Time Value of Money Understanding and Calculating Future and Present Value

Time value of money is a vital part of finance, being used in many financial concepts such as discounted cash flow analysis, financial derivatives pricing, project finance and the calculation of annuities. It can be thought of as the engine powering the Financial World.

The time value of money concept is based on the idea that money is not a constant. In other words, Rs.100 today has a different value than it will have two years from now. Additionally, Rs.100 in two years won’t be worth the same amount as it does today. When mention of time arises, an element of opportunity follows that must be taken into consideration when assessing finances.

In order to assess the worth of money we have today in future terms, we need to figure out its Future Value (FV). Conversely, to determine the current value of money we anticipate receiving in future, we have to calculate its Present Value (PV).

Time affects the value of money, and this must be considered. This process is known as ‘compounding’ when calculating future value and ‘discounting’ when determining present value.

I will avoid getting into the math and just give you the formula to calculate future value (FV) and present value (PV).

What would Rs. 5000/- be worth in five years (2014-2019) accounting for an opportunity cost of 8.5%?

This is a case of computing Future Value (FV). We are measuring the value of the money we have today in the future.

Future Value (FV)= Amount * (1+ opportunity cost rate) ^ No. of yrs.

= 5000 *(1 + 8.5%) ^ 5

= 7518.3

This implies that Rs.5000 today is equivalent to Rs.7518.3 after 5 years, with an opportunity cost of 8.5%.

What is the present value of Rs.10,000/- receivable after 6 years, factoring in an opportunity cost of 8.5%?

We are attempting to ascertain the Present Value of future cash flows in terms of today’s value.

Present Value = Amount / (1+Discount Rate) ^ Number of years

= 10,000 / (1+ 8.5%) ^ 6

= 6129.5

Rs.10,000/- due in six years is equivalent to Rs.6,129.5 at today’s rates based on a discount rate of 8.5%.

This question can be reformulated as: How much would Rs.7518.3 be worth today, if it were to be invested at 8.5% for 5 years?

We know this necessitates us to work out the present value. Since we have done the opposite of this in example 1, we can anticipate the response to be Rs.5000/-. Let us calculate it, just to be sure.

= 7518.3 / (1 + 8.5%) ^ 5

= 5000.0

Now that we have a good grasp of the time value of money, let’s return to the pizza problem.

• The Net Present Value of cash flows

We are still in the process of evaluating the cost of the pizza machine. George will benefit from upcoming cash flows associated with owning the device.

I would like to reiterate our earlier question: what is the present value of future cash flow?

It’s clear that cash flow is consistent throughout the course of time. To ensure accuracy, we need to factor in opportunity cost when computing the expected future streams of money.

The Net Present Value (NPV) of the pizza machine is Rs. 32,80,842. This means that all the future cash flows associated with the machine should cost George no more than this amount. Anything less than this price would be favourable to him as a buyer.

Consider this – If we substitute the pizza machine with a business, can we reduce the value of any upcoming cash flows that the enterprise will generate to assess its share price? Yes, we can, and that is precisely what we will discuss in further depth with the “Discounted Cash Flow” model.