Improving Your Personal Happiness with Time Value of Money Formulas

How to Calculate the Future and Present Value of a Lump Sum

Two Time Value of Money Formulas
There are two time value money formulas that can help you make better, more informed financial decisions by prioritizing your personal happiness. Christian Baltg / E+ / Getty Images

I want to talk to you about the time value of money formulas  Specifically, two-time value of money formulas you can use to make your finances better reflect your actual goals and objectives, changing your behavior to maximize your purchasing power.

A major theme I try to reiterate in all of my portfolio management and personal finance articles is a philosophy that I believe wholeheartedly: Money is a tool.

Nothing more. Nothing less. It is foolish to acquire it for its own sake. Instead, the emphasis should be on an acceptable trade-off between what you have to give up in terms of time, effort, and risk, relative to the benefits you might receive. If you'll be happy living in a trailer by the beach, and don't mind never having a new car or being able to afford luxuries, I'd argue it doesn't make a lot of sense to waste your life in a career you hate, doing work about which you aren't passionate, all so that someday, maybe, at some point in the future, you might be able to sit by that same beach in a nicer house that has little utility to you. I say that because I believe time is the most precious asset you have. The odds are, you only have 27,375 days gifted to you, and that's assuming you're fortune enough to make it to a typical life expectancy. Once those are spent, that's it. Game over.

You can't save them. You can't store them up for future use. They are, as the saying goes, "like sands through the hourglass". It's the nature of the universe. Worse, if you've built a huge fortune and not, yet, enjoyed it, it's going to end up in the hands of other people; perhaps even politicians who take it in the form of Government taxes.

This is the premise from which I start when helping my own friends and family build a financial blueprint. By reminding them of this basic truth, it avoids the temptation to think of saving money as its own end-game; that acquisition is the highest objective. In my view, it would be far preferable for someone who enjoyed traveling to see the world while they are young, healthy, and energetic, ending up with a smaller, less affluent retirement, than try to work non-stop for 40 years, never going anywhere, then hoping to still be in good enough condition to scale mountains and sleep under the stars when they're pulling down Social Security checks. As long as you are explicit in your calculation of the opportunity cost you are giving up, are willing to live with the consequences without expecting others to make up the shortfall, and get more personal fulfillment and happiness out of the funds today than at some point in the future, I think there are situations in which prioritizing investing is a mistake.

To put it a bit more bluntly, I'd go so far as to say that, provided you are doing things mostly right - getting all the free matching money you can from your 401(k) plan and fully funding a Roth IRA, avoiding credit card debt and paying off your student loans - I believe it's sometimes wise to say, "I'm not going to buy another $10,000 worth of that index fund, I'm going to go spend two months living in a rented house in Switzerland to experience a different culture." You can do it.

I know people who have done it; people on ordinary salaries who simply manage their income intelligently.

On the other hand, I sometimes believe it's wise to do the opposite. Instead of buying a new car, deciding to drive your existing one for a couple of years and put the difference in your stock or bond portfolio can give you freedom later to upgrade your home, or get help your grandchildren pay for college. This may sound contradictory but the message is you need to actively choose based on the real cost of what you want, not just wander through life doing whatever feels right at the moment. You'll shortchange yourself that way because it will cause your short-term desires to win out over your long-term happiness.

How do you do that? How do you calculate the real cost? The time value of money.

Let me walk you through two formulas that can change how you view the cash in your pocket or bank account forever.

Using the Future Value of a Lump Sum Time Value of Money Formula to Think of Money as a Tool

First, we need to use a time value of money formula known as the future value of a lump sum to calculate how many dollars you'll have at some point based upon your decision to forego spending them today. I walked you through the calculation many, many years ago in this article but it is worth revisiting here.

