# 11.1Time Value of Money Overview

__The time value of candy__

J: Let’s do a little thought experiment.

K: OK

J: Imagine that you are a 4-year-old child.

K: I’ve got it. I’m a 4-year-old child. I’ll imagine that I am my grandson, Kadan. He’s 4.

J: Perfect. I offer you one piece of chocolate now, or one piece of chocolate tomorrow. Which will you take?

K: Please … I’ll take the chocolate now.

J: Exactly. Any child understands what I will call “the time value of candy.” Candy now is worth more than candy in the future. -- What if I offer you one piece of chocolate now or 5 pieces if you wait until tomorrow?

K: A 4-year-old would probably still take the one piece now.

J: I agree. For a young child, the future is such a vague and unpredictable place that it makes sense to take your candy now. In fact, an important part of growing up is learning that planning and action __now__ have predictable consequences for the future. -- So, let’s change the example. Imagine that you are you. I offer you the following deal: 100 pieces of chocolate now, or you go without chocolate for an entire year, and I give you 100 pieces of chocolate one year from now.

K: I’ll take the 100 pieces of chocolate now.

J: 100 pieces now, or 105 pieces one year from now.

K: 100 pieces now.

J: 120 pieces one year from now.

K: This is getting tough … I’d probably still take the 100 pieces of chocolate now.

J: 100 pieces now, or 200 one year from now.

K: You’ve got me. I’ll wait and take the 200 pieces one year from now.

J: Excellent. You see that people prefer candy or money now to candy or money in the future. But there is some extra amount in the future, some amount of “interest,” that can cause you to wait. In this case, your “chocolate interest rate” was 100%. I had to agree to double your chocolate to get you to wait a year.

K: Hey, I like chocolate.

J: That is the time value of candy. When we are talking about loans or retirement investments, the same concept is called “the time value of money.” If you borrow money now, you will have to pay it back … with interest.

K: But if you save for the future now, in the future you will have your savings… plus interest.

J: Precisely. The time value of money.

K: This exact same idea of the time value of money is crucial in evaluating long-term business decisions.

J: Business projects, such as constructing a manufacturing facility or spending money on research and development, involve spending money now in the hope of receiving more money in return in the future.

K: To properly compare the amount of money you are spending now to the amount of money you expect to receive in the future, you have to adjust for the time value of money.

J: Investing $10 million in a production facility now in the hope of receiving back $10 million 15 years from now completely ignores the time value of money.

K: The time value of money: money now is worth more than the same amount of money to be received in the future… a concept that any 4-year-old child understands.

__Overview of time value of money terms__

With time value of money calculations, we will ask four questions with regard to these calculations: (1) when, (2) how often, (3) how long, and (4) how much.

First, is the question: “When?” Am I dealing with an amount now or an amount in the future? An amount to be paid or received now is called a PRESENT VALUE. We often use the designation “PV.” An amount to be paid or received in the future is called a FUTURE VALUE, or “FV.”

For example, let's say I tell you: "I'll give you a $100." The natural question is: "When?" Right now, next week, next year, or in 100 years? The value of that $100 depends on when you receive it. If you receive it now, the PRESENT VALUE, the equivalent amount that it is worth right now, is $100. If you will receive it in one year, then the $100 is a FUTURE VALUE, an amount to be paid or received in the future.

What is the PRESENT VALUE (the right-now equivalent) of a FUTURE VALUE of $100 to be received one year from now? That depends on the interest rate. If the interest rate is 10 percent, then the PRESENT VALUE of $100 to be received one year from now is about $91.

$91 $100

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Now 1 year from now

PRESENT VALUE FUTURE VALUE

If I give you $91 now, and the interest rate is 10%, you can invest that $91, earn about $9 in interest, and have $100 one year from now. If the interest rate is 10%, the PRESENT VALUE of $100 to be received one year from now is $91. If the interest rate is 10%, the FUTURE VALUE one year from now of $91 received now is $100. By the way, if the interest rate is 10%, the present value of a $100 to be received 100 years from now is less than one CENT, so the question of “when?” is quite important.

