You will be able to use the PV function to price a future payment as a sum held now.
You are selling your old motorcycle to your uncle. He can pay you S$5,000 now, or S$1,100 at the end of each year for five years. The instalments add up to S$5,500, so they look like the better deal. But S$1,100 five years from now is not the same as S$1,100 today, for the reasons in lesson 6.1, A dollar today is worth more than a dollar in five years. To compare the two offers properly, you need to know what each future payment is worth today.
That is present value, and it is the most useful single calculation in this module, because almost every money choice involves comparing something now with something later. Every rate in this lesson is an example.
Present value is what a future sum is worth today, at a chosen discount rate. It is future value in reverse. In lesson 6.2, Future value: what a sum or monthly saving grows to, you multiplied a sum by (1 plus the rate) to the power of the years. To go the other way, you divide the future sum by the same amount.
Take S$10,000 that you will receive in 10 years, discounted at 3% a year. 1.03 to the power of 10 is about 1.3439. S$10,000 divided by 1.3439 is about S$7,441.
You can check this from the other direction. Lesson 6.2 showed that S$10,000 invested at 3% for 10 years grows to about S$13,439. By the same arithmetic, S$7,441 invested at 3% for 10 years grows to about S$10,000. So if you could earn 3% elsewhere, being promised S$10,000 in ten years is worth the same to you as holding about S$7,441 now. Paying more than that today for the promise would be paying too much.
Excel and Google Sheets both have PV, which takes the same arguments as FV:
PV(rate per period, number of periods, payment per period, future value)
For the S$10,000 in 10 years, type =PV(3%, 10, 0, 10000). The answer comes out as minus S$7,440.94. The sign follows the rule from lesson 6.2: you receive S$10,000 later, which is positive, so the sum you would have to put in today is negative. If you would rather see a positive answer, enter the future value as -10000. Either way, the size of the number is what matters.
Run the same S$10,000 at a discount rate of 5%: =PV(5%, 10, 0, -10000) gives S$6,139.13. At 1% it gives S$9,052.87.
So the higher the discount rate, the less a future sum is worth today. That follows from what the discount rate stands for. A higher rate means you could earn more elsewhere, or that you trust the promise less, and either way, waiting costs you more. A promise of money far in the future, from someone you are not sure of, is worth much less than its face value.
It also means the choice of rate can decide the answer, as it did with the schoolmate's loan in lesson 6.1. When the answer flips between two reasonable rates, the decision is close, and other things such as when you need the cash should settle it.
PV also handles a series of equal payments, which is where it is most useful. Put the yearly amount in the payment argument.
Back to the motorcycle. At a discount rate of 3%, type =PV(3%, 5, -1100). The answer is S$5,037.68. That is what five yearly payments of S$1,100, starting a year from now, are worth today. It is slightly more than S$5,000, so at 3% the instalments come out ahead, by about S$38.
At 5%, =PV(5%, 5, -1100) gives S$4,762.42. Now the instalments are worth less than the S$5,000 on offer, by about S$238, and taking the cash now is the better deal.
Notice what PV has done. It has turned a stream of five payments into one number that sits on the same footing as the lump sum: money in your hand today. The S$5,500 total you started with was never the right comparison, because it adds dollars from five different years as though they were the same.
PV assumes each payment arrives at the end of its year. If the first instalment came today, you would add a fifth argument of 1, and the stream would be worth a little more.
The choice of rate is where your judgement goes in. Use what you could earn on a safe option for money you would hold that long, which you can check on product pages or the MAS website, and add something if you doubt the payments will arrive in full. For your own comparisons, run every lump sum and stream at two rates, a low one and a higher one, and see whether the answer holds. A choice between a larger sum now and a series of payments later is the classic test, and it is worth trying with bigger numbers and a longer stream than the motorcycle.
Use PV to compare taking S$20,000 today against S$2,500 a year for 10 years, at discount rates of 2% and 5%.
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