Make wise financial decisions with the time value of money: Definition Compounding, Discounting

Which one is worth more: $100 dollars today or $100 dollars a year from now?

Or does it depend on whether you are receiving the money or paying the money to someone else?

The answer of the above questions depends on the concept of time value of money. Let’s explore this concept in detail and understand how this concept helps in making wise financial decisions.

Understanding the time value of money:

Time value of money is an important concept in the corporate finance field especially when you are dealing with loans, capital budgeting, and investment or other finance related decisions. It is a fundamental block on which the entire finance field is relying or built upon.

But there comes quite a logical question in our mind that why does money has a time value?

TVM is a concept that is based on the principle that a rupee received today has a greater value than a rupee received in the future.

Let’s take a simple example to know the concept:

Just imagine if you want to choose between taking $100,000 today or after 50 years.

Which option would you have opted for?

Of course, the first one, right?

Now yes there are reasons to justify in choosing the option:

1. High purchasing power: The more sum of money can be exchanged with more goods and services today than after 40-50 years. For instance, the value of $1000 was more 100 years ago than today.
2. Risks involved: There are certain risks involved in getting money back that you have today. For instance, you may lend money to a person for a year but that particular person goes bankrupt or runs away, you will lose your money.

Time is money:

Many of you have heard your elders saying that “Time is money” and they are right. The present value of future cash flows is less worthy the longer you wait to receive it since money has time value. That is one of the reasons we expect that the future value of cash flows to be greater than the present value. But interest rates and compounding periods are the biggest factors effecting the future and present values. Moreover, receiving the money instantly also reduces the changes of default payments.

A base of TVM: Compounding and Discounting:

Future and present value can be computed by calculating two aspects that is compounding and discounting. It is important to have a proper understanding of these terms before getting the details of time value of money.

Compounding:

The process of finding the future value of an investment made today or series of investments made over a period of time. In simple terms, it means moving your sum of money forward in time.

For example, your investment of $100,000 at an interest of 10% p.a. will turn into $120,000 in a period of 2 years.

Discounting:

The process of determining present value of an investment or a series of investments to be received in the future. In simple terms, it means moving your sum of money backward in time.

For example, you will receive $120,000 after 2 years from now, thus the present value will be $100,000.

Key components of time value of money:

After knowing the brief about time value of money, let us now look at the key elements:

These five elements are very important in determining the time value of money problems:

1. Rate (i) or (r): It is a rate of interest, which is used in the compounding or discounting a sum of money.
2. Periods (n): It is the total number of periods used in the calculation of time value of money, which can be weekly, monthly, quarterly, semi-annually, and annually.
3. Present value (PV): It represents a sum of future cash flows at a present date. Discounting the future cash flows does it.
4. Future value (FV): It determines the sum of money to be received in the future that is obtained by compounding the present cash flows.
5. Payment (PMT): It represents period payments that are equal to be paid or received in each period. It has a positive value when you receive the payments and negative value when you make the payments.

Let us take a simple example and use formula to determine PV and FV:

You are having $1000 today and you can invest it for a year at the rate of 7% interest (discount rate). The future value of $1000 from now is:

Future value = present value x (1+ discount rate)

Future value = $1000 x (1+ 0.07) = $1000 x 1.07 = $1070.

Alternatively, to have $1000 today, you would have needed to invest some money a year ago. Now your future value is $1000 and if you are using the same interest rate, your present value would have been:

Present value = future value / (1 + discount rate)

Present value = $1000 / 1.07 = $934.58

TVM timeline:

You can solve the TVM problems using simple timelines and formulae.

It is better to portray the 5 key components on a proper timeline in order to visualize the problem. It is simple, just feed the data with 4 components and solve the unknown one.

One can use financial calculators, regular calculators, software, and spreadsheets to solve the TVM problems.

Real life application of TVM:

1. Bond value calculation: One can simply calculate the PV of future cash flows to compare with the sum of money you pay today to judge whether the investment bonds really make sense or not.
2. EMI Calculations: You can use TVM to compute EMI payments together with interest.
3. Determining house loan: It also helps in determining the amount of down payment and interest rate payments of the loan amount, credit card calculations, etc.
4. Bottom line: As they said, time is the greatest asset if used wisely. So, if you are smart enough, you should use your money wisely to create more out of it.

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