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Present Value (PV): Definition, Formula & Calculation

A dollar today is worth more than a dollar tomorrow.

This is the classic phrase that is associated with the concept of the time value of money. But when you’re given a choice between a sum of money today payment, and a future payment, how can you figure out which one to take?

That’s where the present value calculation comes into play.

But what is the present value ? And how can it be used in the business world? Read on as we take a closer look at PV.

KEY TAKEAWAYS

  • Present value helps to figure out whether a sum of money today is worth more than a sum of money in the future. 
  • When calculating present value, a rate of return is assumed.
  • Present value is a quick and easy calculation. However, it can come at the expense of accuracy.

What Is Present Value (PV)

Present value (PV) is the current valuation of a sum of money in the future. It can also be the future sum of a stream of cash flows. Though this is with a specified rate of return. Future cash inflows are typically discounted at the discount rate. This works by the rule that the higher the discount rate is, the lower the present value of the future cash flows will be. 

When it comes to being able to properly value future cash flows, figuring out the correct discount rate is key whether they be debt obligations or earnings. 

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Formula Of Present Value

When looking at the present value of a sum of money or cash flow, you can use the following formula:

Present Value Formula

How to Calculate Present Value

The present value calculation is made up of three steps. They are as follows:

1. Input the future value of the amount you expect to receive in the numerator of the formula. 

2. Figure out the interest rate that you are expecting to receive between now and the future. Put the rate as a decimal number in place of the “r”. 

3. Put in the time period in the place of the “n”. For example, if you wanted to figure out the present value of an amount that you’re expecting to receive in three years’ time, place the number “3” for the “n”. 

There are a number of different present value calculator applications that are available to make this easier for you. 

Example of Present Value

Let’s say that Company X is given the choice of payment. They can be paid $20,000 today for a section of their business where they earn 3% annually. Or they can be paid $22,000 exactly a year from now. Which of the options would be the best for the company?

To figure this out, we can take the information we’ve been given and apply it to the present value formula and calculation. 

Using the formula, we can see that the calculation would be as follows:

PV = $22,200 / (1 + .03) 1 = $21,359.20

So the present value of the $22,200 would be $21,359.20. This would be the minimum amount that Company X would have to be paid today to have $22,000 one year from now. This clearly shows that if Company X was paid $20,000 today with a 3% interest rate, they would end up with less money than if they took the $22,000 one year from now. 

Alternatively, you could figure out the future value of the first sum of money in a year’s time. The calculation would be as follows:

PV = $20,000 x 1.03 = $20,600

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Importance Of Present Value

Present value allows a solid basis where you can assess the level of fairness of any financial liabilities or benefits at a future date. So for example, a future cash rebate discounted to present value could or could outweigh the downsides of having a higher potential purchase price. The same calculation can be applied to 0% financing when someone buys a car from a dealership. 

Pros and Cons of Present Value

Calculating present value is important when it comes to determining the potential value of an investment. Although it is a useful tool, it has some downsides. Let’s take a look at some of the pros and cons of present value. 

Advantages of Present Value

Using present value is a quick and easy way to assess the present and future value of an investment. Investors can use the calculation to get a quick overview of the situation and whether it would be a good idea to invest money today, assuming a consistent annual rate of return. 

Essentially, present value is an effective way of comparing investment decisions or purchase decisions. This is done by evaluating the future sums of money in the present day. 

Disadvantages of Present Value

The present value formula assumes that you are earning an expected forgone rate of return over a predetermined period of time. This can make present value a misleading statement. 

For example, if you were to invest in a company, the assumed rate of return could end up changing in each of the following three years. This could be due to a number of factors such as volatility in the industry or market. 

In the case of not having a consistent rate, it wouldn’t be so easy to calculate the present value. Because you wouldn’t be able to use a realistic annual rate of return. 

Present value is a quick and easy way to get a good idea of the value of a sum of money or cash flow. However, the ease comes at the cost of accuracy which can lessen the financial benefits.

Many things can affect investments – such as inflation. So make sure that you use other metrics alongside present value to get the best idea possible.

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FAQs About Present Value

Present value is used as a starting point for assessing the fairness of a future financial liability or benefit.

Put simply, a present value is good if it is greater than zero. So if your $1 today is worth $2 tomorrow, then you’d have a PV above 1. However, if your $1 is worth $0.90 tomorrow, your PV will be less than 1.

When it comes to present value, there are two rates that affect it. These are the discount rate and the interest rate. If the discount rate is lower, then the present value is higher. Whereas if the discount rate is higher, then the present value will be lower.

Future value is the total sum of money that will accrue over time when that initial sum is invested.

