### Time Value of Money (Part 2 – Inflation, FV, PV)

#### The Background

In my last post, we discussed about how much we need to save regularly to be able to manage to reach a Future Value. In that case we had a target of reaching 5 Lakh and basis the formula we learnt, we deduced an yearly amount which when invested will help us accumulate that corpus.

But, we also had the doubt in mind that will the car still be costing 5 Lakh after 5 years?

A glass of water at the road side vending machine used to cost 50p in 2005.

In 2020, the value of this glass of water moved to Rs.2.00. If you look from an inflation perspective, the value has increased by approximately 10% over the last 15 years.

Going by the same rate of inflation, the value of this glass of water in 2040 will cost approximately Rs. 12.70.

In the graph shown above you can see the cost of inflation as per the index available on the web.

So, what are the options that we have.

Option 1 is that we invest Rs. 2 with a 10% rate of return (net of any taxes)

Or

Option 2 We invest Rs.3.2 with 7% percent rate of interest.

Option 2 would effectively mean that we need to do in investment which is 65% more than our original amount.

### The Plan

So how do we calculate the value for something which we have to purchase in the future. What we may need to do is to be consciously aware of the inflation which may have an impact on the future value of the product.

As an example for the case that we are considering, that of cars, let’s assume that the sectoral inflation for the auto segment is 5% which means that a car costing 100000 rupees this year will cost 105000 next year, 110250 the year after and so on and so forth.

So, for our case let’s see what the value of the car will be after 5 years in case the inflation for the auto segment is assumed at 4%.

For us to find out that value, we now have

PV = – 5,00,000 (Minus because this is the value that we are giving)

N = 5

I/Yr (Inflation) = 4%

PMT = 0 (No Payments being made)

FV = ?

The values on excel will then look something like this.

PV | -500000 |

N | 5 |

I/Yr | 4% |

PMT | 0 |

FV | ??? |

**Adding value of FV as = FV (4%, 5, 0, -500000, 1)**, we get the following results

PV | ₹ -5,00,000 |

N | 5 |

I/Yr | 4% |

PMT | 0 |

FV | ₹ 6,08,326 |

As you can see the value of the car will be around 6 Lakh 8 Thousand by the end of 5 years and thus our goal of buying the car will get missed as we will be short of cash for an amount of around 1 Lakh.

### Let’s learn more

Now, consider the same for a goal which is much bigger and even few years away.

**Q. How much will be the amount required for daughter’s higher education, which is 10 years away, if the same costs Rs. 15 Lakh today. Assume the sectoral inflation for education be at 3%**.

PV | ₹ -15,00,000 |

N | 10 |

I/Yr | 3% |

PMT | 0 |

FV | ₹ 20,15,875 |

We can see quite a significant difference in the amounts that we “may be” planning for and that we may “have to” plan for.

### The other way

Now, let’s have a look at other way which is actually more important when we are planning for certain things like Retirement Planning. More often than note, we have certain figures in mind which we then say we plan to achieve. As an example the most famous figure that is doing rounds these days is the figure of **1 Crore**.

Let’s take a case of **Radhey Shyam who plans to retire after 20 years and for some reason choses that 1 Crore will be a sufficient amount to fund his retirement**. Assuming the rate of Inflation as 5%, let’s find out what the Present Value of that 1 Crore will be. Meaning what will that amount look like which is equivalent of 1 Crore of future (20 years down the line).

In this case, our values will look something like this. We will calculate the value of PV in excel by keying in the following values – **= PV (5%, 20, 0 , 100000000, 1)**

Present Value of Corpus | PV | ₹ -37,68,895 |

Time to Retirement | N | 20 |

Inflation | I/Yr | 5% |

Regular Payments | PMT | 0 |

Retirement Corpus | FV | ₹ 1,00,00,000 |

Thus, 1 Crore of future are actually worth only 37.68 Lakh today.

Now, if we decide that the value that we need is actually Rs. 1 Crore in today’s term, what will this value be at the time of retirement considering again Inflation to be 5% and time to retirement as 20 years.

Present Value of Corpus | PV | ₹ -1,00,00,000 |

Time to Retirement | N | 20 |

Inflation | I/Yr | 5% |

Regular Payments | PMT | 0 |

Retirement Corpus | FV | ₹ 2,65,32,977 |

So, we can see that the value required at the time of retirement will actually be around 2 Crores 65 Lakhs. ?

Hence, Radhey Shyam Ji should start planning for the 2.65 Crores sum of money and not for 1 Crores.

### Summary

So, when we are defining a goal, we need to almost always consider Inflation. Ignoring inflation or not taking the same into consideration when we are planning for future goals may make lead to us not being in a position to fulfil those goals when the right time arrives.

In the next post, we will combine both **Rate of Return **and **Rate of Inflation **and see how this can help plan for our future goals. Till then – **Bachate Rahein, Kamate Rahein** because **EveryPaisaMatters**