is the Fund Attractive?

• Expected return offered by the fund = 11%
• Required return based on CAPM = 12%

📉 Since the fund’s expected return (11%) is lower than the required return (12%), the fund is not attractive.
It does not compensate you enough for the risk you're taking based on market expectations.

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✅ Final Answer:

• (a) Required return: 12%
• (b) No, the fund is not attractive because it underperforms relative to the CAPM benchmark.

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