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What Is Present Value?

How to calculate the present value of an investment

define present worth (p)

Definitions and Examples of Present Value

Types of present value, how present value works, present value vs. future value.

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Present value is what a sum of money in the future is worth in today’s dollars at a rate of interest.

The basic principle behind the time value of money is simple: One dollar today is worth more than one dollar you will receive in the future. This is because you can invest the dollar you have today, and it can grow over time at a rate of return, or interest. The dollar you receive “tomorrow” can’t be invested today, and therefore doesn’t have the same potential to increase in value.

Present value is what cash flow received in the future is worth today at a rate of interest called the “discount” rate.

Here’s an easy way to look at present value. If you invest $1,000 in a savings account today at a 2% annual interest rate, it will be worth $1,020 at the end of one year ($1,000 x 1.02). Therefore, $1,000 is the present value of $1,020 one year from now at a 2% interest, or discount, rate.

The discount rate has a big impact on the present value. What if we changed the discount rate in our example from 2% to 5%? How much money do we need to invest at 5% to have $1,020 at the end of one year? The calculation would look like this: $971.43 X 1.05 = $1,020.

So instead of needing $1,000, we only need $971.43 to reach the same resulting amount. More on this calculation later.

Present Value of a Lump Sum

Think of the present value of a lump sum in the future as the money you would need to invest today at a rate of interest that would accumulate to the desired amount in the future. In the example above, the amount of money you need to invest today that will accumulate to $1,020 a year in the future at 2% is $1,000.

Present Value of an Annuity

An annuity is a series of equal payments received for a fixed period of time. For example, lottery winners often have the option to receive their prize money in equal payments over 20 years. 

The present value of an annuity is the value of all the payments received over a period of time in the future in today’s dollars, at a certain discount rate.

One way to think of the present value of an annuity is a car loan. The initial loan is the present value. The annuity is the principal and interest payments you make every month until the balance of the loan is zero.

Present Value of Unequal Cash Flows

When a business invests in new equipment or a project, it may take time to see results. The revenue or cash flow projected may be low at first but grow over time.

When making investment decisions, a business has to analyze the present value of unequal cash flows.

The easiest way to calculate present value is to use one of the many free calculators on the internet, or a financial calculator app like the HP12C Financial Calculator, available on Google Play and in the Apple App Store. Most spreadsheet programs have present-value functions as well.

Present Value Tables

Another easy way to calculate present value is to use a present value table. These tables have factors and interest rates for annuity payments and lump sums. They look like this:

If we want to know the present value of $100,000 two years in the future at 4%, for instance, the calculation is:

Future value = $100,000

Present value factor at 4% for two years = .925 (see first table above)

Present value = $100,000 X .925 = $92,500

Real-World Example of Present Value

Joseph and Josephine are planning for their retirement . They decide that they will need an income as of age 65 of $80,000 a year, and they project living to age 85. Joseph and Josephine need to know how much money they need at age 65 to produce $80,000 of income for 20 years, assuming they will earn 4% (the discount rate).

Annuity payment = $80,000

Years paid = 20

Discount rate = 4%

Annuity factor from a present value table = 13.9503

Present value = $80,000 X 13.9503 = $1,116,024

At age 65, Joseph and Josephine will need $1,116,024 to produce $80,000 of income for 20 years at 4%.

Unequal Cash Flows

No matter what method you use– spreadsheet , calculator, table, or formula–calculating the present value of unequal cash flows takes a bit of work. An Excel spreadsheet is the easiest way to use the NPV (net present value) function; however, here’s an example of how to use the tables.

We can also measure future value . Future value is what a sum of money invested today will be worth over time, at a specified rate of interest.

As discussed earlier, $1,000 deposited in a savings account at a 2% annual interest rate has a future value of $1,020 at the end of one year. Let's look at what happens at the end of two years:

That $1,000 deposit becomes $1,040.40. The extra change is the 2% return on the $20 earned at the end of Year 1. The process of interest earning interest is called “compounding,” and it has a powerful effect on the future value of an investment.

Future value is the mirror image of present value.

Key Takeaways

  • Present value measures the effect of time on money.
  • Present value is what a sum of money or a series of cash flows paid in the future is worth today at a rate of interest called the “discount” rate.
  • Present value is used to plan for financial goals and to make investment decisions.

Texas A&M University Commerce Department. " Present Value Tables ." Accessed July 29, 2021.

Present Value (PV)

Money now is more valuable than money later on .

Why? Because you can use money to make more money!

You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest.

Example: You can get 10% interest on your money.

So $1,000 now can earn $1,000 x 10% = $100 in a year.

