# Value Investing 101: The Time Value of Money

|*(or the Genius of Wimpy)*

J. Wellington Wimpy is Popeye’s friend and “straight man” in E. C. Segar’s venerable comic strip and cartoon series, *Popeye*. Whereas Popeye is pugnacious, erratic, and courageous (especially after a shot of spinach), Wimpy is, well, wimpy. He’s soft-spoken and clever but he’s also yellow-bellied, lazy, cheap, and sometimes deceitful. And while Popeye loves his healthy spinach, Wimpy has a gluttonous affinity for hamburgers. Indeed, his entire personality – his guile and his greed – can be summed up in his famous catchphrase “I’ll gladly pay you Tuesday for a hamburger today.” Sounds like exactly something an indolent scam artist with a voracity for hamburgers would say, right?

Well, maybe not. I always liked Wimpy’s catchphrase, which I think can be appositely used to illustrate some essential financial concepts. I also always liked Wimpy himself who, despite, all his conniving and scheming, was a good-natured fellow and was actually a much more intellectual character in Segar’s comic strips than was portrayed in the animated cartoon series. So, if you bear with me, I think it’s worth entertaining the notion that *maybe* Wimpy wasn’t poor at all, and that the actual reason he never had any money was because it was all tied up in stocks? Maybe Wimpy was actually a world class investor? Maybe, just maybe, Wimpy was simply applying the fundamental principles of finance?

Enter, stage right: *The Time Value of Money*.

## Introducing the Time Value of Money

The Time Value of Money (TVM) is a concept that says that a dollar received today is worth more than a dollar received tomorrow. Let’s see why:

Investing is the act of purchasing assets – such as stocks or bonds – in order to move money from the present to the future. However, the conversion of present cash into future cash is burdened by the following problems:

- Individuals prefer current consumption over future consumption: delayed gratification is hard for most people and, all things being equal, we would rather have things now than wait for them.
- Inflation: When the money supply increases, prices also often increase. Consequently, the purchasing power of fiat currency decreases over time.
- Risk: The future is uncertain, and there is always a chance that future cash delivery may not occur.

To overcome these problems, investors must be compensated appropriately. This compensation comes in the form of an *interest rate*, which is determined by a combination of the asset’s risk and liquidity and the expected inflation rate (n.b., academically, there are actually 5 determinant components of market interest rates).

This compensating interest rate (also called a *discount rate*) can come in a variety of forms. Sometimes the discount rate used is the safest investment possible – usually the 10- or 20-yr U.S. Treasury rate (often called the risk-free rate, because the notes are backed by the full faith – and taxation and currency-printing powers – of the United States government). Other times the discount rate will be determined by the risk involved in receiving the future cash flow (as in CAPM), by a company’s capital structure (as in WACC), or by the investor’s required rate of return (as in NPV calculations).

No matter the interest rate used, the conclusion is always the same: a dollar received today is worth more than a dollar received tomorrow. This is because you can invest that dollar today (move it to the future) and earn interest on it (receive compensation to account for risk, inflation, etc.).

So if your bank’s savings account pays 3% a day, then a dollar tomorrow is only worth as much as $0.971 received today ($0.971 invested today at a 3% per day interest rate would give you $1.00 tomorrow). Or, in other words, a dollar today is worth $1.03 paid tomorrow; if instead you only received $1.00 tomorrow, you would be upset because you missed out on the opportunity to get that $0.03 in interest.

## Present Value and Future Value

There are two easy formulas to determine the *future* value of money paid/received today*,* or the *present* value of money paid/received in the future:

PV = FV/(1+i)^n

FV = PV*(1+i)^n

where *PV *(Present Value) is the value of future money today, *FV* (Future Value) is the value of today’s money in the future, *n* is the number of time periods, and *i* is the interest rate (quoted in the same terms as the number of time periods).

If you know the value of any three variables, then you can calculate the fourth missing variable. Consequently, you can use these equations to answer questions such as:

- If I invest $500 today at a 5% interest rate, how much money will I have in 3 years?
- How much money will I need to invest today at 5%, if I want to have $600 in 3 years?
- What compounded annual rate of return did I earn if I invested $500 today and had $600 after 3 years?
- How long do I have to wait for my $500 investment to turn into $600 at a 5% interest rate?

It is usually much easier to use a financial calculator or the Excel functions =fv ; =pv ; =rate ; =nper to solve these sorts of calculations. These tools will also help you to easily calculate the future and present values of annuities (e.g., bonds, mortgage payments). These calculations are not covered in the scope of this post – however I believe the concept is a straightforward extension of the basic PV and FV and the calculator and excel inputs are easy to learn (no use bothering with the algebra, which is impractical to use beyond an academic setting).

