What Is the Time Value of Money?

Money is known as a measure of value, but does the value of money itself change over time? Given the choice, would you rather receive a sum of money now or wait until the end of the year? Why does a bowl of pho that cost VND 10,000 ten years ago now cost you VND 50,000? All of this comes down to a very important financial concept: the time value of money.

The time value of money (TVM) is the idea that a sum of money has a different value at different points in time. Generally, money today is worth more than the same amount in the future. That is why we tend to prefer receiving money now rather than at some point in the future

The time value of money is a core principle of finance. It is also known as present discounted value.

Financial basics: the time value of money

Why Does Money Have a Time Value?

Investors prefer to receive money now rather than the same amount in the future because money, once invested, grows over time. For example, money in a savings account earns interest. Over time, the interest added to the principal earns even more interest. That is the power of compounding.

If the money is not invested, on the other hand, its value erodes over time. If you leave VND 100 million sitting in a safe for three years, you lose what it could have earned if invested during that time. Its purchasing power even falls, because inflation reduces the value of money.

Consider this hypothetical situation: you lent a friend VND 100 million when they were going through a hard time. Some time later, they have become successful and come back to repay you. They make you 2 offers:

1. Repay you VND 100 million right now
2. Repay you VND 100 million in 2 years’ time.

This would not be worth discussing if you weren’t torn: in 2 years you plan to study abroad and expect to need exactly VND 100 million, while right now you have no other need for the money.

So would you take the VND 100 million now, or in 2 years?

Many of us might choose option 2, thinking that if we took the VND 100 million now we wouldn’t know what to do with it and might fritter it away on things we don’t need.

But before you decide, answer these 2 questions:

1. Is VND 100 million today equivalent to VND 100 million in 2 years?
2. What is the difference in benefit between receiving VND 100 million now and VND 100 million in 2 years?

To make the right decision, you need to understand how cash flows move over time and compare the value of money today with its value in the future. Once you understand the time value of money, you can make better decisions in daily life and in your own investments.

How Is the Time Value of Money Calculated?

In every case, the basis for comparing and choosing between money now and money later is the principal and how it changes as it earns interest. An important rule of comparison is that the things being compared must be viewed on the same basis, and comparing the time value of money is no exception. We need to convert future sums into present value to see whether an investment earns more than the amount originally put in.

There are 2 concepts in the time value of money: present value and future value.

How to Calculate the Future Value of Money

Future value: the value that can be received at a point in the future (FV_n), including the original principal (PV₀, the present value) and all the interest earned up to that point (I).

The method of calculating interest is one of the most important factors affecting the future value of money. In practice, there are 2 methods: simple interest and compound interest, and compound interest is by far the more common. The formula for the future value of a cash flow using compound interest is:

FV_n = PV₀ * (1+i)^{^}n

or

Future value = Present value*(1+ interest rate per period) ^ (number of periods)

From the future value formula, we can easily derive the formula for the present value of a cash flow:

=> PV₀ = FV_n / (1+i)^{^}n

Going back to the earlier example, let’s work out the present and future value of each option to make the most sensible choice.

In the first option, we take VND 100 million now. Assuming the current interest rate is 10% a year, the future value of VND 100 million after 2 years is:

FV₂ = PV₀ * (1+0.1)²

FV₂ = VND 121 million

So the future value in 2 years of VND 100 million today is VND 121 million. Clearly, taking VND 100 million now is better than receiving VND 100 million in the future (VND 121 million > VND 100 million).

If you’re not yet convinced, let’s work backwards from option 2, converting it to present value by discounting the cash flow. VND 100 million received in 2 years is worth, in today’s money:

PV₀ = FV₂/(1+0.1)²

PV0 = VND 82.64 million

So the present value of VND 100 million in 2 years is only VND 82.64 million, less than the present value of taking the money now. In other words, we should take the VND 100 million today unless we are offered at least VND 121 million in 2 years’ time.

This leads us to one of the most important conclusions in finance – a dollar today is worth more than a dollar tomorrow.

Why Does the Time Value of Money Matter?

The time value of money can guide investment decisions. For example, suppose an investor can choose between two projects, Project A and Project B. They are identical except that Project A promises a cash payment in the first year, while Project B pays the same amount in the fifth year. Based on interest rates, inflation, risk and so on, we can then calculate and make the right decision.

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