Your $1,000 now can become $1,100 in a year's time .

Present Value

We say the Present Value of $1,100 next year is $1,000

Because we could turn $1,000 into $1,100 (if we could earn 10% interest).

Now let us extend this idea further into the future ...

How to Calculate Future Payments

Let us stay with 10% Interest . That means that money grows by 10% every year, like this:

  • $1,100 next year is the same as $1,000 now .
  • And $1,210 in 2 years is the same as $1,000 now .

In fact all those amounts are the same (considering when they occur and the 10% interest).

Easier Calculation

But instead of "adding 10%" to each year it is easier to multiply by 1.10 (explained at Compound Interest ):

So we get this (same result as above):

Future Back to Now

And to see what money in the future is worth now , go backwards (dividing by 1.10 each year instead of multiplying):

Example: Sam promises you $500 next year , what is the Present Value?

So $500 next year is $500 ÷ 1.10 = $454.55 now (to nearest cent).

The Present Value is $454.55

Example: Alex promises you $900 in 3 years , what is the Present Value?

So $900 in 3 years is:

Better With Exponents

But instead of $900 ÷ (1.10 × 1.10 × 1.10) it is better to use exponents (the exponent says how many times to use the number in a multiplication).

Example: (continued)

The Present Value of $900 in 3 years (in one go):

As a formula it is:

PV = FV / (1+r) n

  • PV is Present Value
  • FV is Future Value
  • r is the interest rate (as a decimal, so 0.10, not 10%)
  • n is the number of years

Use the formula to calculate Present Value of $900 in 3 years :

Let us use the formula a little more:

Example: What is $570 next year worth now, at an interest rate of 10% ?

But your choice of interest rate can change things!

Example: What is $570 next year worth now, at an interest rate of 15% ?

Or what if you don't get the money for 3 years

Example: What is $570 in 3 years worth now, at an interest rate of 10% ?

One last example:

Example: You are promised $800 in 10 years time. What is its Present Value at an interest rate of 6% ?

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Meaning of present value in English

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Examples of present value

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  • Present Value (PV)

define present worth (p)

Written by True Tamplin, BSc, CEPF®

Reviewed by subject matter experts.

Updated on July 12, 2023

Get Any Financial Question Answered

Table of contents, what is present value (pv).

Present Value is a financial concept that represents the current worth of a sum of money or a series of cash flows expected to be received in the future.

PV takes into account the time value of money , which assumes that a dollar received today is worth more than a dollar received in the future due to its potential earning capacity.

The time value of money is a fundamental concept in finance, which states that money available at the present time is worth more than the same amount in the future.

This is because of the potential earnings that could be generated if the money were invested or saved.

PV is a crucial concept in finance, as it allows investors and financial managers to compare the value of different investments , projects, or cash flows.

Understanding PV is essential for making informed decisions about the allocation of resources and the evaluation of investment opportunities.

Present Value Formula

Components of the formula.

The Present Value formula is calculated using the following components:

Future Cash Flow: The amount of money expected to be received in the future.

Discount Rate: The interest rate used to discount future cash flows back to their present value.

Time Period: The number of periods into the future when the cash flow is expected to occur.

The formula for calculating Present Value is as follows:

PV = CF / (1 + r)^n

Where PV is the Present Value, CF is the future cash flow, r is the discount rate, and n is the time period.

PV Calculation Examples

Suppose an investor expects to receive $10,000 in five years and uses a discount rate of 5%. Using the Present Value formula, the PV of this future cash flow can be calculated as:

PV = $10,000 / (1 + 0.05)^5 = $7,835.26

This means that the current value of the $10,000 expected in five years is $7,835.26, considering the time value of money and the 5% discount rate.

Applications of Present Value

Investment analysis.

PV is used to evaluate and compare different investment opportunities by calculating the present value of their expected future cash flows. This helps investors determine the most profitable investments.

Capital Budgeting

Companies use PV in capital budgeting decisions to evaluate the profitability of potential projects or investments. By calculating the present value of projected cash flows, firms can compare the value of different projects and allocate resources accordingly.

Bond Valuation

In bond valuation, PV is used to calculate the present value of future coupon payments and the bond's face value. This information is used to determine the bond's fair market price.

Loan Amortization

PV calculations are used in loan amortization schedules to determine the present value of future loan payments. This information helps borrowers understand the true cost of borrowing and assists lenders in evaluating loan applications.

Retirement Planning

Individuals use PV to estimate the present value of future retirement income, such as Social Security benefits or pension payments . This information helps individuals determine how much they need to save and invest to achieve their desired retirement income.