## The Magic of Compounding

It is important to note the role of the exponent *n* and the difference between simple and compounded interest. Simple interest is calculated *onl*y on the principal amount (Principal x n x i). If your buddy asks you to loan him some money you might say, “Sure, I’ll loan you $1,000. Pay me back in 3 years plus $50 per year (a 5% simple interest rate). In three years, your friend would pay you $1,150 ($1000 x 3 x .05 = $150, plus principal of $1,000).

Now let’s suppose you told your friend, “Sure, I’ll loan you $1,000. Pay me back in 3 years plus 5% interest per year (compounded interest).” Using our new FV formulas, FV = $1,000 x (1.05)^3 = $1,157.63. What?! How’d we get $7.63 more? Let’s break out the formula by each year:

Year 0: PV = $1,000 x (1.05)^0 = $1,000

Year 1: FV = $1,000 x (1.05)^1 = $1,000 x (1.05) = $1,050

Year 2: FV = $1,000 x (1.05)^2 = $1,000 x (1.05) x (1.05) = $1,050 x (1.05) = $1,102.50

Year 3: FV = $1,000 x (1.05)^3 = $1,000 x (1.05) x (1.05) x (1.05) = $1,102.50 x (1.05) = $1,157.63

*or,*

Year 0: PV = $1,000

Year 1: FV = $1,000 *+* $1,000 x (.05)

……………= $1,000 + $50

……………= $1,050

Year 2: FV = $1,000 + $50 + $1000 x (.05) + $50 x (.05)

……………= $1,000 + $50 + $50 + $2.5

……………= $1,102.50

Year 3: FV = $1,000 + $50 + $50 + $2.5 + $1,000 x (.05) + $50 x (.05) + $50 x (0.5) + $2.5 x (.05)

……………= $1,000 + $50 + $50 + $2.5 + $50 + $2.5 + $2.5 + $0.13

……………= $1,157.63

As you can see in the above calculations, your *interest is earning interest*, and such is the magic of compounding. In Year 1, you get $50 in interest on the original $1,000. But in Year 2, you earn $50 on the original $1,000 *plus* $2.50 in interest on the $50 of interest earned in Year 1. In Year 3, you also earn $0.125 on the $2.50 earned in Year 2 *plus* $2.50 in interest on the $50 of interest earned in Year 1 *plus* $50 on the original $1,000. And so on.

The effect of compounding is more pronounced at greater interest rates and for longer periods of time. For example, $1,000 at a 5% simple interest rate becomes $1,750 in 15 years; but at a 5% compounded interest rate it grows to be $2,078.93. At a 15% simple interest rate over 30 years, $1,000 grows into $5,500; but at a 15% compounded interest rate it explodes into an enormous $66,211.77!

This is the reason why Berkshire Hathaway’s preferred holding period is forever. It allows Buffett’s and Munger’s investments to compound continuously. It is also the reason why saving for retirement when you’re young almost always beats saving when you’re older, even if the dollar amounts are less and the pay-in period is shorter.

Now back to my case for Wimpy’s exoneration.

People often use Wimpy’s catchphrase, “I’ll gladly pay you Tuesday for a hamburger today,” as an insult used to describe someone (often the U.S. government) who uses debt irresponsibly; “let’s buy stuff today and figure out how to pay for it later… or not pay for it at all.”

But if Wimpy was applying what we now know about the TVM, then by deferring payment on his hamburgers he could invest the money he had, earn interest on it, let it compound, and then ultimately have more money to buy even more hamburgers when Tuesday finally came around!

Okay, maybe it’s a little fantastical (even for a cartoon) and a bit of a stretch of the imagination. But then again, with the amount of hamburgers that Wimpy eats, maybe not.

Besides, Wimpy’s love of hamburgers is shared with another guy who’s pretty good at investing…

*The Time Value of Money and Future/Present Value are essential concepts to know, as they form the basis for many financial calculations (from calculating a rate of return to running a Discounted Cash Flow model). For a complete tutorial, please refer to the following links:*

- http://www.investopedia.com/articles/03/082703.asp
- https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/present-value/v/time-value-of-money
- http://pages.stern.nyu.edu/~adamodar/New_Home_Page/PVPrimer/pvprimer.htm

Any questions on the Time Value of Money, Present and Future Values, or Compounding? Let’s hear ’em in the comments!