A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Correct Answer
C) 80.0%
1200000/1500000×100=80%. The stated purchase-price denominator removes uncertainty about a different appraised value or a lender's lesser-of policy.
Why This Is the Correct Answer
Option C is correct because loan-to-value is the loan amount divided by the value: $1,200,000 / $1,500,000 = 0.80, and 0.80 x 100 = 80.0%. The question specifies the purchase price as the denominator, which removes any question about a different appraised value or a lender's lesser-of policy.
Why the Other Options Are Wrong
Option A: 20.0%
Option A, 20.0%, is the buyer's equity share rather than the loan ratio: ($1,500,000 - $1,200,000) / $1,500,000 x 100 = 20.0%. The question asks for loan/value, which is $1,200,000 / $1,500,000 x 100 = 80.0%.
Option B: 125.0%
Option B, 125.0%, inverts the ratio by dividing value by loan: $1,500,000 / $1,200,000 x 100 = 125.0%. Loan-to-value puts the loan on top: $1,200,000 / $1,500,000 x 100 = 80.0%.
Option D: 0.8%
Option D, 0.8%, takes the decimal ratio 0.8 and labels it a percent without multiplying by 100. The correct figure is $1,200,000 / $1,500,000 x 100 = 80.0%.
Loan on top
In loan-to-value, the loan comes first in the name and goes on top of the fraction.
How to use: Use this to set up the division correctly and avoid inverting the ratio.
Exam Tip
An LTV above 100% means the loan exceeds the value; if the loan is smaller than the value, the answer must be under 100%.
Common Mistakes to Avoid
- -Reporting the equity percentage instead of the loan ratio
- -Dividing value by loan instead of loan by value
- -Forgetting to multiply the decimal by 100
Concept Deep Dive
Analysis
This question tests calculating a loan-to-value ratio. The loan amount is divided by the value denominator, which the question sets as the purchase price. So $1,200,000 / $1,500,000 x 100 = 80.0%.
Background Knowledge
Loan-to-value ratio compares the loan amount with the property's value at origination and is a key measure of lending risk. Lenders often use the lower of purchase price or appraised value as the denominator, but here the purchase price is used. The remaining share of value is the borrower's equity.
Real-World Application
A buyer purchases a property for $1,500,000 with a $1,200,000 loan and a $300,000 down payment. The lender records an 80% loan-to-value ratio and confirms that the appraised value supports at least the purchase price.
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