Time Value of Money (TVM) means money received today is worth more than the same amount received later because it can earn a return in the meantime. Present value converts a future cash flow into today’s value using a discount factor. These ideas underpin investment appraisal and valuation in ACCA and CFA studies.
Imagine someone offers you ₹10,000 today or ₹10,000 three years from now.
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Which would you choose?
Most of us would choose ₹10,000 today. But have you ever thought about why?
It is not just because we want money immediately. There is a financial reason behind this choice.
Money available today can be invested to earn a return. Money received in the future cannot be invested until we actually receive it.
This simple idea is one of the foundations of finance. It is called the Time Value of Money.
Let's start with a simple example
Suppose you have ₹10,000 today and can earn a return of 10% per year.
Your money would grow as follows:
| When? | Amount |
|---|---|
| Today | ₹10,000 |
| After 1 year | ₹11,000 |
| After 2 years | ₹12,100 |
| After 3 years | ₹13,310 |
After three years, your ₹10,000 becomes ₹13,310, assuming the return is compounded annually.
Now think about the original question.
Would you prefer ₹10,000 today or ₹10,000 three years from now?
If you receive ₹10,000 today, you could potentially grow it to ₹13,310 over three years. If you receive ₹10,000 only after three years, you give up that opportunity to earn a return during the waiting period.
That is why money received at different points in time cannot be compared simply by looking at the amounts.
Money has a time value.
From future value to present value
So far, we have moved forward in time. We started with ₹10,000 and calculated how much it would grow to. This is called compounding.
But investment decisions often require us to do the opposite.
Suppose someone promises to pay you ₹13,310 three years from now. If you can earn 10% annually, what is that future payment worth to you today?
Since ₹10,000 invested today grows to ₹13,310 in three years, the answer is ₹10,000.
We have moved backwards from a future amount to its equivalent value today. This is called discounting, and the result is known as Present Value (PV).
Present value tells us what a future amount of money is worth today, given a particular discount rate and time period.
What exactly is a discount factor?
A discount factor is a number used to convert a future cash flow into its present value.
Instead of calculating the entire discounting process from scratch every time, we can calculate a factor and multiply it by the future cash flow.
The formula is:
Discount Factor = 1 ÷ (1 + r)ⁿ
Here, r is the discount rate per period and n is the number of periods until the payment is received.
Let's use a discount rate of 10%.
For a payment received one year from now:
Discount factor = 1 ÷ (1 + 0.10)¹ = 0.9091
What does 0.9091 mean?
It means that ₹1 received one year from now is worth approximately ₹0.9091 today, when the discount rate is 10%.
Therefore, if you receive ₹10,000 after one year:
Present Value = ₹10,000 × 0.9091
Present Value ≈ ₹9,091
Notice that we did not simply subtract 10% from ₹10,000. We used a discount factor to calculate the present value.
The discount factor accounts for the return we could have earned if we had received and invested the money earlier.
Why does the discount factor decrease over time?
Let's assume the discount rate remains at 10% per year.
| Year | Discount factor | What it means |
|---|---|---|
| 1 | 0.9091 | ₹1 received in one year is worth ₹0.9091 today |
| 2 | 0.8264 | ₹1 received in two years is worth ₹0.8264 today |
| 3 | 0.7513 | ₹1 received in three years is worth ₹0.7513 today |
Notice that the discount factor becomes smaller as we move further into the future.
Why? Because the longer we wait to receive money, the more time we give up to earn a return on it.
At a 10% discount rate, ₹1 received three years from now has a present value of approximately ₹0.7513.
A discount factor is therefore generally less than 1 for a future payment when the discount rate is positive.
Let's apply this to a business decision
Imagine you are considering investing ₹1,00,000 in a small business project.
The project is expected to generate ₹40,000 at the end of each of the next three years. Assume you require a return of 10% per year.
How much are those future cash flows worth today?
We already know how to calculate the discount factors. Now we can use them to convert each future cash flow into its present value.
| Year | Expected cash flow | Discount factor at 10% | Present value |
|---|---|---|---|
| 1 | ₹40,000 | 0.9091 | ₹36,364 |
| 2 | ₹40,000 | 0.8264 | ₹33,058 |
| 3 | ₹40,000 | 0.7513 | ₹30,053 |
| Total | ₹1,20,000 | ₹99,475 |
The present value of the three cash flows is approximately ₹99,475.
Although the project is expected to generate ₹1,20,000 over three years, those cash flows are worth approximately ₹99,475 today at a 10% discount rate.
This is the power of discounting. We can compare cash flows received at different times on a common basis: their value today.
Where does this come into actual finance?
The Time Value of Money is not just a theoretical concept. It forms the foundation of Financial Management (FM) and is used extensively in investment and valuation decisions.
Businesses use these concepts when deciding whether to purchase new machinery, open a new branch, launch a product or invest in a project. Investors use them to evaluate bonds and other investments by understanding the value of future cash flows today.
If you are pursuing a professional qualification in finance, accounting or investment analysis, you will encounter these concepts frequently. They are important building blocks in professional courses such as ACCA, CFA and other finance and accounting qualifications.
Present value, discounting and the time value of money help you understand investment appraisal, NPV, IRR, bond valuation and several other financial topics.
Understanding the logic now will make those topics much easier to learn later. Rather than memorising formulas, you will understand what the calculations are actually doing and why they matter.
We will explore NPV in Part 2 of this series: NPV explained.
The takeaway
The Time Value of Money explains why money available today is not equivalent to the same amount received in the future.
Present Value tells us what future money is worth today. A Discount Factor helps us calculate that present value by converting each future cash flow into its equivalent value today.
Once you understand these ideas, investment appraisal becomes much easier to follow.
In finance, it is not enough to ask how much money an investment will generate. We must also ask when that money will arrive and what it is worth today.
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