Applications-of-Present-Value-(PV)

Factors Affecting Present Value

Interest rates.

Interest rates have a significant impact on PV calculations. Higher interest rates result in lower present values, as future cash flows are discounted more heavily. Conversely, lower interest rates lead to higher present values.

Inflation affects the purchasing power of money over time, which in turn influences the present value of future cash flows. Higher inflation rates reduce the present value of future cash flows, while lower inflation rates increase present value.

Risk and Uncertainty

The level of risk and uncertainty associated with future cash flows can impact the discount rate used in PV calculations. Higher levels of risk and uncertainty typically require higher discount rates, which result in lower present values.

Conversely, lower levels of risk and uncertainty lead to lower discount rates and higher present values.

Time Horizon

The time horizon , or the length of time until a future cash flow is expected to be received, also impacts the present value. The longer the time horizon, the lower the present value, as future cash flows are subject to a greater degree of discounting.

Factors-Affecting-Present-Value-(PV)

Present Value vs Net Present Value (NPV)

Definitions and distinctions.

While Present Value calculates the current value of a single future cash flow, Net Present Value (NPV) is used to evaluate the total value of a series of cash flows over time.

NPV is calculated by summing the present values of all future cash flows, including inflows and outflows, and represents the net benefit of an investment or project.

When to Use PV or NPV

PV is suitable for evaluating single cash flows or simple investments, while NPV is more appropriate for analyzing complex projects or investments with multiple cash flows occurring at different times.

Comparison of the Two Methods

Both PV and NPV are important financial tools that help investors and financial managers make informed decisions.

PV provides a snapshot of the value of a single future cash flow, while NPV offers a comprehensive assessment of the net value of an investment or project, considering all cash flows over time.

Limitations of Present Value

Dependence on accurate cash flow estimation.

PV calculations rely on accurate estimates of future cash flows, which can be difficult to predict. Inaccurate cash flow estimates can lead to incorrect present values, which may result in suboptimal investment decisions.

Sensitivity to Discount Rate Changes

PV calculations are sensitive to changes in the discount rate. Small changes in the discount rate can significantly impact the present value, making it challenging to accurately compare investments with varying levels of risk or uncertainty.

Challenges With Non-conventional Cash Flow Patterns

PV calculations can be complex when dealing with non-conventional cash flow patterns, such as irregular or inconsistent cash flows. In these cases, calculating an accurate present value may require advanced financial modeling techniques.

Present Value is a fundamental concept in finance that enables investors and financial managers to assess and compare different investments, projects, and cash flows based on their current worth.

By taking into account factors such as interest rates, inflation, risk, and time horizon, financial professionals can employ Present Value calculations to make informed decisions about resource allocation and investment opportunities.

Understanding the applications and limitations of Present Value, including its dependence on accurate cash flow estimation and sensitivity to discount rate changes, is essential for making sound financial decisions.

Moreover, it is vital to recognize the differences between Present Value and Net Present Value, as each method serves a unique purpose in financial analysis.

While Present Value calculates the current value of a single future cash flow, Net Present Value evaluates the total value of a series of cash flows over time, offering a comprehensive assessment of an investment or project's net value.

By utilizing these financial tools effectively, investors and financial managers can optimize their investment portfolios and maximize their returns on investment.

Present Value (PV) FAQs

What is present value (pv).

Present value is a financial concept that represents the current value of an expected future sum of money, after accounting for the time value of money and the risk associated with the investment.

How is present value calculated?

PV is calculated by taking the future sum of money and discounting it by a specific rate of return or interest rate. This discount rate takes into account the time value of money, which means that money today is worth more than the same amount of money in the future.

What is the significance of present value in finance?

PV is a significant concept in finance, as it helps individuals and businesses to make investment decisions by estimating the current value of future cash flows. By calculating the PV of potential investments, investors can determine if an investment is worth pursuing or if they would be better off pursuing alternative investment opportunities.

What factors affect present value?

The primary factors that affect PV include the interest rate or discount rate used in the calculation, the length of time until the expected future cash flow is received, and the risk associated with the investment. Generally, a higher interest rate will result in a lower PV, while a longer time horizon or higher risk will result in a lower PV.

What are some common applications of present value?

PV is commonly used in a variety of financial applications, including investment analysis, bond pricing, and annuity pricing. It is also used to evaluate the potential profitability of capital projects or to estimate the current value of future income streams, such as a pension or other retirement benefits.

About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide , a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University , where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website or view his author profiles on Amazon , Nasdaq and Forbes .

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present value

Definition of present value

Examples of present value in a sentence.

