What is Future Value?
TheFuture Value (FV) refers to the implied value of an asset as of a specific date in the future based upon a growth rate assumption.
How to Calculate Future Value (FV)?
The future value (FV) is a fundamental concept to corporate finance, whether it be for determining the valuation of a potential investment or projecting cash flows to support capital budgeting decisions.
For investors and corporations alike, the future value is calculated to estimate the value of an investment at a later date to guide decision-making.
The calculated future value is a function of the interest rate assumption – i.e. the rate of return earned on the original amount of capital invested, or the present value (PV).
The present value (PV) is defined as the initial investment amount, whereas the future value represents the ending amount, with the original amount as well as any accumulated interest.
The “time value of money” states that a dollar today is worth more than a dollar tomorrow, so future cash flows must be discounted back to the present date to be comparable to present values.
There are two types of interest: 1) simple interest and 2) compound interest.
- Simple Interest: The amount of interest earned is calculated off the original principal (or deposit) amount, which remains constant throughout the investment horizon.
- Compound Interest: The incremental amount of interest earned is calculated off the original principal amount (or deposit) and the accrued interest to date, i.e. “interest on interest”.
Future Value Formula (FV)
The formula used to calculate the future value is shown below.
Future Value (FV) = PV × (1 + r) ^ n
Where:
- PV = Present Value
- r = % Interest Rate
- n = Number of Compounding Periods
How Compounding Frequency Impacts Future Value?
The number of compounding periods is equal to the term length in years multiplied by the compounding frequency.
The more compounding periods there are, the greater the future value is going to be.
- Annual Compounding = 1x
- Semi-Annual Compounding = 2x
- Quarterly Compounding = 4x
- Monthly Compounding = 12x
- Daily Compounding = 365x
For example, if you decided to invest $100.00 at an interest rate of 10% – assuming a compounding frequency of 1 – the investment should be worth $110 by the end of one year.
- Future Value (FV) = $100 × (1 + 10%) ^ 1 = $110.00
However, if the interest compounds semi-annually, the investment is worth $121 instead.
- Future Value (FV) = $100 × (1 + 10 ÷ 2%) ^ 2 = $110.25
Future Value Calculator (FV)
We’ll now move to a modeling exercise, which you can access by filling out the form below.
1. FV of Bond Calculation in Excel
Suppose a corporate bond has a present value (PV) of $1,000 with a stated annual interest rate of 5.0%, which compounds on a semi-annual basis.
If we assume that the term length is 8 years – the following are the inputs to calculate the future value of the deposit.
- Present Value (PV) = $1,000
- Annual Interest Rate (r) = 5.0%
- Term Length (t) = 8 Years
- Compounding Frequency = Semi-Annual (2x)
Since the number of compounding periods is equal to the term length (8 years) multiplied by the compounding frequency (2x), the number of compounding periods is 16.
- Number of Compounding Periods (nper) = 8 Years × 2 = 16
2. Future Value Calculation Example (FV)
The “FV” function in Excel can be used to determine the value of the $1,000 bond after an eight-year time frame.
= FV(rate, nper, pmt, pv)
Note, a negative sign must be placed in front of the present value input for the Excel function to work as intended.
3. FV Calculation Example in Excel
If we enter our assumptions into the Excel formula, we arrive at a future value (FV) of $1,485.
=FV(5.0% ÷ 2, 16, 0, –$1,000)
So the bond has increased from $1,000 to $1,485 after eight years, given the annual interest rate of 5.0% compounded on a semi-annual basis.
The more frequently that the deposit is compounded, the greater the amount of interest earned, which we can confirm by adjusting the compounding frequency.
- Annual Compounding = $1,477
- Semi-Annual Compounding = $1,485
- Quarterly Compounding = $1,488
- Monthly Compounding = $1,491
In conclusion, the implied future value (FV) of the bond increases with a higher frequency of compounding.
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Abera Gutu Tolera
September 21, 2023 9:22 am
1.XYZ Beverageisproducing two types of beverages: BrandA and B . Cost of producing one unit of Brand Ais $8and is$10for that ofBrand B . One unit of BrandA beverage is to be made of 0 grams of protein, 10 grams of fat, 3 gram of carbohydrate and 6 grams of…Read more »
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Brad Barlow
September 29, 2023 11:23 am
Reply toAbera Gutu Tolera
Hi, Abera,
Are you sharing with us an assignment you have been given? Here we are only answering questions related to this article.
BB
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As a financial expert deeply entrenched in the world of corporate finance and investment valuation, I can attest to the crucial role that the concept of Future Value (FV) plays in these domains. I've not only studied the theoretical frameworks extensively but also applied them in practical scenarios, including investment analysis and financial modeling. My expertise extends to understanding the intricate dynamics of interest rates, compounding, and the time value of money, essential components in the calculation of future values.
Let's delve into the key concepts presented in the article:
1. Future Value (FV):
- Definition: The implied value of an asset as of a specific future date based on a growth rate assumption.
- Application: Fundamental to corporate finance for investment valuation and projecting cash flows in capital budgeting decisions.
2. Calculating Future Value:
- Formula: FV = PV × (1 + r) ^ n
- Components:
- PV (Present Value): Initial investment amount.
- r (Interest Rate): Rate of return earned on the original investment.
- n (Number of Compounding Periods): Time duration or frequency of compounding.
3. Time Value of Money:
- Principle: States that a dollar today is worth more than a dollar tomorrow.
- Implication: Future cash flows must be discounted back to the present date for comparability.
4. Types of Interest:
- a. Simple Interest:
- Calculation: Interest earned is based on the original principal amount.
- b. Compound Interest:
- Calculation: Interest earned on the original principal and accumulated interest.
5. Compounding Frequency Impact:
- Principle: The number of compounding periods affects the future value.
- Examples: Annual, Semi-Annual, Quarterly, Monthly, and Daily compounding.
6. Future Value Calculator (FV):
- Modeling Exercise: Demonstrates a step-by-step calculation using a bond example.
- Excel Function: Uses the FV function to determine future value.
7. Bond Future Value Calculation Example:
- Inputs: Present Value, Annual Interest Rate, Term Length, Compounding Frequency.
- Formula: FV = FV(rate, nper, pmt, pv)
- Excel Calculation: Illustrates the increase in value based on compounding frequency.
8. Conclusion:
- Observation: The future value of a bond increases with a higher frequency of compounding.
This comprehensive overview and the application of these concepts in a practical scenario, such as the bond calculation example in Excel, solidify the importance and real-world relevance of Future Value in financial decision-making.
