The idea behind the time value of money is pretty simple: a dollar today is worth more than a dollar tomorrow, as Harvard Business School Online explains. [1]

So, what does that mean?

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## Understanding the Time Value of Money

The time value of money essentially states that having a dollar in your hand right now holds more value than having the promise of a dollar a year from now.

Why is that?

Well, it all boils down to inflation. According to Forbes, inflation occurs when prices rise across the economy, reducing the purchasing power of your money. [2]

Anything else to it?

Definitely. When you have money in hand today, you have the opportunity to invest it and potentially increase its value over time.

Got it! So, why does it matter?

The significance of this concept spans various financial activities. In finance, it's used to determine the valuations of stocks and bonds and is essential in assessing investment viability using metrics like NPV, IRR, MIRR, discounted payback period, or profitability index.

In the realm of the time value of money, there's a formula we use to calculate present and future values.

Calculating present value involves evaluating future cash flows at a specific discount rate, while determining future value means assessing the future worth of current money at a particular growth rate.

Now, let's talk about how to calculate present and future values. But before we dive in, let's understand the concept of a timeline.

## Exploring Timelines in Time Value of Money

A timeline is crucial because it helps us visualize the value of money over time.

Consider this timeline:

We have time 0, 1, 2, 3, 4, and so forth.

Time 0 represents the present moment. Time 1 is not now; it's one year from now (assuming a yearly timeline).

Clear on the difference between time 0 and time 1?

Great. Now, let's observe the intervals between time 0 and time 1, time 1 and time 2, and so on. These intervals could span a year, six months, three months, or a month.

Since we're using a yearly scale for this timeline, it's important to note that it's an annual timeline.

Now, let's say your friend borrows $10,000 from you and repays it in four yearly installments with no interest (which rarely happens in real life). Here's the timeline for that:

At time 0, your cash decreases by $10,000 because your friend borrows it. Then, at time 1, you receive the first payment, at time 2, the second payment, at time 3, the third payment, and at time 4, the fourth payment—each installment being $2,500, as agreed.

Now that we understand the concept of timelines in the time value of money, let's move on to future value and its practical applications.

## Calculating Future Value

What's future value?

Future value represents the growth value of money invested now over several periods at a specific rate.

For instance, if you deposit $100,000 into an account at time 0 with a 5% annual interest rate, it will grow to $105,000 in one year.

Now, let's say you leave it untouched for two years. In addition to the principal amount, the interest earned in the first year also earns interest in the second year. That's compound interest for you.

Continuing from the previous calculation, the $105,000 from the first year becomes $110,250 at the end of the second year.

By stacking up these calculations, you arrive at a formula like this:

To find the future value (FV) of a present value (PV) at a specific rate (r) after a certain time (n), use this formula:

FVn = PV x (1 + r) x (1 + r) x ... x (1 + r)

or

FVn = PV * (1 + r)^n

So, continuing from our previous calculation, if you want to find the investment value at year 3, here's how it works:

FV3 = $105,000 x 1.05 x 1.05 x 1.05 = $121,552.50

or

FV3 = $105,000 x 1.05^3 = $121,552.50

Calculating future value is also useful for estimating a company's future dividend payouts.

This is crucial because to value a company using the dividend discount model, you need to estimate its future dividend payouts.

How do you do that?

With the future value calculation.

For instance, let's say Johnson & Johnson paid a cash dividend of $4.7 per share in 2023. You want to know the dividend payout in 2028, five years later. After some historical data analysis, you find out that the dividend has been growing at a rate of 6% annually until 2028.

So, to find the dividend value in 2028, you calculate it like this:

FV5 = $4.7 x 1.05^5 = $5.99

So, the dividend value in year 5, or 2028, is $5.99.

Now that we've tackled future value, let's discuss another crucial aspect: present value.

## Determining Present Value

Present value is highly important in finance. Whether you're valuing stocks, bonds, or assessing project feasibility, present value comes into play.

So, what's present value again?

Present value is the current value of future money discounted at a specific rate.

Let's say you want to buy a $2,000 Asus ROG Strix G16 gaming laptop in a year, and a bank offers a 6% deposit rate. How much do you need to deposit now to buy it next year?

It's the reverse of the future value calculation, so you'd calculate it like this: FV / (1 + r)^n or $2,000/1.06, which equals $1,887.

Now, let's say you come across a review of the MSI Titan 18 HX gaming laptop, priced at $5,500, and you decide to buy that instead. You're okay waiting two years for it. With the same 6% deposit rate, how much do you need to deposit now to afford it?

This time, you're finding the present value of future money over several periods back. You just adjust the power of n. Like this:

PVn = FV / (1 + r)^n

PV3 = $5,500 / (1 + 0.06)^2 = $4,890

Simple, right?

Next up, when you're dealing with present value from a future value, say, present value from the FV in year 5, you just change the power or n to 5.

## Closing Thoughts on Time Value of Money

It's somewhat peculiar how straightforward the concept and mathematics of the time value of money are, yet it still manages to confuse many people.

The usefulness of this concept in finance is undeniable. Almost all financial theories use time value of money calculations, whether it's present value or future value.

Did you know that when it comes to calculating the value of a company's stock, you can simply do it by discounting dividends or finding its present value?

Wait, discounting dividends expense?

Hey, remember, dividends aren't a company's expense. I've explained this in a previous post about misconceptions surrounding dividends. Check it out!

So, really grasp this concept. It's basic, yes, but mastering it is key to becoming proficient in finance.

To wrap things up, let me quote Ray Mancini, "the advance level is mastery of the basics." So, to excel in finance, you must nail this time value of money concept.

#### ARTICLE SOURCES

- Time Value of Money (TVM): A Primer. Harvard Business School Online. Catherine Cote. https://online.hbs.edu/blog/post/time-value-of-money. (accessed April 13, 2024)
- How Inflation Erodes The Value Of Your Money. John Schmidt. Forbes. https://www.forbes.com/advisor/investing/what-is-inflation/. (accessed April 13, 2024)