The Discount Point Decision
Suppose that you are offered two loan alternatives. In the first, you pay no discount points and the interest rate is 12%. In the second, you pay 2 discount points but receive a lower interest rate of 11.5%. Which alternative do you choose? To answer this question you must first compute the effective annual rate without discount points. Since the loan is compounded monthly, you pay 1% per month. Because of the compounding, the effective annual rate is greater than the simple annual rate. To compute the effective rate, raise 1 plus the monthly rate to the 12th power and subtract 1. The effective annual rate on the no point loan is thus Effective annual rate =(1.01)12 1 = 0.1268 12.68% Because of monthly compounding, a 12% annual percentage rate has an effective annual rate of 12.68%. On a 30 year, $100,000 mortgage loan, your payment will be $1,028.61 as found on a financial calculator. Now compute the effective annual rate if you pay 2 discount points. Let’s assume that the amount of the loan is still $100,000. If you pay 2 points, instead of receiving $100,000, you will receive only $98,000 ($100,000 – $2000). Your payment is computed on the $100,000, but at the lower interest rate. Using a financial calculator, we find that the monthly payment is $990.29 and your monthly rate is 0.9804%.1 The effective annual rate after compounding is Effective annual rate = (1.009804)12 1 = 0.1242 = 12.42% As a result of paying the 2 discount points, the effective annual rate has dropped from 12.68% to 12.42%. On the surface, it would seem like a good idea to pay the points. The problem is that these calculations were made assuming the loan would be held for the life of the loan, 30 years. What happens if you sell the house before the loan matures? If the loan is paid off early, the borrower will benefit from the lower interest rate for a shorter length of time, and the discount points are spread over a shorter period of time. The result of these two factors is that the effective interest rate rises the shorter the time the loan is held before being paid. This relationship is demonstrated in Table 14.2. If the 2 point loan is held for 15 years, the effective rate is 12.45%. At 10 years, the effective rate is up to 12.52%. Even at 6 years, when the effective rate is 12.65%, paying the discount points has saved the borrower money. However, if the loan is paid off at 5 years, the effective rate is 12.73%, which is higher than the 12.68% effective rate if no points were paid.2