Let's break down the solution step by step: ### **Step 1: Calculate Initial Equity Invested** - **Purchase Price:** $200,000 - **Loan Amount:** $160,000 (80% of purchase price) - **Equity Invested:** $200,000 - $160,000 = **$40,000** ### **Step 2: Total Outflows in Year 1** Add up all expenditures: - Inspection: $500 - Title search: $1,000 - Renovation: $13,000 - Landscaping: $800 - Loan interest: $7,200 - Insurance: $1,800 - Property taxes: $6,000 - Selling expenses: $8,000 **Total Expenditures = $500 + $1,000 + $13,000 + $800 + $7,200 + $1,800 + $6,000 + $8,000 = $38,300** ### **Step 3: Total Cash Outlay (Year 1)** - **Equity Invested:** $40,000 - **Plus Yearly Expenditures:** $38,300 - **Total Outlay:** $40,000 + $38,300 = **$78,300** ### **Step 4: Calculate Required Cash Inflow at End of Year 1** To earn a 20% IRR on the equity invested ($40,000): - Required end-of-year cash flow: \[ \text{Future Value} = \$40,000 \times (1 + 0.20) = \$48,000 \] - But remember, the investor needs to **get back all cash outflows plus 20% return on equity**. He needs to pay off the loan ($160,000) **and** cover all costs, plus his profit. So, the total amount needed at sale = Loan payoff + Expenditures + Required equity return = $160,000 + $38,300 + $8,000 (20% of $40,000) = **$206,300** But let's calculate it more formally by using IRR methodology. ### **Step 5: Set Up the IRR Equation** The investor's net cash flows: - **Time 0 (now):** Outflow = -$40,000 (equity) - **Time 1 (end of year):** Inflow = Sale price - $160,000 (loan payoff) - $38,300 (expenditures) He wants IRR = 20%. So, \[ -40,000 + \frac{(\text{Sale Price} - 160,000 - 38,300)}{1.20} = 0 \] \[ (\text{Sale Price} - 160,000 - 38,300) = 40,000 \times 1.20 \] \[ \text{Sale Price} - 198,300 = 48,000 \] \[ \text{Sale Price} = 198,300 + 48,000 = \boxed{246,300} \] --- ### **Final Answer:** **Sale value of property:** **$246,300** --- **Enter "$246,300" in the box.** Let me know if you'd like the solution for Required B as well!

Let's work through part b step by step. **Part b:** **Scenario:** - The investor plans to hold the property for an additional year if it doesn't sell after the first year. - Starting in year 2, he can rent the property and receive a net cash flow before debt service of $1,200 per month. - During year 2, he will incur an additional interest payment of $7,200 on his loan. - He intends to sell the property at the end of year 2 and wants to achieve a 20% IRR on his initial equity investment. --- ### Step 1: Determine initial equity and costs - **Purchase price:** $200,000 - **Loan amount:** $160,000 - **Initial equity invested:** $40,000 ### Step 2: Year 1 costs (already calculated in part a) Total expenditures during year 1: - Inspection: $500 - Title search: $1,000 - Renovation: $13,000 - Landscaping: $800 - Loan interest: $7,200 - Insurance: $1,800 - Property taxes: $6,000 - Selling expenses: $8,000 **Total Year 1 expenditures:** $500 + $1,000 + $13,000 + $800 + $7,200 + $1,800 + $6,000 + $8,000 = **$38,300** --- ### Step 3: Year 2 cash flows **Income:** - Net rent per month: $1,200 - Annual net rent: $1,200 × 12 = **$14,400** **Expenses during Year 2:** - Additional interest payment: $7,200 - Property taxes, insurance, and other expenses are assumed paid; the question only mentions the additional interest, so we’ll focus on that. **Note:** Since the costs like property taxes, insurance, etc., are ongoing, but only the additional interest of $7,200 is specified for Year 2, we will assume these are either paid or accounted for in cash flows, or that the main variable is the interest. ### Step 4: Determine the sale price at the end of Year 2 The investor wants a 20% IRR on his initial equity of $40,000. --- ### Step 5: Set up the IRR equation **Initial outflow (at Year 0):** $40,000 (equity invested) **Outflows during Year 1:** - $38,300 (expenditures) **Net cash flow at the end of Year 1:** - The investor's equity is still $40,000 (assuming no additional investments). - He has earned rent, paid expenses, and paid interest. **At the end of Year 2:** - The investor receives net rent of $14,400 - Pays additional interest of $7,200 - Sells the property at an unknown price \(P\) **Cash flows at Year 2:** - Revenue from rent: +$14,400 - Less interest: -$7,200 - Sale proceeds: \(P\) (received at end of Year 2) - Repayment of loan: -$160,000 (loan is paid off at sale) --- ### Step 6: Calculate the sale price \(P\) The goal: The initial $40,000 investment should grow at 20% IRR over 2 years. The net cash flows: - Year 0: \(-\$40,000\) - Year 1: \(-\$38,300\) (expenditures) - Year 2: \( (P) - \$160,000 + \$14,400 - \$7,200 \) **Note:** - The loan payoff of $160,000 occurs at sale, reducing the net cash received from the sale. --- ### Step 7: Formulate the IRR equation \[ \text{NPV} = 0 = -40,000 - 38,300 + \frac{(P - 160,000 + 14,400 - 7,200)}{(1 + 0.20)^2} \] Calculating the present value of Year 2 cash inflow: \[ P - 160,000 + 14,400 - 7,200 = P - 160,000 + 7,200 = P - 152,800 \] The discount factor for 2 years at 20%: \[ (1 + 0.20)^2 = 1.44 \] So: \[ 0 = -78,300 + \frac{P - 152,800}{1.44} \] Rearranged: \[ \frac{P - 152,800}{1.44} = 78,300 \] Multiply both sides by 1.44: \[ P - 152,800 = 78,300 \times 1.44 = 112,752 \] Solve for \(P\): \[ P = 112,752 + 152,800 = \boxed{\$265,552} \] --- ### **Final Answer:** The property must sell for approximately **$265,552** at the end of year 2 to achieve a 20% IRR on the initial equity investment. --- **Summary:** | **Part** | **Required Sale Price** | |------------|-------------------------| | **a** | **$246,300** | | **b** | **$265,552** | Let me know if you'd like further clarification!

To achieve a 20% IRR after one year, the property must sell for approximately **$246,300**. If held for an additional year and sold at the end of year 2, the required sale price is about **$265,552**.