 Mortgages Analyzed Blended Rate

# What is Blended Rate? Blended Rate is the weighted average interest rate of all the loans against a real estate. In other words, it is the composite interest cost of all the loans against a real estate. It is used when you have different loans on a property at different rates and you want to calculate a composite rate that represents the total interest cost on the property.

It is also known as Weighted Average Cost of Loan or Weighted Average Interest Rate.

### Example

Assume you have a first lien loan of \$75,000 at 5% and a second lien loan of \$25,000 at 10%. The blended rate in this case is 6.25%, which represents the total interest cost of all your loans on your property. To illustrate further, annually you are paying \$3,750 interest on your first loan and \$2,500 interest for your second loan. The total interest expense is \$6,250. This is the same as saying that you are paying 6.25% on your total loan amount of \$100,000.

## Properties of Blended Rate

1. Being a weighted average, loans having large loan amounts will contribute more to the Blended Rate.
2. If all the loans are of equal size then the Blended rate would equal the simple average of the interest rates.
Source :www.MortgagesAnalyzed.com

# Use of Blended Rate

Blended rate can help answer two types of questions:

1. Calculating Overall Cost: It calculates the total interest cost on the property. It helps answer a question such as, if you have one loan at 6% and another loan at 8%, then what interest rate are you paying by considering all loans together?
2. Loan Comparison: It helps in comparing different loan scenarios to determine which one has the lowest cost. For example, compare the option of taking a single loan of \$100,000 at 6%, to another alternate where you obtain two loans with the first lien of \$80,000 at 5% and a second lien of \$20,000 at 8%. Which loan scenario is cheaper? This answer can be found by calculating the blended rate for the second scenario, which comes to 5.60%. Therefore, it will be cheaper to take the two loans than a single loan.
Source :www.MortgagesAnalyzed.com

# How to Calculate Blended Rate?

## Method 1: Interest Expense Method

Blended rate is calculated by dividing the total interest expense of all the loans by the total loan amount. In other words, it is calculated by taking weighted average of the interest rates where the relative loan sizes act as weights. The formula used for calculation is below.

rb =
r1P1+ r2P2+ r3P3+ ...+ rkPk P1+ P2+ P3+ ...+ Pk
Source :www.MortgagesAnalyzed.com

Rewritten as

rb =
Σ rk × Pk Σ Pk
Source :www.MortgagesAnalyzed.com

Where,

 Rb = blended rate rk = interest rate for loan k Pk = Principal for loan k n = number of loans

### Using the Formula for Two Loan Scenario

Blended Rate =
(1st Loan Interest Rate × 1st Loan Amt) + (2nd Loan Interest Rate × 2nd Loan Amt) Sum of all loan amounts for the property
Source :www.MortgagesAnalyzed.com

## Method 2: LTV Method

This method is used when the loan amounts are not available, but the Loan-To-Value (LTV) is known. The Blended Rate is calculated using the formula below.

rb =
r1LT1+ r2LT2+ r3LT3+ ...+ rkLTk LTV1+ LTV2+ LTV3+ ...+ LTVk
Source :www.MortgagesAnalyzed.com

Or

rb =
r1LT1+ r2LT2+ r3LT3+ ...+ rkLTk CLTV

Rewritten as

rb =
Σ rk × LTVk Σ LTVk
Source :www.MortgagesAnalyzed.com

Where,

 Rb = blended rate rk = interest rate for loan k LTVk = LTV for loan k CLTV = Combined Loan-to-Value (CLTV), which is the sum of LTV of all loans n = number of loans

### Using the Formula for Two Loan Scenario

Blended Rate =
(1st Loan Interest Rate × 1st LTV) + (2nd Loan Interest Rate × 2nd LTV) Sum of all LTV’s for the property

Since sum of all LTV’s for the property is same as the Combined Loan-to-Value (CLTV),

Blended Rate =
(1st Loan Interest Rate × 1st LTV) + (2nd Loan Interest Rate × 2nd LTV) CLTV
Source :www.MortgagesAnalyzed.com

### A Word of Caution When Using LTV Method

The LTV method assumes that the compounding terms (compounding period) same for all loans. For example, you cannot use interest rate in the formula for LTV Method if one loan is compounded daily and another is compounded semi-annually. In such cases where the compounding terms are different you need to do use either of the following to calculate Blended Rate.

1. Calculate the Effective Interest Rate (EIR) for each loan and use the EIR, instead of interest rates.
2. Try finding out the loan amounts and then using the Interest Expense Method.
Source :www.MortgagesAnalyzed.com

# Examples

## Example 1: Two Loan Scenario

Assume that Amit has a first lien loan of \$75,000 at 5% and a second lien loan of \$25,000 at 10%.

