You may have noticed that the sharks and dragons on Dragon’s Den or Shark Tank frequently try to get their money back early. The reason is simple: It’s all about ice cream. It’s more impressive, though, to talk about present value, discounting, and the time value of money.
Imagine you lent a friend $10 for a month. After two weeks, though, your friend comes to you and says. “How about I give you $5 right now and we forget about that $10?” What your friend is asking you to do is give a discount on the loan: less money now instead of more money later. You’ll probably say no to this offer: You’d rather have the full $10 in two weeks rather than $5 right now. On the other hand, if your friend offered you $9 right now, you might take that offer.
The entrepreneurs on the reality TV show “Shark Tank” (or “Dragon’s Den”, as the show is called outside of the United States) sometimes put themselves in the same position. The shark/dragon will make an offer that gets the dragon/shark’s money back early (usually through a royalty on products sold). Yet, if the company is worth investing in, you’d think that the shark/dragon would want to leave their money in the company to help it grow faster. The reason the sharks/dragons want their money back earlier is because they are just like you: They’d rather get all their money back now rather than get more money later.
Everyone understand this: offered the choice between ice cream right now and ice cream tomorrow, we’d all rather have ice cream right now. Ice cream right now is, apparently, better than ice cream some time in the future. An economist would say that ice cream has a “time value” – the value of ice cream changes over time.
The reason ice cream has a time value is that we recognize that much can go wrong if we wait until tomorrow to have ice cream – someone else might eat the ice cream, the refrigerator might break down and the ice cream melt, we might not be around tomorrow when the ice cream is served. In other words we recognize that there’s an element of risk involved in waiting. If we have our ice cream now, the risk is eliminated. We might even be willing to take a discount: take a little less ice cream right now rather than slight more ice cream tomorrow.
Money is like ice cream because money also has a time value: You’d rather have $9 now than $10 in two weeks.
Of course, we can offset the risk by offering a better reward. I might be offered “ice cream” today or “ice cream and apple pie” tomorrow. With that offer, I might wait until tomorrow to have my ice cream. Similarly, the friend who owes you $10 in a month might offer you $11 if you were willing to wait a year to get your money back. In both cases, however, we’re still talking about a discount: less money now in return for more money in a year.
But the reward has to be “good enough.” If, for example, you don’t like apple pie then the “apple pie and ice cream tomorrow” offer isn’t going to tempt you to wait. I suspect that, with a friend who owes you $10, you wouldn’t accept an offer of $11 to wait a year. But you might wait a year if your friend offered to pay you $20 in a year.
But if there’s one offer that you don’t like ($11) and one offer you do like ($20), we can assume that there’s some point in between where, as economists say, you would be “indifferent.” For example, you might not care if you got $10 right now or $14 in a year: you might find both offers equally attractive. Your friend is keenly interested in your “indifference point” because, after all, if you’ll settle for $14 now, that’s a lot less than having to pay you $20 in a year.
But because the dragons/sharks are talking about money, they also consider what else they can do with their money. If, for example, the dragons/sharks get their money back early then they can take that money and invest it in something else. So, really, if someone is going to make the sharks/dragons wait, they need to offer the sharks/dragons enough “more” to be a better offer than anything else the sharks/dragons could do with their money in that year (that “something else they could do with their money” is called “opportunity cost”). To put it another way, if the sharks/dragons can get their money back right now, they can buy a dark chocolate Dove bar tomorrow. For me, at any rate, getting a dark chocolate Dove bar tomorrow is a powerful incentive.
Businesses care about all of this very much because it lets them reduce different amounts of money in the future into a single number: Is that money in the future, worth the same to me as how much money right now…?
For example, if your company can spend $100 now and get $150 a year from now, is your company indifferent to this opportunity? If $150 in a year is worth more than $100 right now then, no, your company isn’t indifferent. But let’s make it more complicated – how does your company feel about spending $100 to get $175 in three years? And more complicated yet – is that $150 in a year a better or worse opportunity than the $175 in three years?
So, the question is whether there’s some way to compare these numbers and measure the business’s indifference?
There is, in fact: some interest rate. Investors assume that some interest rate wraps up risk, opportunity cost, and anything else that investors worry about (inflation, for example). If that interest rate is, for example, 15% then an investor is indifferent between having $10 right now and $10 + 15% in a year. The formula for that is straightforward: amount multiplied by 1 + interest rate. In this case, that’s $10 * 1.15 or $11.50. So, if your interest rate is 15% and your friend offers you $11.50 in a year from now or $10 right now, then you’d say “Sure, I don’t care. It’s the same thing to me.”
Of course, this works backwards, also. If someone offered you $11.50 in a year from now, you could say “How about giving me $10 right now? It’s the same thing to me.” The formula to calculate that is just the flip-side of the previous formula: amount divided by 1 + interest rate. In this case, that’s $11.50/1.15 or $10.
That’s easy for one year. If you want to calculate your indifference value over multiple years then you have to raise the interest rate to the power of years involved. If your friend wanted to pay you back in two years, the formula is $10 * 1.152; for three years, $10 * 1.153. This is true if you’re working backwards, also. If your friend offers you $13.25 in two years then your formula is $13.25/1.152 which (it turns out) is $10. To put it another way, if your interest rate is 15% then you are indifferent between $10 right now and $13.25 in two years. Discounting like this gives you what business people call the “present value” of some “future value”: What is $150 in the future worth right now, in the present? If you subtract out the original $10 you gave up, the result is called the “net” present value.
So, the answer to my business’s problem is to work the $150 back one year and the $175 back three years. It turns out that, at 15%, the $150 in one year is the same as $130 right now ($150/1.15); the $175 in three years is the same as $115 right now ($175/1.153). Since either investment is better than the $100 the company has right now, the company should spend the $100. But, since the $150 investment is the same as having $130 right now while three year investment is only the same as having $115 right now, the company should take the one year investment. Comparing $100 to $115 to $130 of “present value” is a lot easier than comparing different amounts of money at different times in the future.
A more complicated question is whether that single $150 payoff in one year is better or worse than an actual cash flow: What if your $100 investment would give you $125 in one year, $150 in two years, and $175 in three years? For that you need a you need a discounted cash flow: roll each future value back to the present and then add them up.
Of course, I’m ignoring the interesting question of “Where does that interest rate come from?” That requires more room than I have here but we talk about that in Learning Tree’s Finance and Accounting for Non-Financial Managers course. Be warned, though – there may not be any ice cream.