Understanding the time value of money

- Let's consider a very simple investment. You invest money now in exchange you will receive $1,000 one year from now. Pay how much to receive $1,000 in the future? How much now? - Yeah, that's a pretty simple investment. - Well, the question is this, how much would you pay now for the right to receive $1,000 one year from now? - Well, for starters, I would pay less than $1,000 now to receive $1,000 one year from now. - Why less? - Well, because you're asking me to refrain from using that money now. I could use that same money to buy a new computer now, or to go on a driving trip to the Grand Canyon now, or to eat in a really nice restaurant once a month with my family for the next year. - Well, that's good analysis. If you're going to invest your money now in exchange for an investment return one year from now, you have to be paid for the lack of use of your money for that year. - In addition, as you know, it's common for currencies to decline in value over time. We call this inflation. $1,000 one year from now probably won't buy me the same basket of goods and services that $1,000 would buy me right now. - That's correct. For example, in 2019, the inflation rate in the United States was about 2%. Roughly speaking, that means for what you could buy for $980 on January, 1st, that would cost you $1,000 one year later on December, 31st. - So because I have to be compensated for not using my money now and because I need to be reimbursed for any expected inflation, I would invest less than $1,000 now in exchange for $1,000 one year from now. - So perfect. So far, we've assumed that the $1,000 payoff one year from now is certain, no risk. What if there was significant risks that the company or the person who promised to pay you the $1,000 one year from now, won't be around in one year. - They just disappear. - Yes, bankrupt. Their business plan didn't work out. They can't pay you the promised $1,000. Maybe they can pay you something but it'll be less than $1,000. - But maybe they can pay me the entire 1000. - Yeah, sure, maybe they can, and maybe things will go great and they can pay you more than a thousand, but it isn't certain. - So maybe less than a thousand maybe more than a thousand, maybe nothing. Well, this is a bit different than a guaranteed promise of $1,000 one year from now. - So here's the question, will you pay more or less now in exchange for a risky $1,000 one year from now. - Risky? I'll pay less of course, less. - One more question, what if the $1,000 is not to be received one year from now? What if it's to be received 10 years from now? How much would you invest now in exchange for $1,000 10 years from now? - 10 years from now? Well, if I have to wait 10 years for my money, I'll pay less now. - Exactly, so let's summarize the connections among investment amounts now and interest rates, risk, and time. - I will invest less than $1,000 now in exchange for receiving $1,000 one year from now just to compensate me for not being able to use my money during that year. - [Man in Blue shirt] And if inflation is expected to be higher? Then I will invest even less now to compensate me for the drop in purchasing power of $1,000 when I receive it. - And that amount to be received is uncertain, I will invest even less now to compensate me for that risk. Finally, if I have to wait even longer than a year to get my $1,000, I will invest even less now in exchange for the $1,000 future payment. So all of this discussion about investment amounts now compared to payoffs years from now bears the general label of the time value of money.