What is Time Value of Money(TVM)?

The time value of money (TVM) is the concept that a certain amount of money holds more value in the present than it will at a future date, primarily because of its potential to earn during the interim period. This principle is fundamental to finance, emphasizing that having a sum of money in hand is more valuable than having the same sum to be paid in the future. Additionally, the time value of money is commonly known as the present discounted value.

Time Value of Money Formula:

The most fundamental formula for the time value of money has five variables: 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. The formula for TVM is:

Where:
FV = Future Value of Money
PV = Present Value of Money
i = Interest Rate
n = Number of compounding periods per year
t = Number of years

This equation can be rearranged to find any unknown variable. For instance, if any four variables are known, we can calculate the fifth variable, which is unknown.

Example1: Time Value of Money

Let’s assume a sum of $15,000 is invested for two years at 8% interested compounded annually. The future value of that money is:

This equation can be rearranged to find the value of the future sum of money in present-day dollars. For example, the present-day dollar amount compounded annually at 8% interest that would be worth $7,500 two years from today is:

Example 2: Present Value(PV) of Uneven Cash Flows

Let’s assume that $1,500 will be received at the end of the first year, $1,850 at the end of the second year, and $2,100 at the end of the third year . What is the present value (PV) of the cash flow stream if the Interest/ discount rate is 7.25 %?

The present value of the first cash flow (CF1) amounts to $1,398.60, CF2 is $1,608.34, and CF3 is $1,702.27.

PV of CF₁ = $1,500 ÷ (1 + 0.0725)¹ = $1,398.60

PV of CF₂ = $1,850 ÷ (1 + 0.0725)² = $1,608.34

PV of CF₃ = $2,100 ÷ (1 + 0.0725)³ = $1,702.27

Thus, the present value of the uneven cash flow stream will be $4,709.20

Example 3: Future Value(FV) of Uneven Cash Flows

Let’s assume that $1,500 will be received at the end of the first year, $1,850 at the end of the second year, and $2,100 at the end of the third year . What is the future value (FV) of the cash flow stream if the Interest/ discount rate is 7.25 %?

The future value of the first cash flow (CF1) amounts to $1,725.38, CF2 is $1,984.13, and CF3 is $2,100.00.

FV of CF₁ = $1,500 ÷ (1 + 0.0725)² = $1,725.38

FV of CF₂ = $1,850 ÷ (1 + 0.0725)¹ = $1,984.13

FV of CF₃ = $2,100 ÷ (1 + 0.0725)⁰ = $2,100.00

Thus, the future value of the uneven cash flow stream will be $5,809.51.