Time Value of Money

When I go out for Samosa and Chai with my father, he reminisces how it used to cost 50 paisa per samosa when he was younger. Or how they could buy vegetables for family in under Rs 4 to Rs 5.

When I was in school, a cold drink and patty would together come in Rs 10. Patty for Rs 3 and Cold Drink for Rs 7. Today, those Rs 10 can’t even buy me half a patty.

In such conversations, we do remark that even Rs 10,000 today will be worth nothing after few years. This realisation comes from experience for a lot of us.

But the fact is, this lay at the core of everything we do with money.

‘Time is money’ has more to it than just a three-worded gyaan.

What is the role of time, inflation and interest ?

Time has an opportunity cost.

The time I spend writing this article could have been spent watching television or reading a book.  I give up on the opportunity to do those because I think this is more useful for me (better returns).

It is the same with you reading this. You hope to gain something more than may be browsing your social media timeline.

You make a choice, pick one opportunity out of many. And all the other opportunities that you let go off, is the opportunity cost of the choice you made.

In money, time plays an even more important role.

With time, the prices of items (that money is supposed to buy for you) goes up or down. Over a long term, due to inflation, prices tend to go up.

That lowers the purchasing power of money.

Rs 10 could buy me a cold drink and patty 20 years ago. With time, purchasing power of Rs 10 has eroded.

Another way in which time affects money is it’s earning potential. A money invested over long term grows more because of compounding.

Now if I give you an option to take Rs 1 lakh from me today vs Rs 1.02 lakh after one year, the “one year” time criterion should play a major role in your decision making.

If you opt to take 1 lakh today, your opportunity cost is the potential to earn 2000 in one year. If you chose latter, that is Rs 1.02 lakh after one year, your opportunity cost is what you can do with 1 lakh today.

With time, the purchasing power of money will most likely erode. What you can buy for 1 lakh today, you may not be able to buy for even Rs 1.02 lakh after one year.

Every time you have to make this decision, you cannot be sitting and thinking about what are the two things you want to do with the money, what you want to buy, how much it costs, and therefore what will be your opportunity cost.

One option you always have against any choice you make is to invest the money and earn returns as per interest rate.

Time, interest rate and inflation helps in making an informed decision on the opportunity cost and also forms the basis of Time Value of Money concept.

What is Time Value of Money?

TVM is the concept that money today is worth more than the money tomorrow given its earning potential.

Just like Rs 10 was worth more in past than today. It could buy more things.

A literary version of TVM is “a bird in hand is worth two in bush”.

The monetary version means that a rupee yesterday was worth more than a rupee today. And a rupee today is worth more than a rupee tomorrow.

Variables of TVM

All that was said till now is words. Money today is more than money tomorrow, etc etc.

We anyway have that gut feel. For the same amount, if I offer you money today vs money after one year, you will jump and grab today’s offer. You just know you will be better off with the money in hand.

But the most important concept in finance cannot be only words. It is math too.

And math has variables. Hang in with me, the formula looks sleep inducing, but it is not that bad. Plus, I will tell a shorter way of computing it in excel that is more useful.

And most useful is the practical application of the concept, for which knowing formula is important.

The five variables that make up time Value of money are:

FV (Future Value) : Future Value is the value of money after a certain period of time.

PV (Present Value) : PV is value of money as on day.

I (Interest) : Interest is the return your money can generate if invested.

T (Time period) : T is the time period for which the money is invested and earns interest

N (Number of compounding period) : N is the number of times your money earns interest in a given time period. 7% per annum interest means the money invested will earn interest once a year. So N =1.

Your receive Rs 5 lakh today. You want to know what this money will be worth after 1 year, 5 years and 10 years if the best return you can get is 12% per annum.