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'present value.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

1831, in the meaning defined above

Dictionary Entries Near present value

present tense

present writer

Cite this Entry

“Present value.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/present%20value. Accessed 14 Mar. 2024.

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Present Value: An In-Depth Look at Today’s Worth of Future Money

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Present Value Definition

Present value is the concept in finance that determines the current worth of a future sum of money or stream of cash flows given a specified rate of return. It contrasts future cash flows with their value today, factoring in the time value of money – the idea that money available now is worth more than the same amount in the future.

The Concept of Time Value of Money

To fully understand the idea of present value, one must first grasp the underlying principle of the time value of money (TVM).

TVM is a concept that suggests money available in the present time is worth more than the same amount in the future. This value difference stems from the potential of the present money to earn returns or income through investments, interests, or other financial avenues.

Put another way, if you were given a choice between receiving a sum of money today or the same sum a year from now, the rational choice would be to opt for money now. The main factor driving this preference is uncertainty of the future. By taking the money now, you eliminate future uncertainties and possible inflation risks. Additionally, you can put this sum to work through an investment or risk-free saving account and earn interest on it, growing the amount you initially had.

###The Importance of Interest Rates

A crucial aspect of the TVM concept is the interest rate. Technically, the interest rate is the reward for abstaining from immediate consumption and instead saving or investing the money. The higher the interest rate, the more you can earn from your present sum over time, and hence, the larger the difference in value from a future sum.

In essence, the time value of money provides the mathematical backbone for present value computations, allowing us to translate future inflows and outflows into present values. The heart of this calculation lies in the idea that a dollar today provides more value, due to its earning potential, than a dollar in the future. This critical concept should underpin any financial decision you make, from personal investments to corporate finance, given its fundamental influence on the realm of economic and financial dynamics.

Calculating Present Value

The present value formula.

To better understand how to calculate present value, let's dive into the formula. The formula for calculating present value (PV) is:

In this formula, FV stands for future value, r represents the interest rate per period, and n signifies the number of periods.

Future Value

The future value (FV) is the value of a current asset or amount of money in a specified future date. It's based on a certain rate of return or interest rate. This is the number that you plan to discount back to the present.

Interest Rate

Represented by r in our formula, the interest rate is the cost or value tied to borrowing or lending money. It's usually represented as a percentage of the principal amount on an annual basis. This rate, when compounded over time, affects the future value of the money, which we subsequently discount to get the present value.

Number of Periods

Another important element in our formula is n , representing the number of periods. This could be the number of years, months, quarters etc based on your context. Essentially, it gives us the time frame for which the money is invested or borrowed.

Relating Present Value to Interest Rate and Time

Remember that present value demonstrates the concept of time value of money, that is, a dollar today is worth more than a dollar tomorrow. Thus, it is inversely proportional to both the interest rate and the number of periods.

As the interest rate (r) increases, the present value diminishes. This is because a higher interest rate diminishes the worth of future money today.

Similarly, an increase in the number of periods (n) reduces the present value. The concept is that money received farther in the future is not as valuable as an equivalent amount received today. The further out we go in time, the more discounted the future value is, hence a lower present value.

In conclusion, understanding the elements of this formula and how they interact allows us to calculate and better understand the concept of present value.

Influence of Risk on Present Value

Risk and present value.

As we delve deeper into the world of present value, an important factor we need to duly consider is risk. Risk is an inherent part of making investments and it plays a significant role in the calculations of present value.

Firstly, risk influences the discount rate used in the present value formula. The discount rate, or the rate of return required by an investor, increases with the level of risk associated with an investment. This can be understood intuitively – as an investor, if your investment carries a high degree of uncertainty, you would want a higher return to compensate for the potential loss you might incur.

Investors assess the level of risk of an investment and then determine a rate of return that would make the investment worth their while, called the risk-adjusted discount rate. The higher the risk, the higher the required rate of return, and thus, the higher the discount rate. Remember, the discount rate isn't a fixed number, but a measure of the opportunity cost of capital and a reflection of the perceived risk.

The Effect of Risk on Present Value

This link between risk and discount rate brings us to a central point – riskier investments result in lower present values. It's worth noting why this is the case.

When the risk-adjusted discount rate is high, the denominator in the present value formula increases, which in turn reduces the present value of future cash flows. So, an increase in perceived risk has the effect of reducing the present value of an investment.

This scenario is commonly seen in businesses. Companies with high risk are perceived as less attractive to investors, reducing their market capitalisation even if they have high future cash flows. This exemplifies the importance of risk assessment in not just deciding whether or not to make an investment, but also in determining the present value of future cash flows.