The second important question to ask, after “when,” is “how often?”. Am I dealing with one payment or a series of payments? One payment is called a LUMP SUM, and a series of equal payments is called an ANNUITY.

For example, suppose that I am going to prepare for my retirement by saving $1,000. The question of “how often?” is very important. Am I going to save $1,000 just one time right now, am I going to save $1,000 each year, or am I going to be saving $1,000 each month?

The next important question is: “How long?”. For example, you need to borrow $1,000 now, and your brother offers to loan you the money if you repay $100 per month. This, of course, is an ANNUITY, a stream of equal payments. Great, but you want to know “how long?” you have to repay $100 per month. For 10 months? That's great, 10 months times $100 per month is $1,000. You are just paying back what you borrowed with no interest. This is a good brother indeed. But what if your brother says that you have to pay $100 per month for 15 months.

You borrowed $1,000 from your brother but have to repay $1,500. Now we see that there is some interest involved. In fact, the effective annual interest rate on this loan is 91%. Some brother ☹

So, the question of “how long?” makes a big difference. The final question is: “How much?” This “How much?” question relates to both how much cash and what interest rate. Your monthly payment on a mortgage loan depends both on the size of the mortgage loan and the interest rate on the loan. Oh, and that monthly payment also depends on the length of the mortgage … 10 years, 15 years, or the standard 30 years.

With time value of money calculations, we will ask four questions with regard to these calculations: (1) when, (2) how often, (3) how long, and (4) how much.

__Examples of common misunderstandings__

Lottery payouts are an example of a situation in which the reported monetary value is misleading because it ignores the time value of money. On October 23, 2018, the numbers 5, 28, 62, 65, and 70, plus the additional Mega Ball number 5, were chosen in the Mega Millions lottery. The Mega Millions lottery is a state-sponsored lottery offered in 45 of the 50 states in the United States. The prize for the lucky Mega Millions winner on October 23, 2018 was $1.537 billion, the largest single lottery winner in U.S. history.

But lottery prize amounts are typically stated in terms of the sum of a series of annual payments. The $1.537 billion Mega Millions prize is the sum of annual payments spread over 30 years. In this case, as in most large-lottery cases, the lottery winner chose to be paid one large payment immediately. That one large payment was $878 million… a LOT of money, certainly, but substantially less than the stated prize of $1.537 billion. The $878 million is the PRESENT VALUE of the 30 years of future payments that add up to $1.537 billion. Lottery prizes, along with professional athlete contracts, are examples of situations in which the stated dollar amounts intentionally ignore the time value of money to make the prize or the contract seem larger than its true economic value.

Here is an example that is closer to home: Do you feel happy when you receive an income tax refund? Most of us do feel happy. But this happiness is evidence that we aren’t thinking about the time value of money. For example, if you receive an income tax refund of $1,000, that means that you gave the government one thousand extra dollars during the year that the government then returns to you after the end of the year. You don’t earn any interest on this $1,000… you give an extra $1,000 now and receive back that same $1,000 later. And because we know that a dollar received in the future is worth less than a dollar now, an income tax refund is evidence of a bad time-value-of-money tradeoff.

Another example is apartment rental deposits. I recently saw an example in which a family rented a house for 5 years. At the beginning of the rental contract, they had to give the landlord a $1,800 deposit, with the promise that they would receive the deposit amount back when they left the house… if the house was clean and in good repair. Well, at the end of 5 years the renters got back their $1,800 deposit and were quite happy. But in terms of the time value of money, the renters lost a substantial amount of value by allowing the landlord to take $1,800 from them at the beginning and then give them back the same $1,800 amount 5 years later. For example, if the renters had been able to put that $1,800 in a conservative bond investment fund for those 5 years, earning 5% per year, the $1,800 would have grown to $2,300 in those 5 years. And if the renters had invested that $1,800 in a diversified portfolio of stocks, the investment fund would have grown to over $3,000 during those 5 years. In short, $1,800 now and $1,800 5 years from now are not the same thing. After considering the time value of money, the renters received back considerably LESS than the $1,800 they had given to the landlord as a deposit 5 years before.

Unless we train ourselves, it is easy to be overlook the very common existence of time-value-of-money misunderstandings.