# Step 1: **Required Equity Investment and Expenditures** ### ** 1A: Calculate Total Equity Required** - **Purchase price:** $202,600 - **Loan amount:** $160,000 - **Equity invested:** \[ \text{Equity} = \text{Purchase price} - \text{Loan amount} = \$202,600 - \$160,000 = \$42,600 \] ### **Step 1B: Calculate Total Outflows (Year 1)** Add up all expenditures (excluding loan principal, since it's interest-only): - Inspection: $539 - Title search: $1,078 - Renovation: $13,000 - Landscaping: $878 - Loan interest: $7,200 - Insurance: $1,839 - Property taxes: $6,039 - Selling expenses: $8,000 **Total Outflows:** \[ \text{Total Outflows} = \$539 + \$1,078 + \$13,000 + \$878 + \$7,200 + \$1,839 + \$6,039 + \$8,000 = \$38,573 \] **Total Cash Outlay (Equity + Outflows):** \[ \text{Total Equity at risk} = \text{Equity} + (\text{All outflows except loan principal}) = \$42,600 + \$38,573 = \$81,173 \] #### **Explanation:** At the end of Year 1, the investor's total cash investment (equity and all out-of-pocket costs) is **$81,173**. --- # Step 2: **Required Sale Price for 20% IRR (Year 1 & Year 2)** ## **Part 1: Sale After 1 Year** - **Required IRR:** 20% - **Loan payoff:** $160,000 - **Net Proceeds to Investor:** Sale Price – Selling Expenses – Loan Payoff Set up equation: \[ \text{Final Equity} = (\text{Sale Price} - \$8,000) - \$160,000 \] \[ \text{Required: } \text{Final Equity} = \text{Initial Equity and Outflows} \times 1.20 = \$81,173 \times 1.20 = \$97,408 \] \[ (\text{Sale Price} - \$8,000 - \$160,000) = \$97,408 \] \[ \text{Sale Price} = \$97,408 + \$8,000 + \$160,000 = \boxed{\$265,408} \] #### **Explanation:** The property must sell for **$265,408** after one year to provide a 20% IRR on equity. --- ## **Part 2: Sale After 2 Years (With Rental Income)** ### **Year 2 Cash Flows:** - **Rental income:** $1,980/month × 12 = $23,760 (before debt service) - **Additional interest:** $7,200 - **Net Year 2 cash flow:** $23,760 – $7,200 = $16,560 #### **IRR Calculation (20% over 2 years):** - **Year outflow:** $81,173 (calculated above) - **Year 1 inflow:** $ (no sale) - **Year 2 inflow:** Net proceeds from sale + net rental income Let \( S \) = sale price at end of year 2: \[ \text{Net proceeds to investor} = S - \$8,000 - \$160,000 \] \[ \text{Total year 2 inflow} = (S - \$8,000 - \$160,000) + \$16,560 \] Set IRR equation: \[ -81,173 \ (t=),\ \ (t=1),\ (S - 8,000 - 160,000 + 16,560) \ (t=2) \] \[ 81,173 \times (1.2)^2 = S - 8,000 - 160,000 + 16,560 \] \[ 81,173 \times 1.44 = S - 8,000 - 160,000 + 16,560 \] \[ 116,889 = S - 8,000 - 160,000 + 16,560 \] \[ S = 116,889 + 8,000 + 160,000 - 16,560 \] \[ S = 284,889 - 16,560 \] \[ S = \boxed{268,329} \] #### **Explanation:** If sold at the end of year 2, after receiving year 2 rental income, the property must sell for **$268,329** to earn a 20% IRR on equity. --- # **Final Answers Summary** | Scenario | Required Sale Price | |------------------------------|--------------------| | **After 1 year** | $265,408 | | **After 2 years (with rent)**| $268,329 |

# Investment Analysis of Distressed Property ## Step 1: **Required Equity Investment and Expenditures** ### 1A: Calculate Total Equity Required - **Purchase Price:** $202,600 - **Loan Amount:** $160,000 - **Equity Invested:** \[ \text{Equity} = \text{Purchase Price} - \text{Loan Amount} = \$202,600 - \$160,000 = \$42,600 \] ### 1B: Calculate Total Outflows (Year 1) Add up all expenditures (excluding loan principal, since it's interest-only): - **Inspection:** $539 - **Title Search:** $1,078 - **Renovation:** $13,000 - **Landscaping:** $878 - **Loan Interest:** $7,200 - **Insurance:** $1,839 - **Property Taxes:** $6,039 - **Selling Expenses:** $8,000 **Total Outflows:** \[ \text{Total Outflows} = \$539 + \$1,078 + \$13,000 + \$878 + \$7,200 + \$1,839 + \$6,039 + \$8,000 = \$38,573 \] **Total Cash Outlay (Equity + Outflows):** \[ \text{Total Equity at Risk} = \text{Equity} + \text{Total Outflows} = \$42,600 + \$38,573 = \$81,173 \] ### **Explanation:** At the end of Year 1, the investor's total cash investment (equity and all out-of-pocket costs) is **$81,173**. --- ## Step 2: **Required Sale Price for 20% IRR** ### Part 1: Sale After 1 Year - **Required IRR:** 20% - **Loan Payoff:** $160,000 - **Net Proceeds to Investor:** Sale Price – Selling Expenses – Loan Payoff Set up equation: \[ \text{Final Equity} = (\text{Sale Price} - \$8,000) - \$160,000 \] \[ \text{Required: } \text{Final Equity} = \text{Total Cash Outlay} \times 1.20 = \$81,173 \times 1.20 = \$97,408 \] \[ (\text{Sale Price} - \$8,000 - \$160,000) = \$97,408 \] \[ \text{Sale Price} = \$97,408 + \$8,000 + \$160,000 = \boxed{\$265,408} \] ### **Explanation:** The property must sell for **$265,408** after one year to provide a 20% IRR on equity. --- ### Part 2: Sale After 2 Years (With Rental Income) #### Year 2 Cash Flows: - **Rental Income:** $1,980/month × 12 = $23,760 (before debt service) - **Additional Interest Payments:** $7,200 - **Net Year 2 Cash Flow:** $23,760 – $7,200 = $16,560 ### IRR Calculation (20% over 2 years): - **Year 0 Outflow:** $81,173 (calculated above) - **Year 1 Inflow:** $0 (no sale) - **Year 2 Inflow:** Net proceeds from sale + net rental income Let \( S \) = sale price at end of Year 2: \[ \text{Net Proceeds to Investor} = S - \$8,000 - \$160,000 \] Total inflow for Year 2: \[ \text{Total Year 2 Inflow} = (S - \$8,000 - \$160,000) + \$16,560 \] Set up the IRR equation: \[ -81,173 \ (t=0),\ \ 0 \ (t=1),\ (S - 8,000 - 160,000 + 16,560) \ (t=2) \] Calculating for \( S \): \[ 81,173 \times (1.2)^2 = S - 8,000 - 160,000 + 16,560 \] \[ 81,173 \times 1.44 = S - 8,000 - 160,000 + 16,560 \] \[ 116,889 = S - 8,000 - 160,000 + 16,560 \] \[ S = 116,889 + 8,000 + 160,000 - 16,560 \] \[ S = 284,889 - 16,560 \] \[ S = \boxed{268,329} \] ### **Explanation:** If sold at the end of Year 2, after receiving Year 2 rental income, the property must sell for **$268,329** to earn a 20% IRR on equity. --- # Final Answers Summary | Scenario | Required Sale Price | |------------------------------|--------------------| | **After 1 Year** | $265,408 | | **After 2 Years (With Rent)**| $268,329 |