Investing Fundamentals

Understanding The Time Value of Money Formula

Last Updated on July 5, 2019 Last Updated on July 5, 2019
Time-Value-of-money-formula

A dollar today isn’t the same as a dollar tomorrow, that’s the time value of money. Risk and return are expecting a dollar risked to earn more than a dollar.

The time value of money and risk and return are two core concepts in personal finance. Luckily, each boils down to a pretty simple statement.

The core principle of the time value of money means your dollar today is worth more than your dollar tomorrow.

Risk and return say that if you are to risk a dollar, you expect gains of more than just your dollar back. For each unit of risk you take on, you expect a slightly more significant unit of return.

Even though these money concepts are easy to simplify, I want to dig a bit deeper into each of them.

Time Value of Money

Today’s dollar is worth more than tomorrow’s because of inflation (on the side that’s unfortunate for you) and compound interest (the side you can make work for you).

Inflation pushes prices up over time which means that each dollar you own today will buy more in the present time than it will in the future. This is why investing is so important.

Inflation is reported on an annualized basis. That means that to invest a dollar today, you’d have not only to expect to exceed inflation but also have some wiggle room to account for the uncertainty of the future cash flow.

Over time the stock market beats out inflation. So if you put the same amount of money in a savings account and investment account, the money invested would be worth far more than the money sitting in the savings account.

Opportunity Cost

For every choice made, there are choices sacrificed. The choice to go to college is a simple example of opportunity cost.

Choosing to attend means you are giving up four years worth of salary you would have earned at a job and four years of work experience (future payment.)

Of course, you hope that by choosing to go to school, you will make more money over your lifetime than if you don’t attend. So it’s a gamble, but a calculated one that hopefully has a more significant pay off eventually than if you had chosen not to go to college.

Time value of money varies and involves an opportunity cost.

That means that if you’re putting the $1000 in a savings account to save for a house, you may be foregoing an opportunity to be growing that money in an investment account.

For example: Calculating the time value of your money will tell you that instead of investing you should be paid down your 24% APR credit card debt that’s costing you hundreds a month.

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Compound Interest

What’s the point of investing money if it won’t grow faster than inflation? You’d be better off spending it now when it has a higher value. That’s where the compound annual interest rate comes to the rescue.

A standard bond returns a flat percent of the face value each year, which is simple interest. In that case, if you got a 5% annual interest rate on a $1000 face value bond, you’d get $50. That’s not bad, but it’s not where the magic lies.

The-Time-Value(BOND)

When you’re looking at investments like stocks, you expect the annual percentage rate to be 5% a year, or 7% if you count dividends. If you have a $100 stock that increases 5% by the end of the year, you have $105 in that compounding period.

By the end of year two, it’s grown another 5% and is worth $110.25 ($105*1.05). While that’s only an extra 25 cents, in this case over long periods of time and with larger dollar amounts, that can end up being a lot of money.

The-Time-Value

It’s possible to compound interest monthly or even daily – this is called continuous compounding. This means that your balance grows by a small amount every instant.

Time Value of Money Calculator

Assuming you have a financial calculator or access to the internet, it’s pretty easy to see how much your current cash flow would be worth tomorrow, though you do have to make some assumptions.

If you’re not a money nerd like me and don’t have a financial calculator sitting next to you, I recommend using this calculator from Zenwealth. If you’ve never used one before, the interface can be somewhat confusing. Here’s step by step how to break it down and what the abbreviations and terms mean:

PV: This means present value. Enter how much money you have today. If you have a $20 in your wallet, enter 20.

Rate: this is the rate of growth. If you’re calculating how much inflation will be, you can use a number like 3%. If you’re trying to see what your money will grow if you’re getting a 7% real (after inflation) rate of return use 7%. You put in the whole number (7) instead of the actual decimal-y number (0.07).

PMT: This means payment. It’s the amount that you’re adding to the PV per period. Think of it as a monthly contribution to an IRA (assuming you’re doing monthly compounding).

Periods: The number of times you’re compounding your money. It’s important to keep in mind how extended a period is- are you compounding weekly, monthly, annually, weekly?

FVA: This is your future value. If you’re trying to calculate what your money will be worth in the future once you’ve made payments and had to compound, you’ll see your answer here.

If you’re trying to reverse engineer what a future sum of money is worth today with deflation, you start with this number. If you want to get your math hat on, the following formula is to calculate this.

time value of money formula

Using the Time Value of Money Formula

Are you bored yet? I promise you it’s essential. With those variables you can answer questions like these:

How much money would I need to save starting today if I wanted to have $1,000,000 in 20 years assuming 6% growth after inflation?

Enter 6% for rate, nothing in payment, future value $1,000,000, net present value $0, and 20 periods. Please, try it yourself! You could do this for anticipated future costs like weddings, school costs, buying a house or car, or anything else you want to save for over time.

If I start with nothing today and put away $100 a month, what will I have in 10 years if I get 4% growth after inflation?