In conclusion, understanding how risk influences present value is crucial as it underscores the fundamental truth that higher risk investments demand a higher rate of return, which usually results in a lower present value. This allows investors to make informed decisions and better gauge the worth of an investment.

Uses of Present Value in Finance

Capital budgeting.

In the realm of capital budgeting, present value is a critical component that aids in investment decision-making. It is a tool that assists in comparing the value of money today and in the future, thereby helping organizations to prioritize and decide on long-term investment projects. The present value method is often used to estimate the profitability of a potential investment by considering the inflows and outflows of cash over a specific period of time, all discounted back to their current value. This process of discounting future cash flows helps in determining whether the expected return on investment would exceed the initial outlay. Therefore, the higher the present value of future cash flows, the more likely an investment is to be considered profitable.

Bond Pricing

Present value also plays a crucial role in bond pricing. The basic principle of bond pricing is that the price of a bond is the present value of its future cash flows. These cash flows include periodic coupon payments and the repayment of principal at maturity, all discounted back to the current day using a discount rate that reflects the riskiness of these cash flows. By comparing the present value of a bond's cash flows with its market price, investors can determine if the bond is overpriced or underpriced, and thereby make informed investment decisions.

Pension Obligations

In the context of pension obligations, present value is also an invaluable tool. It helps in estimating the current worth of the future pension payments an organization is obligated to make. Given the long-term nature of these payments and the uncertainty surrounding factors like employee longevity and salary growth, discounting these future obligations back to the present using an appropriate discount rate is essential. This enables organizations to adequately fund their pension schemes and ensure they meet their future obligations.

Aiding Decision-making

In essence, present value is a universal tool that aids financial analysts and investors in evaluating and comparing different investment opportunities. By discounting future cash flows back to their current worth, it allows them to make apples-to-apples comparisons and make informed decisions that potentially enhance wealth and ensure long-term financial success. It is a fundamental concept in finance that underpins many financial decisions, from simple investments to complex corporate finance strategies.

Importance of Present Value in Investment Decisions

Understanding the role of present value in financial decision-making allows investors to assess profitability or the value of an investment more realistically. Essentially, present value serves as a tool in investment decision making because it allows investors to translate future dollars or other currencies into their present worth.

Using the concept of present value, investors are able to project future cash inflows from an investment and convert these into their present value or today's dollars. This process helps in accurately assessing the trade-off between the present consumption and future consumption of any investment.

The comparison of investments becomes far more straightforward when these future inflows are converted to their present value. By evaluating the present value of projected cash inflows, investors can analyze and compare different investment options on equal footing. This forms a vital part of the decision-making process in investment since it enables a more streamlined comparison of different investment opportunities.

Consider this simple example. If someone offers you 1000 dollars today or promises to give you 1050 dollars after a year, you may be tempted to wait and take the larger sum later. However, the present value of that 1050 dollars (depending on the discount rate) may be less than 1000 dollars. This could mean taking the money now would be the wise decision.

By calculating and comparing present values, an investor can strategically assess options and choose the one that will potentially offer the highest return in today's dollars. This highlights the important role that present value plays in shaping investment decisions.

Each investment opportunity has a relative worth, and the principle of present value helps to quantify that worth today. It brings clarity to an investment's potential gains or losses, allowing investors to make informed decisions. Consequently, understanding and applying present value is deemed essential for anyone involved in investment decisions.

Present Value and Corporate Social Responsibility (CSR)

Understanding the potential role of present value in CSR activities provides valuable insights into the financial commitments companies make towards sustainability.

Influence of Present Value on CSR Initiatives

The present value concept plays a significant part in the decision-making process of companies when it comes to CSR initiatives, particularly in the field of sustainability. Companies frequently need to decide whether to allocate resources towards sustainable projects that could yield long-term benefits but might require substantial early-stage investments.

By evaluating the present value of the expected future benefits, companies can gain a clearer understanding of the financial trade-off involved. If the expected future benefits, appropriately discounted to their present value, outweigh the project's immediate costs, the companies might be willing to take the plunge and invest now.

Fair consideration of the time value of money allows companies to objectively determine if a potential sustainable project is worth the upfront expense. This ensures that companies' decisions to invest in CSR initiatives today are grounded in sound financial rationale.

CSR and the Consideration of Future Stakeholder Value

Present value calculations in CSR initiatives also extend to considering future stakeholder value. Capital stakeholders, communities, and even the environment could be seen as recipients of long-term benefits from sustainable projects. By ascertaining the present value of these future benefits, companies can take a strategic approach to CSR, ensuring that their investment choices not only serve their financial interests but also contribute to broader social and environmental goals.

