Basically, time value of money is a financial concept to state that for the same amount of money, it is worth more today than it will be in the future. For the most part, this has been one of the most important and applicable financial concepts that I have learnt since my days in university. With this in mind, let’s learn more about time value of money and how it works today.

Table of Contents:

1. Understanding Time Value of Money
2. The Formula
3. Sample Calculation
4. Real Life Application
5. Final Thoughts

One Minute Summary:

• All in all, for the same sum of money, it is worth more today than it will be in the future.
• This is because of the opportunity cost, the earning potential, as well as the risk of default.
• Although this may be true, this is based on the assumption that you will invest the money given to you today. Otherwise, it won’t make too much of a difference in any way.

Part 1: Understanding Time Value of Money (TVM)

To begin with, let’s use two financial instruments to illustrate this concept. Firstly, Financial instrument A gives you $1 million upfront. By comparison, Financial Instrument B gives you $100,000 annually for the next ten years. Although the total payout is the same (i.e. $1 million), time value of money points out that Financial Instrument A is the better deal.

Firstly, this is because of its earning potential over the next decade. Given that $1 million in your hands right now, you are able to accumulate it for potentially better returns. In time to come, it will likely be worth more than $1 million. For this purpose, let’s assume that the bank’s interest rate is 0.05% per annum. Next, we will save the entire amount given by each financial instrument at each time period. Thereafter, we will apply the power of compound interest for the next ten years. In due time,

• Balance from Financial Instrument A: $1,005,011.27
• Balance from Financial Instrument B: $1,002,253.00

Although the total payout from each financial instrument is the same ($1 million), the compounded interest from Financial Instrument A helped us to earn $2,758.27 more than the compounded interest from Financial Instrument B. This is because of the additional interest that continues to compound each year.

Secondly, we live in a world where we need to hedge against inflation. Otherwise, the value of money will decrease and our purchasing power will shrink as well. As I have noted earlier, the larger upfront sum of money from Financial Instrument A gives us more power to fight against inflation. To demonstrate, at the end of the first year,

• Balance from Financial Instrument A: $1,000,500
• Balance from Financial Instrument B: $100,050

Despite that the rate of inflation is the same, you will be able to purchase more items with $500 than with $50.

Finally, there exists an uncertainty or a default risk for Financial Instrument B. As a matter of fact, nobody knows for sure on whether Financial Instrument B is capable of paying you consistently over the next decade. Now, what if it defaults after the third payout?

Part 2: The Formula

After understanding the basic concept on time value of money, let’s use a formula to perform some calculations. To point out, the formula may vary slightly according to the situation. Notwithstanding that, its foundation is built on the following four variables:

• Present Value (PV): The current value of money
• Future Value (FV): The value of money in the future
• Interest Rate (i): The interest rate to compound or to discount the money
• Time (N): The number of periods in years

Accordingly, FV = PV x (1 + i)^N

Part 3: Sample Calculation

In order to understand the formula better, let’s go through two examples together.

Part 3.1: Example 1

As an illustration, let’s invest $100,000 into a financial instrument that yields a rate of 10% annually for 6 years. As a result, you will receive future value = $100,000 x (1 + 10%)^6 = $177,156.10 at the end of 6 years. To point out, it is no surprise that it yields the same result as if you would have used the compound interest’s formula.

Part 3.2: Example 2

Next, let’s invest $100,000 into an instrument that yields a rate of 10% annually for 6 months. For this purpose, we will introduce another variable into the original formula; that is the number of compounding periods per year, n. Accordingly, FV = PV x (1 + i/n)^(n x N) = $100,000 x [1 + 10%/1]^(1 x 6/12) = $104,880.88.

Part 4: Real Life Application

Summing up, I like to use this formula to calculate the amount of capital and the rate of return that we need in order to achieve our financial goals. For example, let’s see how we can accumulate $1 million in 30 years’ time for retirement.

• If you invest $100,000 today, then you will need to find a financial instrument that yields about 7.98% per annum for the next 30 years.
• By comparison, if you invest into a financial instrument that yields 4% per annum, then you need a capital of $308,318.67 today.

Part 5: Final Thoughts

To conclude, time value of money tells us one thing – money on hand today is worth more than the same sum given to you tomorrow. Although this may be true, it ignores one’s ability to manage the money. For instance, if you receive $1 million today and put it under the bed for ten years, then it is indifferent from receiving $100,000 over the same period. In fact, you run the risk that your money may get stolen!

In any case, this is a simple introduction to time value of money and I will definitely be adding more of such content in the future. If you are interested to learn how I apply these financial concepts at work, then subscribe to my newsletter.