Imagine your good friend is feeling incredibly generous and offers you two choices – which one do you pick?
Option 1- He provides you with an immediate sum of Rs.10,000/-.
Option 2- He assures to hand over Rs.10,000 in two years’ time.
If you don’t need the funds right away, why not wait two years and use the money to purchase a brand new car? Doing so would surely provide an interesting twist to your plans.
Would you prefer to accept the funds right now, even though it’s not necessary, or wait two years and take them when they are required?
No doubts, your friend is a reliable person; after two years he will still honour his commitment and you can rest assured that he will give you the money he promised.
Considering these two options along with its surrounding factors, which would you select?
I expect that most of you reading this will choose Option B. There’s no requirement for the money soon, so if you were to get it now, you might splurge and squander it. Consequently, two years from now is the better option.
Given this situation, here are some questions:
Is comparing financial value over time a reasonable approach? In other words, can we effectively measure the worth of money at present and in the future?
What is the best way to adjust for inflation when transferring funds through different timelines?
To choose the best course of action, careful consideration must be given to the difference between current and future financial value. Analysing this data will help you determine which is more advantageous.
The goal of this chapter is to aid you in comprehending the concept of comparing money across different time periods.
At the conclusion of this chapter, you should be able to make an informed decision regarding your friend’s generous proposition, as well as other major life decisions like investing.
We will now explore the concept of the ‘Time value of money’ (TVM). This is one of the bedrock financial principles, and it has various uses in different fields such as project finance, insurance planning, equity derivatives, valuations and personal finance.
The concept of the time value of money has two facets – present and future values.
– Present value of money
We purchase assets with the anticipation of earning a good return over the long run. For instance, if I were to buy a piece of land presently, I would predict that it should increase significantly in value after 15 years. The amount I receive when selling this land in 15 years will be notably higher than its current worth.
Present value can be used to comprehend the worth of funds expected in the future expressed in current terms.
Does that sound confusing? Most probably yes.
Let’s take a look at this with an example.
Contemplate that you bought a piece of land for Rs.15,000,000/- today and kept it for 15 years. At the end of that period, you sold it for Rs.75,000,000/- – on the surface, this appears to be terrific news as you have made a fivefold return on your investment.
It’s time to consider the significance of Rs.75,000,000/- in today’s terms, received 15 years down the line.
What if the value of Rs.75,000,000/- reduces drastically to the point that it’s worth less than Rs.15,000,000/- 15 years from now?
To gain insight into this matter, we should comprehend two points.
What is the cost of forgoing a risk-free opportunity today?
What sum do we need to invest today in order to accumulate Rs.75,000,000/- over the next 15 years, taking into account the risk-free opportunity cost?
The answer to the second question is equivalent to Rs. 75,000,000/- in today’s value that can be received in 15 years. Let us calculate this.
Let’s think about this on a long-term basis: 15 years.
The opportunity cost is the sacrifice of other investments that could be made if we choose not to put our resources into the real estate transaction. To establish the amount, we should identify the risk-free rate present in the economy and afterwards consider a greater reward for taking on more risk.
So the opportunity cost –
Opportunity cost = Risk free rate + Risk premium
The risk-free rate is the rate at which our money can flourish without any type of riisk. Some might claim there is no such thing as a real risk-free rate, but for this particular discussion, let’s take the Government’s 15-year bond as an example. Governments usually do not default on their payments or repayments, making the Sovereign bond a reasonable representation of the risk-free rate.
I’ve highlighted the 2034 bond because of our goal to meet our 15-year horizon. The coupon rate that has been indicated is 7.5%, so, for simplicity, we’ll set the bid-ask yield aside and address this further when discussing bonds. However, it’s important to understand that 7.5% is the risk-free rate for the next 15 years.
A risk premium of 1.5-2% can be added to ascertain the opportunity cost. The amount of the premium is influenced by a number of factors; for simplicity’s sake, this will suffice – therefore, the opportunity cost would be-
7.5% + 1.5%
Having established our opportunity cost, the next step is to calculating how much we must invest now at 9% for it to reach Rs.75,000,000/- in 15 years.
This figure can be determined by experimenting, or even via the process of discounting Rs.7,500,000/- at 9%, which gives the same outcome.
The ‘discount rate’ is the cost at which we discount opportunities.
We equate the future value of money (Rs.75,000,000/-) to its current worth or ‘Present Value’ in this case.
The present value formula is –
Present value = Future value / (1+ discount rate ) ^ (time)
Future value = Rs.75,000,000/-
Discount rate = 9%
Time = 15%
these numbers can be plugged in the equation.
= 75,000,000 / (1+9%)^(15)
This translates to Rs.20,590,353/- today; 15 years in the future will be the equivalent of Rs.75,000,000/-.
If someone makes an offer of Rs.20,590,353/- now, that amount can be invested at a 9% opportunity cost and will equate to Rs.75,000,000/- in fifteen years. In other words, it would be like receiving the same amount fifteen years from today.
The concept of present value is fundamental in finance, and we will now turn our attention to the future value of money.