To sum up, the concept of present value can play a major role in shaping a company's CSR initiatives, helping it to balance immediate expenses with long-term sustainability and stakeholder value.

Present Value Limitations

While the concept of present value provides an essential tool for financial valuation, it is not devoid of certain limitations.

Uncertainty of Future Cash Flows

In an ideal world, future cash flows would be accurately predictable. However, reality often presents a different picture. Uncertainties tied to the global economy, political climate, and other unpredictable factors can significantly influence an organization's anticipated cash flows. This introduces an element of risk and potential incorrect valuation when using the present value formula. Despite employing sound financial forecasting methods, there's always the reality that actual future cash flows may not align with preliminary projections. An unanticipated downturn or even a boom could cause discrepancies between calculated present value and actual return.

Challenges in Estimating the Discount Rate

The discount rate is a critical factor in the calculation of present value. It is essentially the interest rate used to depreciate future income, and its accurate estimation is paramount. However, determining an appropriate discount rate is challenging due to the numerous factors involved – risk-free rate, inflation expectations, risk premium, and more.

Changes in the discount rate can dramatically affect the present value of future cash flows. For instance, a higher discount rate will decrease present value and can make an investment appear less attractive than it may be. Choosing an appropriate discount rate is a subjective process, and slight variations can result in significant deviations in present-value estimates.

Fluctuating Market Conditions

In a volatile market, the target company's future cash inflows and outflows can be impacted, leading to discrepancies between estimated and actual present value. Market instability and fluctuations form an inherent part of business operations and can affect cash flows, inflation rates, and discount rates. Thus, depending on the current market conditions and future predictions, the present value needs to be reassessed periodically.

In summary, while present value is a highly useful tool in finance, the limitations posed by the unpredictable nature of future cash flows, difficulty in accurately estimating the discount rate and volatile market conditions must be accounted for in any financial decision-making processes.

Present Value and Inflation

Inflation has a significant impact on the way present value is calculated and its results in real-world scenarios. Literally put, inflation corresponds to a decrease in purchasing power over a period of time. Therefore, the same amount of money will not be able to purchase the same quantity of goods or services in the future as it can today.

When calculating present value, we discount future cash flows to present terms using an interest rate, often referred to as the discount rate. This discount rate generally includes an adjustment for inflation. Why is that? Suppose you expect to receive a certain amount of money in the future, but over that period, inflation occurs. As a result, the same amount of money will purchase less than it would presently. Therefore, to have an accurate assessment of how much the future cash flow is worth today, you must incorporate the rate of inflation into your discount rate.

Let's consider a practical scenario. Suppose you're considering whether to invest in a long-term government bond that promises an annual return of 5% or in a real estate project that promises the same return. Let's assume inflation is 2%. At a first glance, both investments seem to offer the same potential returns. However, by considering inflation, the real returns on these investments might be very different.

Government bond returns are fixed and are not protected against inflation. So, if you receive a 5% return on your bond, in real terms, after adjusting for inflation, this return might be only 3%. On the other hand, real estate investments are typically a hedge against inflation. As the general price level rises, often the property prices rise too, resulting in higher rental income. Therefore, the real return on real estate investment might be higher than that of the bond.

In sharp contrast, when assessing the present value of future cash flows from real estate investments, inflation might result in a lower discount rate being used (as future cash flows are expected to increase with inflation), resulting in a higher present value. For the bond, the discount rate might be higher (as the fixed future cash flows have lower purchasing power), resulting in a lower present value.

Thus, as we can see, ignoring inflation when evaluating the present value of future cash flows can lead to inaccurate conclusions, severely impacting financial decisions.

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Quickonomics

Present Value

Definition of present value.

Present Value (PV) is a financial concept that describes the current value of a future sum of money or stream of cash flows. That means it is a way to measure the value of money today compared to a future date. To calculate the present value (PV), you need to know the future value (FV), the interest rate (r), and the number of periods until the future date (n). More specifically, it can be calculated using the following formula: PV = FV*(1/[1+r]^n).

To illustrate this concept, let’s assume you are offered a job that pays you USD 10,000 in one year. That means you will receive the money exactly one year from now. Now, if the interest rate is 5%, the present value of this future sum of money is USD 9,523.81 (i.e., 10,000*1/1.05^1). That means you would need USD 9,523.81 today and invest it at 5% interest over the next year, to get the same amount of money. Thus, the present value of the USD 10,000 is USD 9,523.81.

Why Present Value Matters

Present Value is an important concept for investors because it allows them to compare different investments and make informed decisions. If an investor is offered two different investments with the same future value but different interest rates, he can use the present value to determine which one is more profitable. In addition to that, present value is also used to calculate the net present value (NPV) of a project, which is a measure of its profitability. Thus, it is an important tool for financial decision-making in general.

