Example 17.1 Discount Points for Lower Interest Rates

This example illustrates the comparison of two $100,000 loans. The major difference between the two loans is that the nominal interest rate in the second loan is lower than the first with the added expense of paying discount points at the time of initialization.

Both alternatives are 30-year loans. The first loan is labeled “8.25% - no discount points” and the second one is labeled “8% - 1 discount point.”

Assume that the interest paid qualifies for a tax deduction and you are in the 33% tax bracket. Also, your minimum attractive rate of return (MARR) for an alternative investment is 4% (adjusted for tax rate).

You use the following statements to find the breakeven point in the life of the loan for your preference between the loans:

proc loan start=1992:1 nosummaryprint amount=100000 life=360;
   fixed rate=8.25 label='8.25% - no discount points';
   fixed rate=8 points=1000 label='8% - 1 discount point';
   compare at=(48 54 60) all taxrate=33 marr=4;
run;

Output 17.1.1 shows the loan comparison reports as of January 1996 (48th period), July 1996 (54th period), and January 1997 (60th period).

Output 17.1.1: Loan Comparison Reports for Discount Point Breakeven

The LOAN Procedure

Loan Comparison Report Analysis through JAN1996
Loan Label	Ending Outstanding	Present Worth of Cost	Payment	Interest Paid	True Rate
8.25% - no discount points	96388.09	105546.17	751.27	32449.05	5.67
8% - 1 discount point	96219.32	105604.05	733.76	31439.80	5.69

Note:

"8.25% - no discount points" is the best alternative based on present worth of cost analysis through JAN1996.

Loan Comparison Report Analysis through JUL1996
Loan Label	Ending Outstanding	Present Worth of Cost	Payment	Interest Paid	True Rate
8.25% - no discount points	95847.27	106164.97	751.27	36415.85	5.67
8% - 1 discount point	95656.22	106153.97	733.76	35279.26	5.67

Note:

"8% - 1 discount point" is the best alternative based on present worth of cost analysis through JUL1996.

Loan Comparison Report Analysis through JAN1997
Loan Label	Ending Outstanding	Present Worth of Cost	Payment	Interest Paid	True Rate
8.25% - no discount points	95283.74	106768.07	751.27	40359.94	5.67
8% - 1 discount point	95070.21	106689.80	733.76	39095.81	5.66

Note:

"8% - 1 discount point" is the best alternative based on present worth of cost analysis through JAN1997.

Notice that the breakeven point for present worth of cost and true rate both happen on July 1996. This indicates that if you intend to keep the loan for 4.5 years or more, it is better to pay the discount points for the lower rate. If your objective is to minimize the interest paid or the periodic payment, the “8% - 1 discount point” loan is the preferred choice.