Here we use net present value 0, payment 1200, rate 4, ten periods, and solve for future money. Again, I recommend you try it yourself, but I get $14,407. This kind of question is great for seeing where you’ll be if you start today.

I go through these kinds of hypotheticals occasionally because it’s always fun to watch how my money would work for me.

One important note when working with the calculator is that either present value, future value, or payments are a negative number or 0.

A negative denotes a cost, so a negative payment is a payment into the account and a net present negative value means you paid for it with your own money. It’s what you need to do to buy the future value.

Risk And Return

Now that you can calculate the TVM (time value of money), it’s time to look at risk and return. From example 1 we know that you would need to save a whopping $2,308 per month to get from $0 to $1,000,000 in 20 years with 6% growth.

If you’re like me, that number seems pretty high. We need to look at securing a higher rate of return to drop that amount. A 2% higher return would drop the monthly savings by $500 but what does that mean for your investing strategy?

But, you’re unlikely to get extra return without taking on extra risk. Investing in a small startup is a bigger risk than investing in a well-established company, but the investment in the startup has the potential for a bigger payoff.

It’s essential that you are comfortable with and aware of the amount of risk in your investing strategy. If you can stomach the lows and highs that come with extra risk, it could make sense to strive for the extra return and in turn, lower your monthly payment value.

time value of money start early

Time Value of Money Examples

Buying a car

So, you have decided to buy a car that costs $18,000.

The car dealer gives you two choices:

1. Purchase the car for cash and receive $2000 instant cash rebate. This will make your out of pocket expense $16,000 today.

2. Or purchase the car for $18,000 with zero percent interest 36-month loan. In this scenrio, you would make monthly payments with a market interest rate of 4%.

Which option above is cheaper? How much do you save?

The correct answer is option 1 – it will save you $935.38.

A mistake people make is comparing $16,000 to $18,000. If you choose Option A, you are paying out $16,000 now. If you choose Option B, you are paying monthly installments of $500 for 36-months totaling $18,0000.

In finance, the key thing to understand is you need to compare cost always at the same point in time.

This is why it is so important to understand the time value of money.

Investing Your Money

If I offer you the choice of $1,000 right now or $1,000 five years from now, it’s a no-brainer. The $1,000 now is the answer.

But what if we change it up, and offer you $1,000 right now or $1,250 five years from now? If we took the money now and invested it we end up with more than $1,250, or less?

Say we took the $1,000 now and invested it in the market and made a conservative 5% interest. In one year, we’d earn $50 interest (5% of $1,000), so our $1,000 would have grown to $1,050.

If we reinvest those gains the next year we get a little more: $52.50 (5% of ($1,050). Each year, the interest keeps increasing or “compounding.”

By the end of year 5, we have $1,276. So if we know we can get that 5% return, we’d be better off taking the $1,000 now, rather than the $1,250 later.

Real Estate and Leverage

In the stock market, you use 100% of your money to control 100% of your investments.  In real estate, you only use 20% of your money to control 100% of a property. When you sell that property or generate monthly income on that property, you are making money on the full value of the investment.  Your returns are multiplied.

To understand how leverage works and what it has to do with the time value of money, let’s look at the example of three people who have $100,000 to invest in real estate.

Person A bought an $100,000 investment property outright. After taxes, insurance, and property management fees, the property generated a cash flow of $500 a month.

At the end of the year, Person A will have made $6,000, a 6% return on investment. Not bad.

Person B took that same $100,000 but instead of putting it all in one property, they invested $20,000 into five different investment properties. After mortgage payments, taxes, insurance and property management fees, the properties generated a cash flow of $200 a month per house.

At the end of the year, Person B will have made $12,000 – a 12% return on investment. That’s double the return on the same 100k initial investment. 

Not only is Person B making more money than Person A but she also controls $500,000 worth of real estate, compared to only $100,000, which means more opportunities for home value appreciation and lower risk since Person B is better diversified with five different renters.

Why This The Time Value of Money  Important

These concepts are the basis of every recommendation you see, even if the person making the recommendation isn’t explicitly aware of it.

It’s better to invest early because of the TVM concept. Each dollar that you invest now has a time period to grow, but the reason that it’s important to invest that dollar instead of sitting on it is that if it doesn’t grow and outpace inflation, you will lose purchasing power over time.

Gas, movie tickets, and food used to cost less and a $50,000 salary used to mean a lot more. That fantastic investment that promises a huge return? It comes with increased risk as well, or it would have been snapped up already.

Again, that doesn’t necessarily mean it’s a bad decision; you just need to understand what you’re getting in to. You need to take some risk for your money to outpace inflation so just make sure you’re comfortable with the amount you’re taking.

Show Notes

Mikkeller Brewing Passion Pool – Gose-style ale with Passionfruit and Sea Salt

American Solera Movement and Color Member Blend – Foeder Ale Refermented with Chambourcin and Norton Grapes

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