# What is time value of money with examples

## Definition – Time Value of Money (TVM)

A sum of money in the hand has greater value than the same sum to be paid in the future. (Investopedia)

It is a common phenomenon that the value of money decreases with the passage of time. Businesses incorporate the concept of the Time Value of Money in their investment appraisal because the cash flows from the projects accrue over several years. So, businesses want to find out the present value of these future cash flows. In this article, we will explain the basis and the understanding on which businesses value money.

### Factors affecting TVM

• Risk – Funds received sooner are less risky than those received later. As time passes, the risk of non-recovery increases.

• Inflation – The purchasing power of money is reduced as the prices of commodities are increased. For example, if you have \$1,000, you can buy a certain quantity of commodities with it but the same sum of money will not be enough for the same quantity of commodities in the future because, the buying power of the money is eroded.
• Interest – This is the most important point that sets the basis for TVM. Businesses convert the future value into present value based on the potential for earning interest from their surplus.

### Explanation of TVM

As we know that banking network exists everywhere in the world. You can find commercial banks nearby no matter wherever you are. How do these commercial banks work? Their business is lending and borrowing money. They borrow loans at a low rate of interest and provide loans at a high rate of interest and the difference is their profit. For instance, if they borrow at 8% and lend at 10%, then 2% is their profit. This is the main activity of the banks.

On the other hand, a businessman doesn’t want to keep his money in the current account. He wants to invest surplus money into different savings accounts and different investments so that the money can be increased.

To understand the concept of TVM, you must keep two things in mind. First, businesses invest the surplus into different investments and the easiest investment is in the bank where they can simply put the money and earn interest. Secondly, banks exist everywhere and they will take the money from businesses and add interest to it. Let us take a basic example as shown below:

Now keep the above table in mind and suppose you have \$100,000 and you invest it in the bank which has an interest rate of 10%. You can see that the bank adds interest of 10,000 (10% of \$100,000) to your invested amount and your bank balance at the end of year 1 increases to \$110,000.

Similarly, If you do not withdraw the money, the bank will add a further 10% interest of \$11,000 (10% of \$110,000) to your outstanding amount of \$110,000 which makes it \$121,000 at the end of year 2.

At the end of 3rd year, \$121,000 will become \$133,100 (if you did not withdraw it of course!)

You can see that, if you are a businessman, you can easily convert this \$100,000 into \$133,100 in 3 years without doing any additional activity except depositing \$100,000 in the bank. So that’s how the banks work and businesses think about the TVM.

Businesses set the minimum required rate of return which is also called the cost of capital. The cost of capital can be calculated using bank interest rate or other factors such as rate of return to shareholders etc. In the above example, the target is to convert \$100,000 into \$110,000 at the end of year 1, \$121,000 at the end of year 2, and \$133,100 at the end of year 3. If the business knows this, it will perceive that:

• \$133,100 received after 3 years = \$100,000 received now (Year 0).
• \$121,000 received after 2 years = \$100,000 received now (Year 0).
• \$110,000 received after 1 years = \$100,000 received now (Year 0).

## Compounding

Conversion of Present Value (PV) into Future Value (FV) is called compounding.

### Formula

FV = PV(1+r)n

Where:

FV = Future Value
PV = Present Value
r    = Rate of Interest in decimal
n   = Time period in years

### Explanation of compounding

An investor wants to estimate how much money he/she will have after a certain period if he/she deposits it into the bank. Let us use the same example as above:

Well, this is an example of compounding. \$100,000 is increasing with time and is increased to \$133,100 at the end of year 3, However, it was a very basic example. We easily calculated the future value by putting the values in the table. But, let’s say, an investor has \$75,000 and he wants to invest it in the bank with an interest rate of 8%. What will the future value be after 7 years? Now things become complex. There is a shortcut to calculate future values without referring to tables and that is by using the formula:

FV = PV(1+r)n

FV = 75,000 (1+0.08)7

FV = \$128,537 approx.

### Example 01 – Compounding

A company invests \$2,000 at 12%. What is the FV after 5 years?

#### Solution

FV = PV(1+r)n

FV = 2,000 (1+0.12)5

FV = \$3,525 approx.

### Example 02 – Compounding

Bilal invested \$100,000 in a bank with an interest rate of 15%. What amount will he receive after 3 years?

#### Solution

FV = PV(1+r)n

FV = \$100,000 (1+0.15)3

FV = \$152,088 approx.

## Discounting

Conversion of Future Value (FV) into Present Value (PV) is called discounting.

### Formula

PV = FV/(1+r)n

Where:

FV = Future Value
PV = Present Value
r    = Rate of Interest in decimal
n   = Time period in years

### Explanation of discounting

An investor wants to estimate how much money he/she has to invest today to receive an estimated sum after a certain period. Let us use the same basic example:

Investor invests \$100,000 and received \$133,100 in 3 years’ time. However, if the tables are not given, it will be very hard to reverse-calculate the present value. There is a shortcut to calculate present values without referring to tables and that is by using the formula:

PV = FV/(1+r)n

PV = 133,100/(1+0.1)3

PV = \$100,000

The above formula can also be presented in the following way.

PV = FV x Discount Factor

Where,

Discount Factor = 1/(1+r)n

r    = Rate of Interest in decimal
n   = Time period in years

### Example 01 – Discounting

A company wants to have \$23,000 in 7 years. How much investment is required if the rate of interest is 8%?

#### Solution

PV = FV/(1+r)n

PV = 23,000/(1+0.08)7

PV = \$13,420 approx.

## Example 02 – Discounting

Saad wants to have \$300,000 in 3 years. What amount will he have to invest today if the rate of interest is 18%?

#### Solution

PV = FV/(1+r)n

PV = 300,000/(1+0.18)3

PV = \$182,589 approx.