Where,

 P1 = \$75,000 P2 = \$25,000 r1 = 5% r2 = 10%
Blended Rate =
[ (75,000 × 5%) + (25,000 × 10%) ] (75,000 + 25,000)
= 6.25%
Source :www.MortgagesAnalyzed.com

## Example 2: Three Loan Scenario

Assume that Amit has a first lien loan of \$75,000 at 5%, a second lien loan of \$25,000 at 10%, and a third lien of \$25,000 at 12%.

Where,

 P1 = \$75,000 P2 = \$25,000 P3 = \$25,000 r1 = 5% r2 = 10% r3 = 12%
Blended Rate =
[ (75,000 × 5%) + (25,000 × 10%) + (25,0000 × 12%) ] (75,000 + 25,000 + 25,000)
= 7.40%
Source :www.MortgagesAnalyzed.com

## Example 3: Comparing Different Loan Scenarios

Assume that Amit has two choices for taking a loan - a single loan of 6% for \$100,000 or two into loans comprising of a first lien of \$80,000 loan at 6% and a second lien of \$20,000 at 8%. Which option is better?

The interest cost for first option is 6.00%

The interest cost for second option is the blended rate of 6.40%

Where,

 P1 = \$80,000 P2 = \$20,000 r1 = 6% r2 = 8%
Blended Rate for second option =
[ (80,000 × 6%) + (20,000 × 8%) ] (80,000 + 20,000)
= 6.40%

In this case the interest rate for the second option is higher than the first option. Amit would be better off taking the single loan.

Source :www.MortgagesAnalyzed.com

## Example 4: Evaluating Refinance Options

Assume that Amit wants to refinance his existing loan of \$100,000 at 6%. He is offered an option of taking a first lien fixed mortgage for \$80,000 at 5.5% and a second lien of \$20,000 at 8%. Should he refinance?

The interest cost for first option is 6.00%

The interest cost for second option is the blended rate of 6.00%

Where,

 P1 = \$80,000 P2 = \$20,000 r1 = 5.5% r2 = 8.0%
Blended Rate for second option =
[ (80,000 × 5.5%) + (20,000 × 8%) ] (80,000 + 20,000)
= 6.00%

In this case the interest rate for both options is the same. There would be no reason for Amit to refinance.

Source :www.MortgagesAnalyzed.com

## Example 5: Using LTV Method for Two Loan Scenario

Assume that Amit has a first lien loan with LTV 75% at 5% interest rate and a second lien with LTV 25% at 10% interest rate.

Where,

 LTV1 = 75% LTV2 = 25% CLTV = 100% r1 = 5.0% r1 = 10.0%
Blended Rate =
[ (75% × 5%) + (25% × 10%) ] (75% + 25%)
= 6.25%
Source :www.MortgagesAnalyzed.com

## Example 6: Using LTV Method for Three Loan Scenario

Assume that Amit has a first lien loan with \$60% LTV at 5% interest rate, a second lien loan with 20% LTV at 10% interest rate, and a third lien with 20% LTV at 12% interest rate.

Where,

 LTV1 = 60% LTV2 = 20% LTV3 = 20% r1 = 5.0% r2 = 10.0% r3 = 12.0%
Blended Rate for second option =
[ (60% × 5%) + (20% × 10%) + (20% × 12%) ] (60% + 20% + 20%)
= 7.40%
Source :www.MortgagesAnalyzed.com

## Example 7: Using LTV Method for Two Loan Scenario

Assume that Amit had a first lien loan with LTV 80% at 5% interest rate and a second lien with LTV 10% at 8% interest rate.

Where,

 LTV1 = 80% LTV2 = 10% CLTV3 = 90% r1 = 5.0% r2 = 8.0%
Blended Rate =
[ (80% × 5%) + (10% × 8%) ] (80% + 10%)
= 5.33%
Source :www.MortgagesAnalyzed.com

## Example 8: Using LTV Method for Comparing Different Loan Scenarios

Assume that Amit want to purchase a home that is valued at \$125,000 and he needs a loan for \$90,000. Milli, the loan agent, offers Amit two options - a single loan of 6% for \$90,000, or two loans comprising of a first lien of \$75,000 loan at 6% and a second lien of \$15,000 at 9%. Which option is better?

The interest cost for first option is 6.00%

The interest cost for second option is the blended rate of 6.50%

Where,

 P1 = \$75,000 P2 = \$15,000 LTV1 = 75,000/90,000 = 60% LTV2 = 15,000/90,000 = 12% CLTV = 72% r1 = 6.0% r2 = 9.0%
Blended Rate (LTV Method) =
[ (60% × 6%) + (12% × 9%) ] (60% + 12%)
= 6.50%
Blended Rate (Interest Expense Method) =
[ (75,000 × 6%) + (15,000 × 9%) ] (75,000 + 15,000)
= 6.50%

In this case the interest rate for the second option is higher than the first option. Amit would be better off taking the single loan.

Source :www.MortgagesAnalyzed.com

# Calculators

Updated: Jul 22, 2013

Blended Rate is used when you have different loans on a property at different rates
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