Let's break down the problem and calculate the **unlevered Net Present Value (NPV)** step by step. ### **Given:** - **Year 1 NOI:** \$120,000 - **NOI increases:** 5% per year - **Purchase Price:** \$620,000 (all equity, so ignore debt) - **Holding Period:** 4 years - **Sale Price at end of Year 4:** \$800,000 - **Selling Costs:** 4% of sale price - **Required Unlevered Rate of Return (Discount Rate):** 10% --- ### **Step 1: Calculate Annual NOI for Years 1-4** - Year 1: \$120,000 - Year 2: \$120,000 × 1.05 = \$126,000 - Year 3: \$126,000 × 1.05 = \$132,300 - Year 4: \$132,300 × 1.05 = \$138,915 --- ### **Step 2: Calculate Net Sales Proceeds (End of Year 4)** - **Gross Sale Price:** \$800,000 - **Selling Costs:** 4% × \$800,000 = \$32,000 - **Net Sales Proceeds:** \$800,000 - \$32,000 = \$768,000 --- ### **Step 3: Calculate Cash Flows** - **Year 0:** -\$620,000 (purchase price) - **Year 1:** \$120,000 - **Year 2:** \$126,000 - **Year 3:** \$132,300 - **Year 4:** \$138,915 (NOI) + \$768,000 (net sales proceeds) = **\$906,915** --- ### **Step 4: Discount the Cash Flows at 10%** NPV = \[ -\$620,000 + \frac{120,000}{(1.10)^1} + \frac{126,000}{(1.10)^2} + \frac{132,300}{(1.10)^3} + \frac{906,915}{(1.10)^4} \] Now, let's compute each term: - Year 1: \$120,000 / 1.10 = \$109,090.91 - Year 2: \$126,000 / (1.10)^2 = \$126,000 / 1.21 = \$104,132.23 - Year 3: \$132,300 / (1.10)^3 = \$132,300 / 1.331 = \$99,436.14 - Year 4: \$906,915 / (1.10)^4 = \$906,915 / 1.4641 = \$619,484.85 --- ### **Step 5: Add Up** \[ \text{NPV} = -620,000 + 109,090.91 + 104,132.23 + 99,436.14 + 619,484.85 \] \[ \text{NPV} = -620,000 + (109,090.91 + 104,132.23 + 99,436.14 + 619,484.85) \] \[ \text{NPV} = -620,000 + 932,144.13 = \boxed{312,144.13} \] --- ## **Final Answer** ### **The unlevered NPV is approximately \$312,144.**