FV = pmt (1+i)n
FV = Future Value
Pmt = Payment
I = Rate of return you expect to earn
N = Number of years

An illustration might help you understand its power. Imagine you are standing in a store and you see a new cashmere sweater you want for $399. (The typical investor is disproportionately in the top 50% of median income in the United States so such a purchase would not be out of the ordinary if you are reading this article and fall into its usual demographic. If you can't imagine spending that much on an item of clothing, substitute any other object; a Kitchen Aid mixer or a new iPad) You live in a state with no sales tax on clothing so we can ignore it. You can either buy the sweater, and enjoy it for the next few years, or you can throw the money in your index fund or blue chip stock portfolio to spend or gift to someone else 25 years from now.

Historically, large market capitalization stocks have returned 10% and small market capitalization stocks have returned 12% when acquired using a low-cost, tax-efficient, buy-and-hold investing strategy with little to no turnover, dividends are reinvested, and dollar cost averaging is maintained to take advantage of market collapses. (The data on this is clear.  Interestingly, almost nobody does it except the rich and successful which to paraphrase Vanguard founder John Bogle in a comment he made in one of his books, probably why they are rich and successful in the first place.)

You decide to be even more conservative and calculate a future compounding rate of 8%. You pull out your calculator and plug in the relevant figures.

Step 1: FV = $399 (1+.08)25

Step 2: FV = $399 (1.08)25

Step 3: FV = $399 (6.848475)

Step 4: FV = $2,733

What about inflation, though? Surely inflation matters as you need to protect yourself from its constant drain. You're right. It does. If money is a tool, all that counts is how much it can buy. Inflation is depreciation in the currency. It represents a loss of value so it needs to be included in our numbers.

Adjusting This for Inflation By Discounted It Using the Present Value of a Lump Sum Time Value of Money Formula

The way in which we achieve this is to take the future value you have from the last calculation and discount it back to the present at an estimated inflation rate. Let's imagine you think inflation is going to run 3% over the next 25 years. In this case, you would use a different time value of money calculation known as the present value of a lump sum.

PV = FV / (1+i)n
PV = Present Value
FV = Future Value
Pmt = Payment
I = Discount Rate
N = Number of years

In this case, we plug in your relevant numbers:

Step 1: $2,733 / (1+.03)25

Step 2: $2,733 / (1.03)25

Step 3: $2,733 / 2.09

Step 4: $1,308

This means the question you need to ask yourself is whether or not spending $399 today is worth more to you than having an extra $1,308 in today's equivalent purchasing power 25 years from now. Even if you don't want that money for yourself, as you get older and more prosperous, you'll probably find helping others along the way is more rewarding. For example, for Christmas this year, we gave our niece and nephews shares of The Hershey Company for Christmas along with a big industrial box of their favorite candy. We also give through the family charitable foundation as a way to support causes that matter to us. Those types of things have much more value to us than adding another car or taking another trip.

It becomes second nature after awhile to perform these trade-off analyses that I now do a lot of the calculations in my head as I've memorized the factors that allow me to quickly arrive at the end result. My husband and I make it a game. We have an account setup that anytime we make a decision to forego something - say we can save $8 by picking up a cheaper bulk bag of our favorite coffee at Sam's Club instead of buying it in smaller containers at the corner market - we'll sweep the money into it instantly from our phones. From time to time, we put the accumulated cash to work, acting as if we had spent it; that it doesn't exist. Over the years, seemingly tiny decisions - not ordering a drink at lunch, switching the light bulbs to more energy efficient models in our home - has resulted in significant additional wealth accumulation while helping us avoid decimal creep (the tendency of the financially successful to spend more as their income grows without reflecting on whether the additional spending makes them happier or provides utility). As the spare change compounded over the past decade and a half, we now find ourselves holding extra shares of oil and gas giants, banks, packaged food companies, industrial conglomerates, and other enterprises that pay us regular dividends; dividends that otherwise wouldn't have existed if we hadn't decided what was more important to us, based upon our own, personal values.

These time value of money formulas empower us. They let us more easily identify what we really want, increasing our happiness. Knowledge is power and memorizing the formulas is absolutely free, provided you're willing to write them down a few times and stick them in the back of your mind. Once you go down this path, it's so useful, it can be unthinkable to even consider stopping. Do it. It's unlikely you'll ever have cause to regret it.