LOAN Procedure
Example 22.1 Discount Points for Lower Interest Rates
(View the complete code for this example.)
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;
Figure 10 shows the loan comparison reports as of January 1996 (48th period), July 1996 (54th period), and January 1997 (60th period).
Figure 10: Loan Comparison Reports for Discount Point Breakeven
| 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.