# Loan to Value Ratio

Loan to value ratio is the ratio of the principal balance of the loan to the market value of the asset used to secure the loan. It is an important factor used by lenders in deciding whether to approve a loan or not.

Let’s say you have spotted a property that’s worth $1 million and you want to buy it with$250,000 of your own savings and take out a 5% fixed-rate mortgage for the rest i.e. $750,000 requiring you to pay$4,026 per month. Your loan balance to value ratio is 75% calculated by dividing the loan balance of $750,000 by the property value of$1,000,000.

Lenders consider the LTV ratio of a mortgage together with other factors such as your income level, credit score, etc. A high loan to value ratio is risky for the lender because the cushion between the value of the collateral and the loan obligation is thin. Any adverse movement in interest rates and real estate values may wipe out the difference between loan balance and property value. This is why may lenders require homeowners to obtain insurance if the loan to value ratio is higher than a certain threshold which is 80% in most cases.

## Formula

Loan to value ratio can be calculated using the following formula:

$$\text{Loan to Value Ratio}=\frac{\text{Oustanding Loan Balance}}{\text{Property Value}}$$

You can calculate your equity in a property as follows:

$$\text{Equity}=\text{1}-\text{LTV}$$

Your LTV may fluctuate as the outstanding balance of your loan decreases as you pay off the loan and due to changes in market value of the property. This would result in corresponding fluctuation in your equity. In fact, in crisis situation, your equity may get negative which effectively means that you have pay cash when selling the property.

You might be interested in calculating your combined loan to value ratio which is the ratio of outstanding balance of all your loans to the market value of all your property.

## Example

Let’s consider the example above. Because the initial loan balance was $750,000 and the property value was$1 million, your initial loan to value ratio was 75%. What would be your loan to value ratio (a) at the end of 3rd year when the property value has dropped by 30%, and (b) at the end of 10th year when property value is $1.1 million Remember that a fixed-rate mortgage is an annuity so the outstanding balance on your mortgage at a point in time is the present value of your remaining mortgage payments. At the end of 3rd year, you have 324 (i.e. 27 years into 12 months per year) outstanding mortgage payments of$4,026 each. This translates to outstanding mortgage balance of $715,077 (i.e. PV(5%/12,324,-4026) using Excel). Your property has dropped to$700,000 recording a 30% drop in value. You loan to value ratio is hence 102.15% which shows that you owe more than the current worth of your property.

At the end of 10th year, your outstanding mortgage balance is $610,065 and your property value is$1.1 million resulting in a LTV of 55.46%.