A property is purchased for $1,500,000 with a loan of $1,200,000. What is the loan-to-value ratio?
Correct Answer
B) 80%
Loan-to-value ratio = Loan amount ÷ Property value = $1,200,000 ÷ $1,500,000 = 0.80 or 80%.
Why This Is the Correct Answer
Option B is correct because the LTV calculation follows the standard formula: Loan Amount ÷ Property Value. Using the given figures: $1,200,000 ÷ $1,500,000 = 0.80 or 80%. This means the borrower is financing 80% of the property's value through the loan. The calculation is straightforward division converted to a percentage, which is the industry standard method for expressing LTV ratios.
Why the Other Options Are Wrong
Option A: 75%
75% is incorrect because it results from an improper calculation or confusion with other ratios. This percentage doesn't match the mathematical result of $1,200,000 ÷ $1,500,000, which clearly equals 0.80 or 80%.
Option C: 25%
25% is incorrect and represents the down payment percentage rather than the LTV ratio. This is calculated as ($1,500,000 - $1,200,000) ÷ $1,500,000 = 25%, which shows the borrower's equity percentage, not the loan-to-value ratio.
Option D: 125%
125% is mathematically impossible for this scenario and suggests confusion about which number should be the numerator and denominator. This would indicate the loan amount exceeds the property value, which doesn't occur in this problem.
LTV = Loan over Value
Remember 'LTV = Loan over Value' - the acronym spells out the formula. Think 'Loan Takes Value' where you put the loan amount on top and property value on bottom, then convert to percentage.
How to use: When you see LTV questions, immediately identify the loan amount (numerator) and property value (denominator), then divide and multiply by 100 for the percentage.
Exam Tip
Always double-check that you're dividing loan amount by property value, not the reverse, and remember to convert the decimal to a percentage by multiplying by 100.
Common Mistakes to Avoid
- -Dividing property value by loan amount instead of loan by value
- -Calculating the down payment percentage instead of LTV
- -Forgetting to convert the decimal result to a percentage
Concept Deep Dive
Analysis
The loan-to-value (LTV) ratio is a fundamental financial metric used in real estate to assess lending risk and borrower equity. It represents the percentage of a property's value that is financed through debt, calculated by dividing the loan amount by the property's appraised or purchase value. LTV ratios are critical for lenders to determine loan approval, interest rates, and whether private mortgage insurance is required. Lower LTV ratios indicate higher borrower equity and lower lender risk, while higher ratios suggest greater leverage and potential risk.
Background Knowledge
Loan-to-value ratio is expressed as a percentage and calculated by dividing the mortgage loan amount by the appraised value or purchase price of the property, whichever is lower. LTV ratios typically range from 70% to 97% for conventional loans, with 80% being a common threshold where private mortgage insurance requirements often apply.
Real-World Application
Appraisers must understand LTV ratios because they directly impact loan approval and terms. When an appraised value comes in lower than expected, it can increase the LTV ratio beyond lender guidelines, potentially requiring additional down payment or causing loan denial.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
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