So,

PV = 5 lakh | Interest = 12% | Time = 1 year | N = 1 (compounding annually)

After 1 year you will have

500000 +12%*500000

=500000*(1+12%)^1

After 5 Years you will have

=500000*(1+12%)^5

After 10 years, you will have

=500000*(1+12%)^10

So you see, FV = PV*(1+I)^T

When the compounding period(N) is not equal to 1,

FV = PV*(1+I/N)^(N*T)

And therefore,

PV = FV/[(1+I/N)^(N*T)]

TVM functions in Excel

  • To calculate Future Value

=FV(rate,nper,pmt,[pv],[type])

Rate = Interest rate (In our example 12%)

Nper = time period (In our example 1)

Pmt = payment amounts (mark 0)

PV = Present value (In our example -500000. PV is invested, goes out from your pocket, so negative)

Type = when payments (pmt) are due. (leave blank for now)

  • To calculate Present Value

=PV(rate,nper,pmt,[fv],[type])

The future value is positive since we will receive that future value.

Similarly, you have functions to calculate nper(), rate(), pmt().

You can calculate any one variable of other four are known. But for now, only PV and FV are enough.

And that is that.

The formulae that you won’t remember by the time you reach end of this article.

Chuck the math, why should I care?

That, I must say, is a good question.

You need it to understand how with time, you may need to shell out more than what something costs today.

You need it to understand what you should invest today to be able to buy something tomorrow.

Remember I said time, inflation and interest rate form the basis of TVM?

Let us now see how.

The first thing to understand is what inflation and interest rate are doing.

Inflation is making things costlier, it increases the cost price of an item over a period of time.

Interest rate makes money grow, it generates interest on the money that, when reinvested, generates more interest.

So you see, while inflation makes things costlier, interest rate makes money grow.

TVM shows us how.

Future cost of an Item

If you want to buy a house after 5 years that costs Rs 80 lakh today, you should know what it will cost after 5 years. Inflation ( at approx 5%) will cause rise in the cost and you want to know how much you will need after 5 years.

Using inflation rate in place of Interest rate in Future Value calculation,

PV = -8000000

I(or rate) = 5%

T (or nper) = 5

N = 1

Using FV function, FV = 1.02 crores

Effectively, the present value of the house is “compounded” at 5% per annum for 5 years.

Without this knowledge, you will probably plan to accumulate 80 lakh in 5 years and to your horror realise you still can’t buy that house.

Inflation has eroded the purchasing power of money.

With knowledge of how inflation affects cost of an item with time, you know how much you will need.

Current investment for a future purchase

Now you know you will need 1.02 crores in 5 years. The best investment option you know can give you 9% return.

You want to know how much lump-sum you should invest today that you can withdraw after 5 years and buy the house.

You have a future value, and you want to know present value.

FV = 1.02 cr

I (or rate) = 9%

T (or nper) = 5

N = 1

Using PV function, we get Present value equal to Rs 66,35,963.56

Meaning, if you invest Rs 66.35 lakh today in an instrument that gives 9% return per annum, you will be able to buy a house that will cost 1.02 cr after 5 years.  

Effectively, future value is “discounted” at 9% per annum for 5 years.

Money today is worth more than money tomorrow. After 1 year, Rs 66 lakh won’t be sufficient to grow to 1.02 cr in 4 years

TVM is everywhere

Any financial planning you do for yourself, TVM is the foundation on which your plan is built.

For retirement, big ticket purchases, child’s education, vacations, wedding etc.

You first arrive at the future value of current cost by accounting for inflation and then discount the future value by interest rate to arrive at the lump-sum investment required today.

Any financial decision you make, between two instruments, two options to spend your money etc, TVM is at play.

In practice, we rarely invest in lump-sum. We do SIPs.

Also, we sometimes need reimbursement of funds every year or every month.

The “pmt” value in the Future and Present Value calculation takes care of additions or withdrawal of money at regular interval. But that is not for today.

It is not something you have to fret about. It is just something you should be aware of. You do know it by instinct, but sometimes knowing the math opens your mind more to the possibilities and opportunities.

In the end, all we try to do is minimize our opportunity cost by trying to identify the best option possible.  

And that makes TVM so important.


Also published on Medium.

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