Let's break down the problem step by step: ### **Given Data** - **Year 1 NOI:** $120,000 - **Annual NOI Growth Rate:** 5% - **Purchase Price:** $620,000 - **Equity Financing:** 100% (so, ignore debt) - **Holding Period:** 4 years - **Sale Price at End of Year 4:** $800,000 - **Selling Costs:** 4% of sale price - **Discount Rate/Required Return (Unlevered):** 10% --- ## **Step 1: Calculate NOI for Each Year** - **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 Sale Proceeds at End of Year 4** - **Gross Sale Price:** $800,000 - **Selling Costs:** 4% × $800,000 = $32,000 - **Net Sale Proceeds:** $800,000 - $32,000 = $768,000 - **Total Cash Flow in Year 4:** NOI (Year 4) + Net Sale Proceeds = $138,915 + $768,000 = **$906,915** --- ## **Step 3: Find the NPV** - **Initial Outlay (Year 0):** \(-\$620,000\) - **Year 1 Cash Flow:** $120,000 - **Year 2 Cash Flow:** $126,000 - **Year 3 Cash Flow:** $132,300 - **Year 4 Cash Flow:** $906,915 - **Discount Rate:** 10% ### **NPV Formula:** \[ NPV = \sum \frac{CF_t}{(1 + r)^t} - Initial\ Outlay \] But since the purchase price is already an outlay at year 0, the NPV is just the sum of the present values of all future cash flows **minus** the purchase price (which is negative cash flow at time 0). \[ NPV = -\$620,000 + \frac{120,000}{(1.10)^1} + \frac{126,000}{(1.10)^2} + \frac{132,300}{(1.10)^3} + \frac{906,915}{(1.10)^4} \] --- ### **Calculate Each Term** #### 1. Year 1: \[ \frac{120,000}{1.10} = 109,090.91 \] #### 2. Year 2: \[ \frac{126,000}{(1.10)^2} = \frac{126,000}{1.21} = 104,132.23 \] #### 3. Year 3: \[ \frac{132,300}{(1.10)^3} = \frac{132,300}{1.331} = 99,415.18 \] #### 4. Year 4: \[ \frac{906,915}{(1.10)^4} = \frac{906,915}{1.4641} = 619,441.18 \] --- ### **Sum the Present Values** \[ NPV = -620,000 + 109,090.91 + 104,132.23 + 99,415.18 + 619,441.18 \] \[ NPV = -620,000 + 932,079.50 \] \[ NPV = 312,079.50 \] --- ## **Final Answer** ### **The unlevered net present value (NPV) is:** \[ \boxed{\$312,080} \] --- **(rounded to the nearest dollar)** --- If you want to see the steps or have any follow-up questions, let me know!