Many of you might already know about it. But I get a lot of mails from people whose questions clearly show that there is some confusion about the concept of ‘Time Value of Money’
Hence in this post, I will try to write in detail about everything that is related to the time value of money and, is important for a saver / investor to know about.
Request: If you think someone can benefit from reading this post (and clear their doubts about this important concept), then please share this post with them.
So lets get on with it…
The core idea behind time value of money is that, a rupee ‘today’ can earn and grow with time (if saved / invested). That is why a rupee today, is worth more than a rupee in the future.
Lets put it in another way.
A rupee today is not the same as a rupee in the future. Why not? Its because I can take a rupee today and earn something (interest, dividends, etc.) on it. So it takes more than a rupee in the future to equal a rupee today.
So now that you have understood the concept broadly, here is one of the accepted definitions of Time Value of Money:
The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.
Now there are 2 basic and very important concepts within the idea of Time Value of Money. These are Present Value and Future Value.
Present Value determines today’s value of a cash flow, which is to be received in the future.
Future Value determines the value, an investment made today, will grow to in the future.
Lets now explore these in detail.
Present Value (PV)
Whenever the words ‘Present Value’ are used, always remember the saying ‘A bird in the hand is worth two in the bush.’
Suppose you have two options:
Option 1: Get Rs 1 lac today
Option 2: Get Rs 1 lac after one year
Assuming that there are no obligations or hidden terms and conditions, which option will you choose?
It’s a no-brainer. You will choose option 1.
Now think of it. Why did you actually chose that option?
It is simply because you can take Rs 1 lac today and earn risk-free interest on it. Waiting an year to get the same amount doesn’t make any sense. You should be adequately compensated (monetarily) for waiting a year. You should get more than Rs 1 lac if you wait.
That’s it. This is the whole concept of Present Value.
To calculate Present Value, the formula takes a future amount, and discounts it using the interest rate to find today’s worth of this money.
Lets apply this logic in above Rs 1 lac example.
So lets say you want to know the Present Value (PV) of Rs 1 lac, which is available after 1 year – which is Option 2.
The formula is,
Let’s use this formula to figure out the present value of Rs 1 lac, assuming a 6% interest rate and a 1-year time frame.
So the calculation looks like this:
= Rs 1,00,000 / ( (1 + .06) ^ 1)
= Rs 94,339.
This means that today, the value of Rs 1 lac which you will get after 1 year (Option 2), is Rs 94,339. This is clearly a bad deal compared to the 1st option, where you are getting Rs 1 lac today itself.
Another way of looking at this is that you need to invest Rs 94,339 today, at 6% interest rate, to grow it to Rs 1 lac after one year.
So at 6% interest rate, Rs 94,339 today is same as Rs 1,00,000 after one year.
But what if this Rs 1 lac was available to you after say, 3 years? What will be its present value then?
Using the above-described formula, it will be Rs 83,961
= Rs 1,00,000 / ( (1 + .06) ^ 3)
= Rs 83,961
This points towards an important fact. The value of a rupee tomorrow is less than that of a rupee today. But the value of a rupee, day after tomorrow is even lesser.
Now lets see what happens if we have higher interest rate scenarios.
Suppose you can invest this amount for a year at 8%.
In this case, the value of Rs 1 lac (which is available after 1 year) will be Rs 92,592.
This shows that higher the interest rate is, lower the present value will be today. Similarly, lower the interest rate is, higher the present value will be today.
The concept of Present Value (PV) is the basis of most of the calculators which are used for estimating the amount of money needed to achieve a future goal (ex: retirement).
So if you want to know how much you need to invest (one-time) today, to have it grow into Rs 1 Crore in 15 years, then it will be calculated as follows:
Note – Assumed 9% returns in below calculation:
= Rs 1,00,00,000 / ( (1 + 9%) ^ 15 years)
= Rs 27.45 lacs
It means that if you put Rs 27.45 lacs today into an investment, which will earn you an average of 9% every year, then this money will grow each and every year at 9% until it becomes Rs 1 crore after 15 years.
Lets verify it:
That is all I could think about Present Value. But the above table used for (verification) has inadvertently resulted in the concept of Future Value being displayed. But that is not surprising as PV and FV are two sides of the same coin.
So lets move onto the discussion in Future Value (FV).
Future Value (FV)
As the name suggests, Future value is the future worth of an amount of money, invested today. So if you have Rs 1 lac available today, and you invest it in an asset which pays 8% every year, then after exactly 1 year, your Rs 1 lac investment will become Rs 1.08 Lacs.
By using the below formula for future value:
Calculation will be as follows,
= Rs 1,00,000 x ( (1 + 8%) ^ 1 year)
= Rs 1,08,000
If you want to see an example which has more number of years, then you can just go through the Rs 1 crore example, given earlier in this post again. It uses the concept of FV to verify the results received in PV calculations.
So in that example, Future Value of Rs 27.45 lacs after 15 years (at 9% interest) is Rs 1 crore.
It is worth observing that after completion of 1st year, the interest from there on is not only earned on the initial investment of Rs 27.45 lacs, but also on the Rs 2.47 lacs interest that was generated after the 1st year. This occurs ofcourse, because of compounding – interest is earned not only on the initial principal but also on the accumulated interest.
Now you might be wondering that these are mathematical calculations and you don’t need to pay attention to them. But ‘Time Value of Money’ is one of the most important financial concepts, which one needs to understand if he / she wants to live a financially comfortable life.
It is worth noting that whenever you make a financial decision, you sacrifice something. For example, you might sacrifice current buying to invest for future purchases, preferably more valuable ones. On the other hand, you might gain access to an expensive item now, by taking a loan and sacrificing future earnings and servicing EMIs from them.
So if we were to focus just on saving and investing (and not loans) for time being, then whenever you save or invest a rupee, you need to judge whether this sacrifice of a rupee today, will result in a future amount which is more than a rupee or not. If its not, then there is no point in saving or investing. Isn’t it?