## Wednesday, March 24, 2010

### The Time Value of Money: Making Better Purchasing Decisions

PERSONAL FINANCE 101

Say you’re looking for a brand new netbook for your blogwork. You already have a specific brand and model in mind, and you start to shop around for the best deal you can find. You come across a store which offers the netbook that you want at a retail price of 18,000 pesos and a “0% interest” credit card offer of 1,500 pesos per month for 12 months. Being some sort of a math whiz back in the day, you make a few, quick mental computations and verify that, indeed, 1,500 pesos per month for 12 months totals 18,000 and the offer is a gee-nyu-wine 0% deal. But before you whip out your plastic, you suddenly recall something you recently read in the country’s fastest growing personal finance blog and ask the sales clerk what the cash price of the netbook is (that is, how much you can buy it for if you paid in full with cash and not with your credit card). Without batting an eyelash, the clerk tells you that the cash price is 16,364 pesos. Assuming that you actually have 16,364 to spend, you are now faced with a payment quandary: should you buy the netbook for 16,364 pesos cash up front, or pay for it with 12 monthly installments of 1,500 each? If we ignore the time value of money, then the “less expensive” cash upfront choice is the clear winner. But we know that the time value of money is real, and that paying in installments has a cost (definitely not “0%” as the offer asserts). The question is, what is that cost, and is paying that cost worth it? At first glance, it seems that the cost is simply 10%, which is difference between 16,364 and 18,000 divided by 16,364, but because the installments are made monthly, it is not as simple as that.

Now unless you brought your trusty financial calculator with you, you will need Excel to compute for the implied cost (in percentage terms per month). The internal rate of return(IRR) function of Excel can help you find the implied interest rate between the two financing options. In the image below, we see that since we are looking at the cost of choosing the installment option, the 1,500 installments should be treated as cash outflows or negative cash flows; the 16,364 in month 0 is positive because by choosing the installment option we are not paying 16,364 and the amount should be treated as a cash inflow or positive cash flow.

Using Excel's IRR function gives us an IRR of 1.50% per month; this means that choosing the installment option will cost us 1.50% per month, or that, essentially, we will be borrowing at an interest rate 1.50% per month or 18% per year (in Annual Percentage Rate terms; how this animal differs from others in the interest rate jungle will be the topic of another post). So does this mean we should choose the installment option over cash up front, or is it the other way around? Well, it depends on borrowing interest rates (or investment rates of return) that are available to you. For example, if you can borrow from someone at 12% per year, then paying for the netbook in installments at 18% per year would cost you more; it means you’ll be better off borrowing 16,364 at 12% and buying the item in cash. It also follows that if have 16,364 now and you can only earn 12% per year on any investment, the better option would be to use your money to buy the netbook now than invest the amount. Following the same line of thinking, if your only available debt choices have interest rates that are greater than 1.5% per month (like credit card debt), or that you can invest money at a rate of return that’s higher than 18% per year, you should invest whatever money you have now and pay for the netbook in installments.

With this example, we see how we can use the time value of money to make better purchasing decisions. Borrowing at a lower rate, like 12%, and choosing the cash up front payment option over the 18% installment option, you’ll be able to save 6% in one year or around 982 pesos on a 16,364 peso purchase. Now that may not seem much, but if we scale our purchase to, say, a 50-inch LED TV which costs 200,000 pesos or something even more expensive, the impact of making the right decision becomes significantly more substantial.

The time value of money concept is a powerful tool that we should always use in making important purchasing decisions. Next week, we’ll take a look at how we can use it to choose among a number of available investment alternatives.