Time Value of Money

The time value of money is the concept that money available today is worth more than the same amount in the future due to its potential to grow. This is because money typically loses value over time, often due to inflation. In this discussion, we will explore the key elements of the time value of money and explain how to calculate it.

But what exactly is the value of money? Simply put, it is the amount of goods and services that money can buy. This aligns with our intuition that the value of money decreases over time as inflation erodes its purchasing power.

At first glance, it might seem that spending your money immediately preserves its value. However, this is not always the case. If you purchase something unnecessary, you may lack the funds in the future for essential goods and services. Additionally, most goods lose value over time and are generally not ideal for preserving or storing value. For this reason, the best option to preserve the value of your money is investment.

The importance of the time value of money becomes clear when making investment decisions. Investing means postponing the use of your money for immediate goods and services and instead allocating it to a security or project. The goal is to grow your money’s value over time, allowing you to afford more goods and services in the future.

Elements of the Time Value of Money

Three key elements affect the value of money over time:

Inflation
Impatience to Consume
Risk Let’s explore each of these elements with examples.

Inflation

In 2014, a car cost about $30,000, but by 2024, the same car costs about $60,000. This means that in 2014, your money could buy 100% of the car, but by 2024, it can only buy 50% of it. Over time, the value of money has decreased, and in this example, money has lost 50% of its value.

We can calculate the average annual inflation rate as follows:

\text{Inflation Rate} = \frac{\text{Price}(\text{in } 2024) - \text{Price}(\text{in } 2014)}{ (2024 - 2014) \times \text{Price}(\text{in } 2014)}

Substituting the values:

\text{Inflation Rate} = \frac{30,000}{10 \times 30,000} = 0.1 = 10 \%

this calculation suggests an average inflation rate of 10% per year [1].

To interpret this, consider two perspectives:

My $1000 this year will have value of $900 next year.
My $1000 next year has the value of $1111 now.

The second perspective is particularly useful. If you don’t need to spend your money immediately, you should consider investing it to preserve its value over time. For example, if you invest $1000 today in an asset that grows to $1111 next year, you’ve successfully maintained your money’s value. However, if you simply leave $1,000 in a bank account, it will still be $1000 next year, effectively losing value due to inflation.

Impatience to Consume

Even if there is no inflation, people tend to prefer consuming now rather than later. This is called impatience to consume. For example, suppose you have an extra $2,000. You might want to buy a PlayStation now to enjoy playing video games immediately rather than waiting a year. This preference for immediate consumption is another important factor in the time value of money. Unlike inflation, impatience to consume is subjective and varies from person to person.

To quantify this, you can ask yourself: how much additional money would someone need to offer you to wait a year before spending your $2,000? If your answer is at least $100, your impatience to consume rate is:

\text{Consumption Impatience Rate} = \frac{100}{2000} \times 100 = 5\%

Risk-free Return (RFR)

The sum of return for inflation and impatience to consume is called risk-free return or RFR. To calculate RFR in the given example:

\text{RFR} = (1 + \text{Inflation Rate}) \times (1 + \text{Impatience to Consume Rate}) - 1

Substituting the values:

\text{RFR} = (1 + 0.1) \times (1 + 0.05) - 1 = 0.155

Risk Premium

When you choose to invest your money in a security or project, you take on risk in the hope of earning a reward. A risk premium is the extra return an investor earns for accepting higher risk with an investment. While all investments share the same baseline risk-free return (RFR), the risk premium varies depending on the investment.

To justify giving up immediate spending in favor of investing, the investment should provide the following return rate:

\text{\color{blue}{Required Return }} (\text{\color{red}{ Time Value of Money }}) = \text{\color{blue}{RFR}} + \text{\color{blue}{Risk Premium}}

The required return is time value of money—the return rate you should expect from an investment to compensate for delaying consumption.

or example, if the risk-free return is 0.155 and the risk premium is 0.045, the required return is:

\text{Required Return} = 0.155 + 0.045 = 0.2 = 20 \%

This means that $1,000 today is effectively worth $200 more than $1,000 a year from now. You would only agree to invest your $1,000 if the investment generates at least $200 in additional value by next year.

Calculate Using Python

You can install free Open-Source xarizmi library to calculate time value of money. You need to know python programming language to use this. First open a terminal or command prompt and install xarizmi library:

pip install xarizmi

Once you installed the library you can write a python script or open python shell to calculate time value of money. For the case we were discussing in this post you can use the following code to calculate:

from xarizmi.fundamentals.time_value_money import time_value_money


value = time_value_money(
    impatience_to_consume=0.05,
    inflation=0.1,
    risk=0.045,
)

print(f"Time value of money is {value}")
print(f"A $1000 one year later worth  ${value * 1000 + 1000} now")

Footnotes

The actual average inflation rate is closer to 7% because inflation compounds over time, and the compound interest formula should be used for a more accurate calculation. For simplicity, we’ve used a straightforward approach that gives an approximate rate of 10%.