Economists have a way of making things sound dull.
If I tell you that this tutorial is about the time value of money, it’s unlikely to set your pulse racing. If I mention that we’ll cover present value, future value and discounted cash flow analysis, I can just see your itchy trigger finger hovering over the mouse button, ready to click away to something more interesting.
That’s a shame, because the time value of money is a crucial business concept, and understanding it can help you in so many ways. CEOs, investors and entrepreneurs use it all the time to help them decide which projects to focus on, value companies, and do a cost-benefit analysis of potential investments.
So in this tutorial, we’ll take the dusty, old economic concept and shake it loose, making the time value of money into something you can use in your daily work life. We’ll walk you through what the time value of money is, how you can calculate it, and show practical examples of how you can use it to make better business decisions.
1. What is the Time Value of Money?
If I offer you the choice of $1,000 right now or $1,000 five years from now, it’s a no-brainer. You’ll probably grab the $1,000 out of my hands before I can finish the sentence.
But what if I change the equation, and offer you $1,250 five years from now? Which would you take? Now it gets a little more complicated.
Most of us would try to weigh it up based on gut instinct, but there’s actually a formula to give a more accurate answer. As you’ve probably guessed, it’s the time value of money (TVM) formula.
Having a dollar today is worth more than the promise of a dollar in the future. Time value of money calculations simply measure exactly what that difference in value is, and help you decide between different investment options.
Our example is purely hypothetical, but similar situations come up all the time in the day-to-day lives of people in business.
If you sell goods on credit, how much are you losing for every month that a customer fails to pay? If you have two potential investments with different expected payoffs over different time periods, how do you decide which one is better? If you need to save up $20,000 to start your business, how long will it take you to get there?
We’ll look at some of these scenarios as we go through the tutorial, but first let’s see whether you’d be better off taking the $1,000 now, or the $1,250 five years from now.
2. How to Calculate Future Value
To see which option is better, we need to see what happens if we take the $1,000 and invest it for five years. Do we end up with more than $1,250, or less?
Say we invested it in a bond paying 5% interest. In one year, we’d earn $50 interest (5% of $1,000), so our $1,000 would have grown to $1,050.
We reinvest that interest, so the next year we get a little more: $52.50 (5% of ($1,050). Each year, the interest keeps increasing or “compounding.” Here’s how it looks:
At the end of year 5, then, we have $1,276. So if we know we can get that 5% return, we’d be better off taking the $1,000 now, rather than the $1,250 later.
The economists would say that we’ve just used the time value of money to calculate the future value of a present lump sum. As you can see, it’s not too complicated.
We can make it even easier, though. After all, you don’t want to draw up a table every time you make a decision.
The easiest way is to use a free online calculator. For PV (present value) you’d enter -1,000. It’s negative because we’re talking about paying out that $1,000 and seeing how much we get back in five years. The Rate is 5%, and there are 5 Periods. Leave PMT blank — that’s for different types of calculation, which we’ll cover in the next section.
Click FV to find the future value, and it will give you the answer: $1,276.28. The same result as before, but using the calculator was much easier than drawing up a table and calculating interest payments.
If you’re comfortable using formulas in Microsoft Excel, you can also use these to calculate the time value of money, or you can use a financial calculator (the physical kind). But plugging numbers into a website is as simple as it gets.
3. The Value of a Regular Income Stream
So far, we’ve looked at lump sums, comparing an amount now with an amount in the future. But often in business you need to look at regular income streams.
For example, say you have the chance to invest in your friend’s new business venture. In return for your cash, she promises to pay you $10,000 a year out of her profits for the next ten years. How much is it worth paying for this investment?
The answer is not simply $10,000 x 10, because you have to take into account the deteriorating value of money over time. There’s a cost to tying your money up for ten years, and we need to estimate that.
So we return to our online calculator, and plug in new numbers. This time we leave PV blank, because that’s the number we’re trying to find — the present value of that future income. We also leave FV blank, because there’s no future lump sum payment. We’re looking at a regular income stream, so we use the PMT (payments) option.
We expect to receive $10,000 a year for 10 years, so enter 10000 for PMT, and 10 for the Period. For the Rate, enter what you estimate you could make over those ten years by investing your money elsewhere. Let’s be conservative this time, and enter 3%.
Click PV to calculate the present value.
As you can see, the answer turns out to be about $85,302. It’s expressed as a negative number, because it’s the amount of money you’d pay out in order to receive that $10,000 a year.
