Understanding the Time Value of Money

• What is the time value of money? 
• The mathematics of TVM
• Applications of TVM
• How to calculate TVM
• TVM in personal finance 
• Challenges and considerations 

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• The time value of money (TVM) is the concept that a dollar today is worth more than a dollar tomorrow.
• Understanding TVM allows you to evaluate financial opportunities and risks.
• The principle underlies almost every financial and investing decision you make.

The time value of money (TVM) is the concept that the money you have in your pocket today is worth more than the same amount would be if you received it in the future because of the profit it can earn during the interim.

For example, let's say you can either receive a $100,000 payout today or $10,000 per year for the next ten years totalling $100,000. Ignoring taxes, the $100,000 payout today is worth more, according to the TVM principle, because you can put your money to work. For example, you can invest in stocks, buy real estate, or put it in a certificate of deposit (CD).

Understanding the time value of money can help you in making decisions ranging from which job has better salary terms, what's a good rate for a loan, or whether the investment you're considering has good growth potential.

What is the time value of money? 

Definition and basic principles 

The time value of money is an important concept to keep in mind because your money, once invested, can grow over time. Even if you were to just put it into a CD or savings account, the money can earn compound interest, and the impact of compounding on investment growth can be significant. 

On the flip side, money that is not invested will lose value over time. Just think about what you could buy for $1 when you were a child compared to what that same $1 would get you today. This is because inflation and loss of potential earnings erode the value of your dollars. If you keep your money under your mattress for 10 years, not only will it be worth less because of inflation, but you'll also miss out on the interest it can earn when invested. 

"So many young people are so busy juggling life, they are missing out on the compounding returns of investing smaller amounts of money," says Jeff Rose, founder of GoodFinancialCents.com. "Say, for example, a 25-year-old were to invest $50 per month today. They would have to invest 3-4 times that to make up the difference if they procrastinated until they were 35."

TMV is a fundamental concept that provides the foundation for virtually every financial and investing decision. From taking out a loan to negotiating a salary or making a purchase decision, use the time value of money to evaluate the best financial course of action.

Quick tip: "An understanding of the time value of money could help when deciding between a job that offers a decent salary and sign-on bonus, and one that pays more on a yearly basis but offers no sign-on incentives," says Brenton Harrison, a certified financial planner based in Nashville, Tennessee.

The mathematics of TVM

To calculate TVM, you need a handful of variables. 

Present value (PV) 

Present value (PV) is the value that a future sum of money (or combination of income streams) has right now. For example, the present value of $1,050 that you will earn one year from today with an interest rate of 5% is $1,000. 

Future value (FV) 

Future value (FV) is the value that a current sum of money (or asset) will have at a predetermined future date based on an expected return (or rate of growth). For example, the future value of $1,000 one year from today based on a 5% annual growth rate is $1,050. 

Discount rate 

The discount rate is the rate of return used to determine the present value of an asset or investment. Another way of putting this is that the discount rate is the return an investor would miss out on by accepting an amount in the future as opposed to accepting it immediately. 

Compounding frequency

The compounding frequency, or how often interest is assessed, can have a significant impact on future value. If an investor puts their money into an interest-bearing asset, this interest can be assessed on a monthly or quarterly basis, for example. 

Applications of TVM

Investment analysis 

The TVM can be harnessed when evaluating different investments. For example, interested parties can use TVM when valuing bonds, as these securities have a par value, meaning a price that issuers have promised to pay the buyer at a specific point in time. Further, many bonds make regular (coupon) payments to their owners. Armed with this information, interested parties can calculate a bond's present value. 

Loan amortization 

The TVM plays a key role in amortization, which is basically the process of lowering the book value of a loan over time. Lenders need to calculate payment schedules when extending credit to borrowers. A dollar lent to a borrower today is worth more than a dollar paid back either tomorrow, next month or a year from now. 

Retirement planning 

When planning for retirement, investors can benefit from compound interest, which refers to interest that is charged on top of interest that has already built up. For example, if an investor puts $100 into an asset that pays 5% in interest every year, it will be worth $105 at the end of the first year. However, at the end of the second year, it will be worth $105 (1.05) or $110.25. 

