You appraise a 28 -unit apartment house using the income approach. Units rents for \( \$ 775 \) a month. The past 5 years the annual expenses of operation averaged \( \$ 82,460 \) with a vacancy rate of \( 5 \% \). A investor is only interested if the return is \( 9.5 \% \). What value would you arrive at using these variables?

To find the value of the apartment building using the income approach, you first need to calculate the effective gross income (EGI). The monthly rent per unit is $775, and with 28 units, the gross monthly income (GMI) is: \[ 28 \text{ units} \times 775 \text{ dollars/unit} = 21,650 \text{ dollars/month} \] The annual gross income (AGI) is: \[ 21,650 \text{ dollars/month} \times 12 \text{ months} = 259,800 \text{ dollars/year} \] Taking into account the vacancy rate of 5%: \[ EGI = AGI \times (1 - \text{vacancy rate}) = 259,800 \times (1 - 0.05) = 259,800 \times 0.95 \approx 246,810 \text{ dollars/year} \] Next, subtract the annual expenses of operation which average $82,460: \[ Net Operating Income (NOI) = EGI - \text{Expenses} = 246,810 - 82,460 = 164,350 \text{ dollars/year} \] Now that you have the NOI, you can find the property value using the formula: \[ Value = \frac{NOI}{Cap Rate} = \frac{164,350}{0.095} \approx 1,729,473.68 \text{ dollars} \] Thus, the value you arrive at using these variables would be approximately $1,729,474.