Miscellaneous Ratio Problems

1)   What is the indicated overall capitalization rate of a property having a $185,000 mortgage, NOI of $27,980, and debt service of $24,680 if the desired equity dividend rate is 15%? [2100]

Equity dividend rate = Equity dividend / Equity

Equity dividend = $27,980 – $24,680 – $3,300

0.15 = $3,300 / Equity

Equity = $3,300 / 0.15 = $22,000

Value (price) = $185,000 (mortgage) + $22,000 (equity) = $207,000

Cap Rate = $27,980 / $207,000 = 0.1352

Answer – 13.5%

2)   A property generates net operating income of $50,000 with annual debt service is $43,264. If the mortgage constant is 0.1565 and the loan to value ratio is 76%, what is the rate of capitalization? [2101]

Mortgage Constant = Debt Service / Mortgage (see formula page)

0.1565 = $43,264 / Mortgage therefore Mortgage = $43,264 / 0.1565 = $276,447

Value x 0.76 = $276,447 therefore Value = $363,746

Cap Rate = $50,000 / $363,746 = 13.7%

Answer – 13.7%

3)   What is the indicated capitalization rate using the band of investment method if the annual debt service is $14,366 on a property with a 75% loan–to–value ratio mortgage of $96,500 and a required equity dividend rate of 18%? [2102]

Mortgage Constant = Debt Service / Mortgage Amount

Mortgage Constant = $14,366 / $96,500 = 0.14887

Cap Rate = ( 0.75 x 0.14887) + (0.25 x 0.18)

Cap Rate = (0.11165) + (0.045) = 15.67%

Answer – 15.6%

4)   If net operating income is $45,000, annual debt service is $25,000, and the equity investment is $100,000, what is the equity dividend rate? [2103]**

Equity Dividend Rate = Equity Dividend / Equity Investment

Equity Dividend = $45,000 – $25,000 = $20,000

Equity Dividend Rate = $20,000 / $100,000 = 20%

Answer – 20%

5)   An apartment complex, has a potential gross income of $500,000.  Vacancy and bad debt losses are 6%.  If operating expenses are $205,000, what is the operating expense ratio? [2104]

Operating Expense Ratio = Operating Expenses / Effective Gross Income

EGI = $500,000 x 0.94 = $470,000

Operating Expense Ratio = $205,000 / $470,000 = 43.6%

Answer – 43.6%

6)   If the mortgage constant is 0.098762, the loan to value ratio is 80%, and the overall capitalization rate is 12%, what is the equity dividend rate? [2105]

0.12 = (0.098762 x 0.8) + (Equity Dividend Rate x .2) therefore

0.12 – (0.098762 x 0.8) = 0.2 x Equity Dividend Rate and

0.04099 = 0.2 x Equity Dividend Rate and

Equity Dividend Rate = 0.04099 / 0.2 = 20.5%

Answer – 20.5%