1. **State the problem:** Calculate the following real estate investment metrics using the provided data: Capitalization Rate (Ro), Annual Debt Service, Debt Coverage Ratio (DCR), Loan to Value Ratio (LTV), Debt Yield, Operating Expense Ratio, Net Income Ratio, Mortgage Constant (Rm), Cash-on-Cash Return, and leverage sustainable at a DCR of 1.25. 2. **Given Data:** - Purchase Price = 17,500,000 - Loan Amount = 13,125,000 - Interest Rate = 6% annually - Amortization = 25 years monthly payments - Net Operating Income (NOI) = 1,403,320 - Annual Debt Service = 1,014,775 - Total Operating Expenses = 700,000 - Gross Operating Income = 2,103,320 - Cash Flow Before Taxes = 363,545 3. **Calculate Capitalization Rate (Ro):** $$R_o = \frac{NOI}{Purchase\ Price} = \frac{1,403,320}{17,500,000} \approx 0.08019 = 8.02\%$$ 4. **Annual Debt Service is given as:** $$1,014,775$$ 5. **Calculate Debt Coverage Ratio (DCR):** $$DCR = \frac{NOI}{Annual\ Debt\ Service} = \frac{1,403,320}{1,014,775} \approx 1.38$$ 6. **Calculate Loan to Value Ratio (LTV):** $$LTV = \frac{Loan\ Amount}{Purchase\ Price} = \frac{13,125,000}{17,500,000} = 0.75 = 75\%$$ 7. **Calculate Debt Yield:** $$Debt\ Yield = \frac{NOI}{Loan\ Amount} = \frac{1,403,320}{13,125,000} \approx 0.107 = 10.7\%$$ 8. **Calculate Operating Expense Ratio:** $$Operating\ Expense\ Ratio = \frac{Operating\ Expenses}{Gross\ Operating\ Income} = \frac{700,000}{2,103,320} \approx 0.333 = 33.3\%$$ 9. **Calculate Net Income Ratio:** $$Net\ Income\ Ratio = \frac{NOI}{Gross\ Operating\ Income} = \frac{1,403,320}{2,103,320} \approx 0.668 = 66.8\%$$ 10. **Calculate Mortgage Constant (Rm):** Mortgage constant is Annual Debt Service divided by Loan Amount: $$R_m = \frac{Annual\ Debt\ Service}{Loan\ Amount} = \frac{1,014,775}{13,125,000} \approx 0.0773 = 7.73\%$$ Alternatively, we verify mortgage constant for 6% interest, 25-year amortization monthly payments matches approximately 7.73%. 11. **Calculate Cash-on-Cash Return:** Cash invested = Purchase Price - Loan Amount = 17,500,000 - 13,125,000 = 4,375,000 $$Cash\ on\ Cash\ Return = \frac{Cash\ Flow\ Before\ Taxes}{Cash\ Invested} = \frac{363,545}{4,375,000} \approx 0.0831 = 8.31\%$$ 12. **Calculate leverage sustainable at DCR = 1.25:** At DCR = 1.25, maximize Annual Debt Service: $$Annual\ Debt\ Service_{max} = \frac{NOI}{1.25} = \frac{1,403,320}{1.25} = 1,122,656$$ Calculate maximum loan amount with mortgage constant: $$Loan_{max} = \frac{Annual\ Debt\ Service_{max}}{R_m} = \frac{1,122,656}{0.0773} \approx 14,515,582$$ Calculate Loan to Value at max leverage: $$LTV_{max} = \frac{Loan_{max}}{Purchase\ Price} = \frac{14,515,582}{17,500,000} \approx 0.829 = 82.9\%$$ **Final answers:** - Capitalization Rate (Ro) = 8.02% - Annual Debt Service = 1,014,775 - Debt Coverage Ratio (DCR) = 1.38 - Loan to Value Ratio (LTV) = 75% - Debt Yield = 10.7% - Operating Expense Ratio = 33.3% - Net Income Ratio = 66.8% - Mortgage Constant (Rm) = 7.73% - Cash-on-Cash Return = 8.31% - Maximum Loan Amount for DCR 1.25 = 14,515,582 (Loan-to-Value 82.9%)