# Don't Worry – Use a Sensitivity Analysis

Mar 28, 2011 by

Imagine that you are considering buying a car. On the one hand, prices might drop over time. On the other hand, interest rates might go up. Should you wait or should you buy? To answer this question, you need to consider three scenarios: the most likely case, the worst case, and the best case. Alternatively, you should look at how much the second variable would have to change to keep the cost of the purchase the same if there was an assortment of shifts in the first. Doing this is called performing a sensitivity analysis.

Let’s perform a sensitivity analysis on the car. Imagine that the interest rate is now 5% and the cost of the car is \$20,000. It is very likely that the interest rate will go up over time, given that things are now at historic lows. So, perhaps the best-case scenario a year from now would be that the interest rate would be 4.5%, the likely scenario would be that the interest rate will be 5.5%, and the worst-case scenario would be that the interest rate will be 7%.

Under the current scenario (\$20,000 at 5%), a five year loan will require monthly payments of \$377.42. Given the three potential interest rates (4.5%, 5.5%, and 7%), what would the car have to cost next year for the payments to remain the same? While this could obviously be calculated manually, if you download a mortgage calculator in Excel, you can simply tweak the car value until the monthly payment is the same in order to determine this number. If the interest rate went down to 4.5%, you would be better off waiting a year unless the price went up to beyond \$20,275. If the interest rate went up to 5.5%, you would only be better off if the price went below \$19,750. If the interest rate went to 7%, the price would have to dip below \$19,075 for you to be better off.

What should you do? It depends on which combination of scenarios you think is most likely. Personally, I believe that interest rates will go up over the next year as they are at historic lows. I do not think that prices are likely to drop, as they may increase in nominal terms due to inflation. Also, prices have dropped substantially over the last three years, and there may not be much margin for further reductions. If the cost of a loan goes up 2% per year over the next year, I would have been much better off getting the loan this year, so long as the price of the car in question does not drop by more than \$925; about 5%.