How to Calculate Discount Factor? Example, Formula

When money flows through in a business transaction, the amount and period involved can make a difference in precisely calculating the cost of money. Knowing what causes the impact and how it could be assessed is important. The study of the Discount Factor helps us understand this important phenomenon in Financial Management. Once understood, it becomes easy to devise ways for discount factor calculation and develop a simple discount factor formula.

Did You Know? A small change in the discount factor can greatly impact the amounts paid over a long period.

What is the Discount Factor?

To understand the concept of the Discount Factor, let us say that you gave a loan of ₹4,00,000 to a friend today. The friend promises to repay you ₹20,000 every quarter over five years. He promptly repays the loan as promised. At the fifth year's end, you got your money in full. Now, what is the question you need to ask yourself? Am I a gainer or loser in this loan transaction? 

To a layperson, it is a no-profit, no-loss situation. But, if you are a businessman, you will see the loss. For example, the interest you would have earned if you had invested in a bank is an apparent loss. Also, because of inflation, the purchasing power of ₹4 lakhs today will surely be lesser than it was five years ago. This means if you could buy 100 Nos of a component five years ago, you will get fewer features for the same amount today. 

Such a fall in value is called Discounted Value or Present Net Value. The quantification of such a drop in value is done using a multiplier. The multiplier is called the Discount Factor, and the process is called Discount Factor Calculation.

Also Read: What is Accounting Cycle: Definition and Steps in the Accounting Cycle Process.

What is the Definition of a Discount Factor?

Discount Factor can be defined as the numerical figure applied for evaluating the Net Present Value of the amounts flowing in over a pre-determined period. The Discount Factor will depend upon the cost of money (interest or discount rate), the period of repayment and the frequency of such payments.

How is the Discount Factor Useful?

The Discount Factor is a crucial tool in determining the value of the money received over several years compared to the value of that money if it were available with you today. Thus, it becomes very important when there are deferred payments, especially if the duration is long and over several years. The secret of the huge impact of Discount Factor calculation lies in the power of compounding. There is a famous statement attributed to Albert Einstein. "Compound interest is the eighth wonder of the world. He who understands it earns it; he who doesn't pay it".

An Example of Discount Factor

You may have read about an old story often told by mathematical and finance pundits. The story goes like this:

Once, a simple-looking subject of the kingdom came to the King and presented him with a game he had developed. The King loved the game so much that he told the creator, "Ask whatever you want. I will reward you." The man replied, "King, I don't want anything big. I just need a grain of rice on the board's first square, double the amount on the next, double the previous number in the next, and so on, till all 64 squares are filled. Please grant me those grains."

The King was surprised at this man's limited ambition and naivety. The King offered to give him much more in gold and silver. But the man politely declined and said, "No, Your Majesty. Just give me the small gift I asked for, and that will do".

The King called his servants and ordered them to comply with this request immediately. After a while, the servants came and told the King, "Your Majesty. We have exhausted all the stocks of rice in the kingdom but are unable to fill the quantity required for the 64 squares. It seems impossible".

The shocked King only then realized that this genius was asking for what looked so simple 1:2 4:8 16: 32 64:128 and so on until 64 iterations. Through a simple compounding formula of Final amount = Initial amount raised to the power of 64, the number is a staggering 18,446,744,073,709,600,000. This is the power of compounding.

Thus, the compounding stages become extremely crucial in negotiating a transaction using the Discount Factor.

Also Read: What is Double Entry System of Accounting ? Understanding Double Entry System

Steps for Calculation of Discount Factor

Following are the simple steps for the calculation of the Discount Factor.

• Step One: Study and assess the Discount Rate (or the interest rate) prevailing in the market. Let us call it “r%” per annum. This has to be carefully done by studying the trends in the financial markets, comparing historical data for similar businesses or industries and trends in banking rates. An error here could prove costly.
• Step Two: Determine the duration of the payment from start to finish. It is normally in years. Let us denote it as “t”.
• Step Three: Choose the agreed frequency of assigning interest (or Discounting Factor). It could be annual, half-yearly, quarterly or monthly, as per the contract. Let us denote it as “n.”
• Step Four: Use the Discounting Factor Formula to calculate the Discounting Factor to be applied.

The formula for Discount Factor

The formula for Discounting Factor calculation is as shown below:

Discount Factor = 1 / (1 + Discount Rate) ^ Period Number

where

“r” is the Discount Rate (rate of interest) per annum in %

“t” is the period in years

“n” is the number of times compounded in a year

As you can see, the Discount Factor calculation is simple to understand and easy to use. However, as mentioned earlier, each component greatly impacts the results. A small change in any components in the Discount Factor Formula calculations could lead to a potentially huge loss.

Continuous Compounding

Continuous compounding is a hypothetical concept where it is assumed that the principal amount is compounded perpetually. This means that, in theory, the number of compounding steps could be infinite. Though not a practicable exercise, this concept is used by Financial Management analysts. It is purely hypothetical.

For theory lovers, the formula for the Discount Factor Formula for Continuous Compounding is shown below:

A = Pe^rt 

where,

• P = the initial amount
• A = the final amount
• r = the rate of interest
• t = time
• e is a mathematical constant where e ≈ 2.7183.

In Excel, use the Exponential formula as EXP(minus the rate of interest multiplied by the number of years)

Also Read: What is the Difference Between Single Entry and Double Entry Bookkeeping?

An Example of Discount Factor Calculation

In this example, we shall calculate Discount Factors for different cases of compounding.

We can clearly see the value of money gets much lower as the period extends.

Conclusion

The power of the Discount Factor is now clear to you. A lot of attention must be paid when negotiating a transaction that involves extended payments. As you have seen, three factors must be considered such as the rate of interest for discounting, the duration of payment and most importantly, the compounding frequency. If these are taken into account, using the discount factor formula, you will obtain the true value of money that you will realise.

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