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.