Use the PV function to work out what a future payment is worth as a sum in hand today.
You're selling your old motorcycle to your uncle. He offers either S$5,000 now or S$1,100 at the end of each year for five years (both are example figures), and you have to pick one.
The instalments add up to S$1,100 x 5 = S$5,500, so they look like the better deal. Adding them up is the wrong comparison, though, because it treats dollars from different years as if they were equal. A dollar you receive in the future is worth less than a dollar today, for the reasons set out in lesson 6.1, "A dollar today is worth more than a dollar in five years". To compare offers paid at different times, you convert each future payment to its value today. Present value is the most useful single calculation in the module, because almost every money choice compares something now with something later. Every rate used below is an example and is not a recommendation.
Present value is what a future sum is worth today at a chosen discount rate. The discount rate is the rate you use to convert future money into today's value. It reflects what you could earn elsewhere and how much you trust that the payment will come. Present value is future value in reverse. In lesson 6.2, "Future value: what a sum or monthly saving grows to", you grew a sum by multiplying it by (1 + rate) raised to the number of years. For present value, you divide the future sum by (1 + rate) raised to the number of years.
Say you're promised S$10,000 in 10 years and you discount it at 3% a year. Add the rate to 1 to get 1.03. Raise that to the power of 10, which gives about 1.3439. Divide S$10,000 by 1.3439 and you get about S$7,441.
You can check the answer by growing it forward at the same rate for the same number of years. Multiply it by (1 + rate) to the power of the years and you should get back the future sum. Lesson 6.2 showed that S$10,000 at 3% for 10 years grows to about S$13,439. In the same way, S$7,441 at 3% for 10 years grows to about S$10,000, the sum you started with. If you can earn the discount rate elsewhere, a promise of S$10,000 in 10 years is worth exactly its present value to you today. If you pay more than the present value for that promise, you're overpaying.
Excel and Google Sheets both have a PV function. It takes the same arguments as FV: =PV(rate per period, number of periods, payment per period, future value). For a single sum, set the payment to 0 and enter the future value. Typing =PV(3%, 10, 0, 10000) returns minus S$7,440.94.
The minus sign follows the same rule as in lesson 6.2. Money you receive later is positive, so the amount you would put in today comes out negative. If you want a positive answer, enter the future value or the payment as a negative number. Entering the future value as -10000 gives a positive result. Only the size of the result matters.
When you change the rate, the answer moves. =PV(5%, 10, 0, -10000) gives S$6,139.13. The same S$10,000 at 1% for 10 years is worth S$9,052.87. The higher the discount rate, the lower the present value of a future sum. A higher rate means either that you could earn more elsewhere or that you trust the promise less, and in both cases waiting costs you more. Money promised far in the future by someone you're unsure of is worth much less than its face value.
PV can also value a series of equal payments. Put the per-period amount in the payment argument and leave out the future value. The function turns the stream of payments into a single figure for its value today, which you can compare directly with a lump sum.
Your uncle's offer pays at the end of each year for five years, so the first instalment arrives one year from now. At 3%, =PV(3%, 5, -1100) gives S$5,037.68. That's about S$38 more than S$5,000, so at 3% the instalments win. At 5%, =PV(5%, 5, -1100) gives S$4,762.42. That's about S$238 less than S$5,000, so at 5% you're better off taking the S$5,000 now.
By default, PV assumes each payment arrives at the end of its period. If the first payment arrives today, at the start of the period, add a fifth argument of 1. The stream is then worth a little more.
The discount rate is where your judgement goes in. Start with what a safe option would earn over the same holding period, which you can check on product pages or the MAS website. If you doubt the payments will arrive in full, add something on top. The choice of rate can decide the answer. It did with the schoolmate's loan in lesson 6.1, and it does with the motorcycle, where the instalments come out ahead at 3% and the cash comes out ahead at 5%.
For that reason, run every comparison at two rates, one low and one higher. At each rate, work out the PV of the stream and compare it with the lump sum. Whichever has the higher value today is the better deal at that rate. If the answer holds at both rates, act on it. If it flips between two reasonable rates, as the motorcycle does, the decision is close. Other factors should then settle it, such as when you need the cash.
Choosing between a larger sum now and a series of payments later is the classic present value test. Set up your own comparison with bigger numbers and a longer stream than the motorcycle. Run the lump sum and the stream at a low rate and at a higher rate, and see whether the answer holds.
Use PV to compare S$20,000 today with S$2,500 a year for 10 years. Do it at a discount rate of 2% and again at 5%.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).