How to Calculate the Present Value of Past Money?

Have you ever thought that the 100 TL you have today is more valuable than the 100 TL you will have a year from now? That’s because the value of money changes over time; inflation erodes it, while interest and investments can grow it. That’s why it is so important to know the concept of the time value of money, one of the most fundamental principles of the financial world. When planning your investments, you need this concept to calculate the present value of the income you will earn in the future or to see what today’s savings will turn into years later. In this Papel Blog article, we cover the time value of money in all aspects, explaining how it affects everything from your daily life to investment decisions.

What is the time value of money?

The time value of money, one of the most fundamental principles of the financial world, is based on the understanding that “money today is more valuable than the same amount of money in the future.” The reason is that while money is held, it can generate returns through investments such as interest or dividends, and inflation reduces the purchasing power of future funds. For example, the 100 TL you have today can turn into 105 TL next year if invested with 5% annual interest. However, receiving the same 100 TL a year later means missing out on potential returns. This also reveals the concept of opportunity cost. The time value of money is widely used in investment decisions, loan and debt calculations, savings plans, and financial reporting. With formulas that calculate the present value of future cash flows or the future value of today’s money, individuals and businesses can make accurate financial decisions.

Calculating the present value of past money

The commonly used method to calculate the present value (PV) of a sum of money you had at a particular time in the past (or a sum to be received in the future) is the Present Value formula. This formula is expressed as follows:

 

PV = \frac{FV}{(1 + i)^n}

 

Here, FV represents the future value, i represents the periodic (e.g., annual) interest or discount rate, and n represents the number of periods. Let’s say you will receive 1,000 TL five years later, and you want to discount it to today at a 10% annual discount rate. Substituting the values into the formula:

 

PV = \frac{1,000}{(1 + 0.10)^5} = \frac{1,000}{1.6105} \approx 620.92 \, TL

 

According to this result, receiving 1,000 TL in five years is equivalent to having approximately 620.92 TL today.

 

This calculation method, which is very useful for determining the present purchasing power of past or future money, is often used in investment decisions, loan repayment plans, and financial analyses.

The time value: future value of money

This calculation shows how much value money can gain over time by indicating how much a certain amount today will be worth after a given period through interest or investment returns. The Future Value (FV) formula is expressed as:

 

FV = PV \times (1 + i)^n

 

Here, PV is the present value (the invested amount), i is the periodic interest rate, and n is the number of periods. For example, if you invest 1,000 TL today at an annual interest rate of 12% for 3 years, the calculation would be:

 

FV = 1,000 \times (1 + 0.12)^3 = 1,000 \times 1.4049 = 1,404.90 \, TL

 

According to this example, the amount you will receive after 3 years is 1,404.90 TL.

 

In addition, the discounted cash flow (DCF) method is also used to calculate the present value of expected future cash flows. This method, which discounts the income expected from an investment in coming years to its present value using a specific discount rate, is one of the fundamental financial analysis tools frequently used in investment decisions and company valuation.

Inflation and the purchasing power of money

Inflation, which refers to the increase in the general price level over time and directly reduces the purchasing power of money, means that the funds you hold today will buy fewer goods and services in the future. For instance, in an environment with 20% annual inflation, a product you purchase today for 100 TL may rise to 120 TL a year later; this shows that your money has lost value. Interest is the most essential tool used to protect against this loss in value. When you invest your savings with interest, your money increases nominally over time; however, for this increase to translate into tangible gains, the interest rate must be higher than the inflation rate. If not, even though you earn interest, you inevitably suffer a real loss of purchasing power. Therefore, when making financial decisions, it is essential to look not only at the nominal interest rate but also at the genuine interest remaining after inflation.

The use of time value in financial investments

Investors use the time value particularly in discounted cash flow (DCF) analyses, where the future cash returns of assets are discounted to the present value. In this way, cash flows occurring in different years become comparable; thus, the investment’s present value is calculated and its profit potential is evaluated with the net present value (NPV) measure. TVM is a critical decision-making tool, especially in areas such as capital projects, bonds, and real estate investments that provide income over the long term. For example, by discounting the cash flow expected from a project or asset in the future to the present at a specific annual discount rate, the investor can clearly see the equivalent return today. In addition, portfolio managers and pension fund managers also use TVM when creating retirement plans or evaluating investment opportunities, by calculating the total profit and risks that today’s investment will bring in the future. A similar approach is used in real estate investments as well. Rental income or sales estimates spread over future years are discounted to the present with an appropriate discount rate to determine the current value of the investment. Thus, investors can compare different alternatives and objectively analyze which is economically more advantageous.

 

Sources: 1, 2.

 

This blog post contains general information, not legal, financial, or investment advice. The content is prepared for informational purposes only, and you are advised to seek professional advice for your specific circumstances. The expressions in this article do not carry any binding nature or responsibility and reflect only the author’s evaluation. All your decisions are your responsibility, and Papel Electronic Money and Payment Services Inc. accepts no liability for any consequences arising from them.