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 determine the value of the 28-unit apartment house using the **Income Approach**, we'll follow these steps: 1. **Calculate Gross Rental Income** 2. **Adjust for Vacancy Rate** 3. **Determine Net Operating Income (NOI)** 4. **Apply the Capitalization Rate (Investor's Required Return)** Let's break down each step: ### 1. Gross Rental Income - **Monthly Rent per Unit:** \$775 - **Total Units:** 28 \[ \text{Monthly Gross Rent} = 28 \times \$775 = \$21,700 \] \[ \text{Annual Gross Rent} = \$21,700 \times 12 = \$260,400 \] ### 2. Adjust for Vacancy Rate - **Vacancy Rate:** 5% \[ \text{Effective Gross Income} = \text{Annual Gross Rent} \times (1 - \text{Vacancy Rate}) \] \[ \text{Effective Gross Income} = \$260,400 \times 0.95 = \$247,380 \] ### 3. Determine Net Operating Income (NOI) - **Annual Operating Expenses:** \$82,460 \[ \text{NOI} = \text{Effective Gross Income} - \text{Operating Expenses} \] \[ \text{NOI} = \$247,380 - \$82,460 = \$164,920 \] ### 4. Apply the Capitalization Rate - **Investor's Required Return (Cap Rate):** 9.5% or 0.095 \[ \text{Property Value} = \frac{\text{NOI}}{\text{Cap Rate}} \] \[ \text{Property Value} = \frac{\$164,920}{0.095} = \$1,736,000 \] ### **Conclusion** Based on the income approach and the given variables, the **estimated value of the apartment house** is **\$1,736,000**.