How to calculate TVM

Formulas and examples 

Practical examples of TVM calculations can help provide clarity for interested parties. We'll use one here. Let's say someone would like to buy your car and they can offer you $15,000 for it today or $15,500 if they can pay you two years from now. TVM teaches us that $15,000 today is worth more than $15,500 in two years. 

Here's the basic formula used for this example:

• PV is the present value of money.

• i is the interest rate or other return that could be earned.

• t is the number of years to take into consideration.

• n is the number of compounding periods of interest per year.

This will help you determine how much money you will have if you took the $15,000 and invested it today or if you waited two years for the $15,500. 

An example of using TVM

Using the example above, let's say you can invest the money from selling the car today for $15,000 in a CD that pays 2% every year, compounded monthly. To calculate the value of the money in two years, here's how it works:

FV = $15,000 x (1+(0.02/12))(12x2)=$15,612

This means the $15,000 you get for the car today will be worth $15,612 in two years. If you wait until two years from now to receive the $15,500 payment, you will lose out on $112 in interest you could have earned in that time. With investments that have higher returns, such as stocks or real estate, the missed opportunities will be even bigger.

While you probably won't be using this formula regularly to calculate future value by hand, it gives you an idea of the opportunity cost of money today versus money tomorrow. This can help you make better financial decisions in the future. 

For example, when budgeting, keep in mind that your annual expenses will go up because of the time value of money. The return used is usually the inflation rate.

"We've seen the time value of money come into play in the past year as rent and grocery prices skyrocketed," says Jay Wu, CFA, founder of MoneyKnock.com. "Failure to include time value of money in expenses can cause you to under budget."

Quick tip: The formula for figuring the future value of money shows us that money only grows through investment. Delaying an investment is a lost opportunity to grow your wealth.

TVM in personal finance 

Budgeting and saving 

When budgeting, individuals should keep in mind that every dollar they avoid spending can be saved, which can in turn be invested in something that will generate a positive return over time. Any dollar saved and invested today will be worth more than the same dollar saved and invested tomorrow. 

Debt management 

When managing debt, individuals should keep in mind that any dollar eliminated from their debt today will be less costly than the same dollar eliminated from their debt tomorrow (or further down the line). As a result, many individuals can benefit from focusing on frugality, keeping their expenses down and using whatever excess funds they have to reduce their existing debt load. 

Planning for future expenses 

Individuals can use the TVM to their advantage when planning for future expenses. More specifically, they can invest now in assets that will rise in value over time so that they can make these purchases. 

Challenges and considerations 

Inflation and its impact on TVM 

Inflation has a negative impact on the TVM, because it causes the purchasing power of money to decrease over time. In other words, a dollar will be worth less in the future than it is today. 

Interested parties can overcome the inevitable deterioration of their purchasing power by investing in assets that generate positive returns. 

Estimating future costs and returns

 Nobody knows for certain what will happen in the future. For example, you have no idea how much the car you want to buy now will cost five years from now. It is impossible to know how much the components, for example steel, will rise in value. 

When it comes to investment, risk is an inherent factor. You never know for certain what returns a specific investment will provide. While a bond may have a par value, the issuer of that bond could potentially default and never pay you back the amount you invested in the first place. 

The time value of money is an important concept to understand for personal finance. It can help you decide how much to budget, evaluate a job offer, figure out if a loan is a good deal and help you save for the future. TVM showcases why your money loses value over time because of inflation. 

Apply the TVM formula to any loans you have to determine if it's better to pay them off or invest. You can also use it to see how increasing your retirement contributions can affect the future value of your dollars. It's a great tool that gives you information that can help you make smarter financial decisions.

FAQs

The time value of money is crucial because it allows individuals and businesses to evaluate how much money will be worth in future terms, which can in turn enable them to make better-informed saving, investment and borrowing decisions. 

Inflation has a negative impact on the time value of money, because it decreases the purchasing power of money over time. A dollar will purchase more today than it will in the future. 

Being aware of the time value of money can certainly motivate an individual to build up personal savings, as money saved today will be worth more than money saved tomorrow. 

Simple interest is assessed on the principal, for example the amount saved, whereas compound interest is assessed on the original principal and all interest payments that have been made thus far. 

You can pick the right discount rate by harnessing the risk-free rate, expected inflation and the risk premium for the investment in question. As a general rule of thumb, the higher the perceived risk, the greater the discount rate needs to be to compensate for that risk. 

Reference

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