# What is Time value of money?

### Author: Jins Victor

“Time value of money” is one of the central concepts in finance. Every financial decision involves the application of this concept directly or indirectly. For example, if a bank lends you Rs 10,000 for 6 months, you will have to repay Rs 10,000 + interest at the end of 6 months. What you paid to the bank as interest is actually the time value of Rs 10,000 for 6 months. Now, let’s assume that you gave Rs 10,000 as fixed deposit to the bank for 6 months. The bank, at the end of 6 months will pay back Rs 10,000 + an interest as a compensation for allowing them to use your money for 6 months. Hence, Time value of money is the compensation that one receives for foregoing the use of money for a given period of time or the compensation one will have to suffer in future for spending money now. The calculation of time value involves simple mathematics and it’s easy to calculate.

**Time value of money.**

The principle is – Rs 100 today is more valuable than Rs 100 a year from now. The reasons for this is quite simple to understand –

- Since the cost of living goes up, your money will buy less goods and services in the future. So your money has more value today.
- If you have that money today, you can invest and earn returns. When you receive the money at a future date instead of receiving it today, you lose the interest or profit you would have made, had this money been invested somewhere.
- You prefer to have money today since the future is uncertain.
- You have saved money by sacrificing present needs; hence in future you need to be compensated for this.

**Many sides of time value of money.**

The concept of time value of money comes into play in many scenarios:

- One, when you are eligible to receive some money now, but the actual receipt is delayed. In this case, you need to be compensated for the time delay – A calculation called future value or (FV)
- Second, you will become eligible for receiving some money in future (say Rs 5 lakh) but the value of 5 lakhs in future will not be the same as it is today ( it would be less). Hence, you need to calculate the present value of money (PV) to be received in future for actual comparison. This calculation is also called discounting.
- Third, you have some money right now but instead of spending it, you decide to save it for the future. In this case, you need to know the value of money which will be received in future – here you need to calculate the future value of money that may accumulate. But order to understand the actual value of money to be received in future; you will have to discount it to the present. So, the calculation involves both finding FV and also the PV. Such an exercise becomes necessary because, there will be difference between the return expected and the rate of inflation.

**Frequency factor of returns.**

One more interesting factor in calculation of time value of money is that depending upon your assumption as to the frequency of interest payment in a year, the end result will change. For example- you have Rs 1 lakh right now. You want to know the future value if the amount is put into a investment that returns 8% per annum. The answer will be 1, 08,000 lakhs.

However, if you assume that the interest rate is paid every 6 months, then the end amount will differ because, at the end of 6 months you receive an interest of Rs 4000 which will also start earning interest for the balance 6 months.

- At the end of 6 months you get Rs 1.04 lakhs.
- From the 7
^{th}month Rs 1.04 lakhs starts earning interest and you get Rs 4160 as interest for the last 6 months. Total for the year works out to Rs 1, 08,160.

The frequency of interest can be any interval of time, even on a daily basis.

**Example:**

Lets’ assume that you are 25 years old. You have Rs.2500 with you now. You can either put it in bank FD or buy yourself a new dress. Now, let me further assume that you opt for buying new dress. The reality is that you are spending far more than Rs 2500. How? Let’s try to calculate the real cost of not investing that money.

FV = pmt (1+i)n |

FV = Future Value |

Pmt = Payment |

I = Rate of return you expect to earn |

N = Number of years |

**How to solve the equation?**

N = Number of years invested – The money you’ve spend on a dress is lost forever. That means, that Rs 2500 could have compounded in the bank for at least 35 years. How did we get that ’35′ figure? We assumed that you’ll retire at 60 and since you are 25 now, there’s 35 years left. Let’s substitute 35 for “n” in the equation.

I= Rate of return expected – The ‘I’ in the formula stands for the expected rate of return. Since bank fixed deposits would pay around 8% per annum and stock markets have returned an average of 15 %- 17% , Let’s assume you would earn somewhere in between – an average of 10% rate of return. So, we’ll assume ’I’ as 10%.

PMT – is the value of the single amount you want to invest (in this case, Rs 2500).

Now substituting the figures, our formula would be: FV = 2500 (1+.10)^{35.}

Enter 1.10 into your calculator (this is the sum of 1+.10). Raise this to the 35th power. The result is 28.1024. Multiply the 28.1024 by the pmt of Rs 2500. The result (Rs 70,256) is the true cost of spending the Rs 2500 today. Now go back and think how much you have already missed in future wealth.

That was easy, I guess.

**Now, let’s take you one more step ahead.**

One important point you would have noticed here is that, you are going to get Rs 70,256 after 35 years. Remember what we said in our first paragraph – the time value principle says that – Rs 100 today is more valuable than Rs 100 a year from now. Applying the logic here, let’s find out how much Rs 70,256 is worth now.

For that, we will have to find out the present value of Rs 70,256 which will be received 35 years later. Assuming that the average inflation rate in India Is around 8% per annum, the present value of Rs 70,256 discounted at 8% would work out to Rs 4752.

Now, after realizing the actual cost of spending Rs 2500, would you prefer to buy a dress for Rs 2500 today or Rs 4752 in the future? The answer is entirely personal.

Once you understand this vital concept, you would realize that all those bits and pieces of money you spend unnecessarily are costing you thousands in future wealth. This is why time value of money is considered as the central concept in finance.

**Key ideas:**

- Time value of money is basically the compensation for postponement of consumption of money.
- Time value of money can be different for different people because each has a different desired compensation for postponing the consumption of money.