So if your friend asks for around $85,000 up front, it’s a decent investment. If she asks for more, you may still do it out of friendship, but it wouldn’t be a good business decision.
Congratulations! You’ve just done a discounted cash flow analysis. It’s a method that’s popular in a wide variety of business situations. Real estate investors use it, for example, to estimate their profits on a deal. Wall Street analysts use it to value a company. The calculations get more complex in situations with more moving parts, but the principle is the same.
4. Changing the Variables
You may be thinking that these calculations are not realistic. After all, the one certain thing we can say about the future is that it’s always uncertain. Calculating “future value” to the nearest cent seems foolhardy.
It’s true that doing TVM calculations can sometimes create a false sense of certainty, giving mathematical legitimacy to what amount to guesses and assumptions.
But these calculations actually become most powerful when you recognize the limitations of your assumptions, and start changing them to see what happens.
If we thought we could invest our money elsewhere at 5%, for example, our friend’s promise of $10,000 a year for ten years is only worth $77,217.
If we’re more conservative, and think we could only get 1.5% a year, it’s worth $92,222.
As we change our assumptions, the time value of money changes dramatically, and so do our resulting decisions.
You can do a similar thing with any TVM calculation. Take the assumptions and play with them, changing the numbers in the online calculator and seeing what difference it makes to the outcome.
Now we’ve seen all the different elements of TVM calculations:
- Present Value (PV)
- Future Value (FV)
- Number of Periods
- Interest Rate
- Regular Payments (PMT)
Using our online calculator, we can now easily do different types of calculation, and change our assumptions to see how it affects our decisions.
Let’s see how this works by looking at another example. You want to start up a coffee shop in your local town, and have worked out that you need $10,000 to acquire the lease, purchase equipment, hire staff and cover your initial running costs. Right now you only have $2,000 in your bank account, but figure you can put aside $250 a month in your savings account, which is yielding 2% interest. How long will it take before you can open your business?
In this case, we know the PV ($2,000), the FV ($10,000), the interest rate (2%) and the PMT ($250). What we want to know is the number of months it will take to get to $10,000.
So we go to our online calculator and plug in the numbers.
As before, any money you’re investing needs to be entered as a negative, because in the eyes of the calculator it’s money you’re paying out to receive a future return. So it’s -2000 for PV, -250 for PMT, and a positive 10000 for FV. Then enter 2 for the interest Rate, choose Monthly from the dropdown menu, and click Periods to do the calculation.
The answer? It will take about 30 months — 2 ½ years — to save enough to open the coffee shop.
Now let’s change the assumptions, and see what happens.
If you could find an investment yielding 5%, for example, the extra interest would enable you to open a month earlier. If you can also bump your savings up to $400 a month, you could start your business a whole year earlier. That’s a pretty powerful incentive.
Other Practical Applications
Time value of money concepts can be applied in many different areas of business. Let’s say you run a furniture shop, for example, and are running into cash flow problems. Your corporate customers often take six months to pay for their purchases, meaning you have to dip into your overdraft to cover your costs while you’re waiting.
A quick time value of money calculation can show you a potential solution. If the bank charges you 15% interest on your overdraft, then plugging the numbers into the online calculator reveals that the present value of a $100 payment received six months from now is $92.82.
In other words, you’d be better off giving your customers a 5% discount if they pay upfront. That way, you’d only get $95 on every $100 sale, but having that $95 immediately is worth more than getting $100 six months from now.
You could also use the time value of money to decide whether it’s worth paying for equipment upfront or via a payment plan, to evaluate the merits of different products you’re developing, or in more or less any situation that involves comparing amounts of money paid and received at different times. The key is to figure out what amounts you know or can assume, fit them into the five categories we’ve looked at, and then solve for the unknown amount.
Students in business school often spend weeks on the time value of money. If you want to get deep into the theory, there’s plenty more scope. But at the simple, practical level, as we’ve seen, it’s not too complicated.
We’ve seen that you have five variables to play with: present value, future value, interest rate, payment amount, and number of periods. You now know what these variables are, and how to manipulate them so that if you know some, you can find the missing one.
Most importantly, you understand how these calculations are more than just abstract mathematical problems. You’ve seen some practical business applications, and now you’re ready to use the theory of the time value of money to help you make better decisions in real-life situations.
You can now calculate how long it would take to save up for starting a business, see the cost of selling on credit, and decide whether a potential investment is worthwhile. And in the unlikely event that someone comes along and offers you the choice between $1,000 now and $1,250 in the future, you now know which one to pick!