## Discounting Tutorial Continued

Mortgages and loans are bought or sold at discounts or premiums. A mortgage that is Completely Discounted is discounted to the full amortization period. A Term Discounted mortgage is discounted only to the end of the term which is less than the amortization period. An IRD Discount is just another way of looking at an IRD calculation, which is the “penalty” paid to a lender for a premature exit from a mortgage before the term expires. The Total Cost of Borrowing (TCOB) also known as APR in the USA is a variation of a discount calculation. When your credit card company offers you a 9% interest rate but charges a yearly fee of \$50 you are actually paying a Credit Card Premium over and above the 9% rate. The Discounting program is a very flexible tool that allows what appears to be many different types of calulations to be performed quickly.

## Complete Discount

A \$100,000 mortgage or loan at 8.25% rate amortized for 30 years to a lender is just a cash flow of 360 payments of \$751.267 per month. If the the lender wants to sell that mortgage (or sell that 30 year cash flow) to an investor who will accept a 7% return, then the investor pays a premium of \$10,567.33 (C) for a total amount of \$110,567.33 (B) to buy the mortgage.

On the other hand if that same investor wanted a return of 10.1% on that same cash flow he would pay \$84,891.74 (B) for the mortgage a discount of \$15,108.26.

## Cost Of Borrowing

Effective Interest Rates:

The Total Cost of Borrowing, TCOB, is nothing more than a fair method for showing borrowers the impact of the total fees charged by a Lender or Mortgage Broker on the quoted annual interest rate. The total fees are typically up front moneys paid by the borrower to the Lender or Mortgage Broker or both.

First of all, nominal rates are always associated with an effective rate because of the compounding. Thus a 12% nominal rate with semi-annual compounding has an effective rate of 12.36%. An 11.7106% nominal rate with monthly compounding has an effective rate of 12.36%. Isn’t that a coincidence! You can now see the advantage of quoting an effective interest rate, EIR, because there is no need to be concerned with the method of compounding. A lender quoting you an EIR of 12.36% on a loan of \$1000 for one year actually earns \$123.60 in interest on the initial \$1000 loan for a total return of \$1,123.60 at the end of the year.

The intent of the TCOB legislation in Canada, is to ensure that the lender, or mortgage broker, will quote you the effective interest rate, EIR, of the new rate after all the costs (fees and points ect) are factored into the loan.

In the USA the TCOB is often called the APR, Annual Percentage Rate. It matters not what you call it as long as you understand the mathematics.

TCOB for Term:

A Lender hands you a cheque for your \$45,000 mortgage and you hand your mortgage broker a cheque for \$3,500 to cover his/her total fee. The monthly payments for a loan of \$45,000 are \$464.35 based on an amortization period of 25 years, using semi-annual compounding. In effect you are receiving \$41,500 but will be making monthly payments of 464.35 as if you borrowed the \$45,000. The impact of the \$3500 total fee is going to be spread over 60 months. This is reality if you intend on selling this home in 60 months.

The Total Cost of Borrowing (TCOB) is 14.84% if the \$3500 fee is spread over 60 months as compared to the full amortization period. The difference between \$3,500 and \$3,500.24 is due to the fact that the DISCOUNTING module uses an iterative approach to calculating and in order to get the two numbers to agree exactly the calculation time would be extremely slow even with current Pentiums.

To save time if you are performing many calculations you can click on the “High Speed, Standard Precision” selection rather than the “Standard Speed, High Precision” selection. The difference of \$4.27 in the calculated premium (B) is not significant as the EIR/TCOB is still 14.84% at two decimal places.

TCOB for Amortization Period:

TCOB spread over the entire Amortization Period

A Lender hands you a cheque for your \$45,000 mortgage and you hand your mortgage broker a cheque for \$3,500 to cover his/her total fee. The monthly payments for a loan of \$45,000 are \$464.35 based on an amortization period of 25 years, using semi-annual compounding. In effect you are receiving \$41,500 but will be making monthly payments of 464.35 as if you borrowed the \$45,000. The term is 25 years the same as the amortization period. There are still some types of mortgages like these around. The impact of the \$3500 total fee is going to be spread over 300 months so change the Discount term to 300 months. The TCOB is 13.67%

When a credit card company states a nominal interest rate for your card and then charges you a yearly fee, the effective interest rate that you are paying is HIGHER. Time and money are related in an exact relationship. Not all card companies follow the same methods of interest calculation but a quick and simple method is as follows;

If you borrowed \$1000 for a year, but paid the lender a fee of \$50 upfront (in advance) for the privilege of doing business in the upcoming year, and the lender quoted you a nominal rate of 12%, YOU would actually be paying a nominal interest rate of 21.86%, which is an effective rate of 24.19% (the TCOB% or the Truth in Lending Rate is 24.19%). The real interest rate you are paying in effect has doubled. That is why financial planners usually tell people to pay off the plastic cards ASAP!

## IRD Discount

Two years ago, Bob and Mary borrowed \$152,135 amortized for 27 years, and signed a five year term at an interest rate of 11%. Now, three year term interest rates are 7%. Bob and Mary would like to pay 7% interest for the remaining 3 years of monthly payments, instead of 11%. The Lender asked them for a \$15,440 interest rate differential (IRD) payment along with their 24th monthly payment if they wanted the interest rate lowered to 7% for the remaining 3 years. How can Bob and Mary make an informed decision about paying the \$15,440?

This is the same example as the IRD example in the Mortgage Article section. The only difference is the way one thinks about discounting. Instead of thinking of the IRD amount of \$15,440.04 as a “penalty” just think of it as the amount of money required to give to the lender so that the lender make a return of 7% instead of 11% over the next 36 months.

## Term Discount

A \$100,000 mortgage or loan at 8.25% rate amortized for 30 years to a lender is just a cash flow of 360 payments of \$751.267 per month. If the the lender wants to sell that mortgage to an investor who will accept a 7% return, for just 36 months, then the investor pays a premium of \$3,334.35 (C) or a total amount of \$103,334.35 (B) for the 36 month cash flow.

If that same investor wanted a 12% return over the 36 months he would get a discount of \$9,302.16 (C) and pay only \$90,697.84 (B) for the 36 month cash flow.