A Simple Guide to Understanding Discount Rate

If you read my earlier column (A Simple Guide to Understanding the Time Value of Money), you know that a dollar today is worth more than a dollar a year from now. But this is too easy; we are comparing similar amounts of money. Things get much more complicated when we compare different amounts of money. For instance, which is worth more to you: a dollar to day or $100 dollars in a year?

For me, even taking into consideration the time value of money, I'd take the $100. There is no bank in the world that would let you deposit $1 and give you anything close to $100 a year from now. Inflation typically hovers somewhere around 2-3%. And the risk of losing $1 is probably worth the chance of having $100 in a year.

It's worth noting however, that this is a subjective question. (Remember my crack about the one-handed Business Type?). It is strictly a matter of opinion, although I have to admit that it is the rare individual would rather have $100 in a year. But imagine someone with six months left to live, or someone who had figured a way to beat the lottery, and turn $1 into $1,000,000, or who lived in a country with 80,000% annual inflation. For these people, the cost of waiting a year is just too high, even to get that additional $99.

Just how much you are willing to pay to wait for money is a personal decision. It is different for individual, for every BT, and every company. But everyone has a tipping point.

Now I don't know what your tipping point is, but we could easily find out. I could offer to give you some amount of money in a year such that you would be completely indifferent between receiving $1 now and receiving that amount of money in a year. The additional money you would receive after waiting an entire year would be exactly equal to your own personal cost of waiting.

There are two ways we could calculate this amount. The first would be to try to add up the different percentages. We could try to quantify what type of interest rate the banks would give you. (That we could do pretty easily.) We could try to predict inflation for the coming year. We could try to quantify how much having a dollar right now that you can spend as you please is worth to you. That's a little more difficult. And we could try to asses the risk, or the chances of you getting your money in a year. That's a difficult task, but not impossible.

Many BT's spending a significant amount of time trying to get this calculation exactly correct. It is very complex and anything but an exact science, but it is very important to them. Business deals have fallen apart because one party decided that they would have to wait longer to be repaid than they were willing. This can all get extremely complicated, but there is another, easier way to calculate your own tipping point. I can simply ask you a series of questions until I hit on the exact number.

Consider the following short play below that outlines my own personal cost of capital.

ODE TO HOTDOGS: A PLAY IN ONE ACT

ME: Get your hotdogs!

TOM: I'll take a hotdog.

ME: That'll be one dollar.

TOM: I don't have a dollar, but I could give you $1.09 in a year. Would that work?

ME: You know what? I'd rather have the dollar now. I'm sure if I had that dollar now, I could turn it into more than a $1.09 in a year.

TOM: How about if I guarantee you $1.11 in a year?

ME: Sold!

My answers to these three questions have shown that I am completely indifferent between $1 now and $1.10 a year from now. If you promise me $1.09 in a year, I will take the dollar. But if you promise me $1.11, I will be willing to wait.

Ten cents is 10% of one dollar. My personal cost of waiting for money is 10%.

This 10% is very helpful, because it means we no longer have to think of the time value of money in terms of one dollar. If I'm offered $100 now, I know that the number I am indifferent towards in a year is $110. And I can also use that 10% to calculate what you would be indifferent to in two years or half a year.

In finance, this is called your discount rate. It helps us determine whether to enter business proposals or not. Suppose that I approach you with a scheme that will make you $1,500 in three years, only I am asking for $1,000 today. If you know your discount rate, you can figure out whether this makes sense or not.

Remember that because the discount rate includes your own potential return from the money you're receiving, it is different for each person. For instance, Warren Buffet is a fabulous investor. Suppose he knows enough about the market that if you give him a dollar, he can turn it into $1.20 in a year. His discount rate is going to be much higher than 10%. My grandmother, however, would probably only put the money in the bank (or maybe even under her mattress). Her discount rate is going to be much lower.

Your personal discount rate isn't even the same each time.

Businesses rely on discount rates all the time. A fast-food restaurant, for instance, may consider opening a new branch in a new city. But before they invest the money, they'll want to examine (among other things) how much capital expenditure (upfront costs like building the restaurant and advertising in the local paper) it will require, how long it will take the restaurant to make a profit, and what the eventual returns will look like. Their own personal cost of waiting will be an important factor in weighing the attractiveness of the deal.

What makes the discount rate and the time value of money so annoying is that it means that you have to look at more than just dollar amounts when examining a business transaction. Imagine if, before you read that last chapter, a friend of yours came up to you and said, "I have a business plan. If you give me $100 I can turn it into $150." Assuming that the risk was minimal, you probably would have jumped at this idea.

But now, we've got this issue of time to deal with. When are you going to get this $150? If you get it tomorrow, great! But if you get it in twenty years, you could have just put the money in the bank or the stock market and have done better.