Time value of money

Reference

1. https://www.investopedia.com/terms/t/timevalueofmoney.asp

Time value of money

It is the concept that

A sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim.

A delayed payment is a missed opportunity. It can grow only through investing.

1. Present value of money - the discounted value today of a future revenue stream.
2. The time value of money is also referred to as the present discounted value.
3. A sum of money in the hand has greater value than the same sum to be paid in the future.
4. It is one of the core principles of finance
   1. It would be hard to find a single area of finance where the time value of money does not influence the decision-making process.
   2. The time value of money is the central concept in discounted cash flow (DCF) analysis, which is one of the most popular and influential methods for valuing investment opportunities.
   3. It is also an integral part of financial planning and risk management activities. Pension fund managers, for instance, consider the time value of money to ensure that their account holders will receive adequate funds in retirement.
5. The formula for computing the time value of money considers the amount of money, its future value, the amount it can earn, and the time frame.
6. Inflation has a negative impact on the time value of money because your purchasing power decreases as prices rise.
7. Businesses use it to gauge the potential for future projects.
8. Knowing what TVM is and how to calculate it can help you make sound decisions about how you spend, save, and invest.

Details

1. Investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time.
   1. Investors use TVM to pinpoint investment opportunities.
2. The power of compounding interest comes into play here.
3. If it is not invested, the value of the money erodes over time. If you hide $1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation reduces its value.

Formula

Time Value of Money Formula

The most fundamental formula for the time value of money takes into account the following: the future value of money, the present value of money, the interest rate, the number of compounding periods per year, and the number of years.

Based on these variables, the formula for TVM is:

𝐹  = 𝑃  (1 + 𝑖/𝑛) ^ (𝑛 × 𝑡)

where:

1. 𝐹 = Future value of money
2. 𝑃 = Present value of money
3. 𝑖 = Interest rate
4. 𝑛 = Number of compounding periods per year
5. 𝑡 = Number of years

Example 1

Let’s assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

𝐹  = $10,000  (1 + 10%/1) ^ (1 × 1)

= $11,000

Example 2

The formula can also be rearranged to find the value of the future sum in present-day dollars.

𝑃 = F / (1 + 𝑖/𝑛) ^ (𝑛 × 𝑡)

For example, the present-day dollar amount compounded annually at 7% interest that would be worth $5,000 one year from today is:

𝑃 = $5,000 / (1 + 7%/1) ^ (1 × 1)

= $4,673

Effect of Compounding Periods on Future Value

The number of compounding periods has a dramatic effect on the TVM calculations. Taking the $10,000 example above, if the number of compounding periods is increased to quarterly, monthly, or daily, the ending future value calculations are:

1. Quarterly Compounding:

   𝐹  = $10,000  (1 + 10%/4) ^ (4 × 1) = $11,038
   

2. Monthly Compounding:

   𝐹  = $10,000  (1 + 10%/12) ^ (12 × 1) = $11,047
   

3. Daily Compounding:

   𝐹  = $10,000  (1 + 10%/365) ^ (365 × 1) = $11,052
   

How does it relate to Opportunity Cost?

Money can grow only if it is invested over time and earns a positive return. Money that is not invested loses value over time. Therefore, a sum of money that is expected to be paid in the future, no matter how confidently it is expected, is losing value in the meantime.