Related Terms

  • Financial Economics

Balanced Investment Strategy

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Table of Contents

Present value.

Present value (PV) is a financial term that refers to the current worth of a future sum of money or stream of cash flows given a specific rate of return. It computes the value of future money in today’s terms. The calculation helps determine what an investment or any amount of cash could be valued at today.

The phonetic pronunciation for “Present Value” is: /ˈprɛzənt ˈvæljuː/

Key Takeaways

<ol><li>Present Value showcases the concept of time value of money: The main takeaway of present value is that it illustrates the idea that money today is worth more than the same amount of money in the future. This serves as the foundation of many financial concepts and decisions.</li><li>It is used in financial modeling and investment decision making: Present value is used in financial modeling to determine the current worth of future cash flows. It helps in comparing investment options, pricing bonds, determining rates of return or understanding the impact of different financing options.</li><li>Present Value depends on the rate of interest: The rate of interest, also referred to as the discount rate, plays a crucial role in determining the present value. Higher the discount rate, lower the present value of future earnings since a high discount rate decreases the value of future cash flows.</li></ol>

The concept of Present Value (PV) is crucial in business and finance as it allows companies and investors to determine the current worth of a future sum of money or stream of cash flows given a specified rate of return. This is important because money loses value over time due to factors like inflation, risk, and opportunity cost. The Present Value calculation aids in making investment decisions, comparing financial products, pricing bonds, and setting up amortization schedules for loans. It essentially helps in understanding if the future cash inflows from an investment, project or financial product are worth more than the current outflow of cash or vice versa, enabling informed decision-making around investments, loans, and other financial commitments.

Explanation

Present Value (PV) serves as a fundamental concept in finance and business that helps decision makers understand the worth of a future amount of money in terms of today’s value. This concept is crucial in deciding whether an investment is profitable by comparing the value of money today to the expected value in the future. For businesses, PV can be used in evaluating projects’ profitability, planning fiscal procedures, and capital budgeting. PV gives discernment into how much a future cash flow is worth today, enabling companies to make well-informed decisions concerning investments, loans, leases, and other financial commitments.PV’s role is evident in the determination of discounted cash flows, which is a method used for valuating a project, a company or an asset based on the principle that a dollar in the future is not worth a dollar today. Cash today can be invested to generate more money in the future, so money received in the future is not as valuable as money received now. This concept elicits the understanding that the value of money decreases over time due to potential earning capacity, inflation, risk and preference for consumption. While the concept may seem complex, understanding present value is fundamental for assessing the profitability of investments, thereby playing an essential role in financial decision making.

1. Education Fund: Let’s say parents want to build a college fund for their child who will go to college in 15 years. The estimated cost of college at that time is expected to be $100,000. To determine how much they need to invest now, they would calculate the present value of $100,000 by taking into account expected inflation and average investment returns over that 15-year period.2. Buying a House: Consider a person who wishes to purchase a house valued at $300,000, and he pledges to make the payment three years from now. To calculate how much he needs to save or invest today considering the investment returns and inflation, he would find the present value of that $300,000.3. Business Investments: A company plans to undertake a project which is expected to bring in a profit of $500,000 in 5 years. To determine whether it is worth investing in the project, the company will calculate the present value of $500,000, by taking into account the expected return on investment over that 5-year period. This present value will then be compared with the total cost of the project to see if it’s a profitable venture.

Frequently Asked Questions(FAQ)

Present value (PV) refers to the concept that money available today is worth more than the same amount in the future, due to its earning potential. This principle, often referred to as the time value of money, allows investors to compare the value of dollars at different points in time, hence influencing investment decisions.

The present value calculation involves three elements: the future cash flow, the discount or interest rate, and the number of time periods in the future. The formula is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

Present value is a critical principle in finance as it quantifies the opportunity cost of investing or spending money today, making it possible to compare the worthiness of different investment opportunities.

Inflation reduces the purchasing power of a dollar over time, therefore reducing the present value of future cash flows. This is why we typically discount future cashflows when calculating present value.

While present value provides an estimate of how much a future sum of money is worth today, future value provides an estimate of how much a sum of money today will be worth in the future, given a certain interest rate or growth rate.

Yes, the present value can be negative. It usually happens when the cash outflow (or expense) is expected to occur before the cash inflow, indicating that you have to spend money before you make it.

The discount rate applied in the present value calculation directly impacts the present value of cash flows. A higher discount rate will decrease the present value of future cash flows, while a lower rate will increase their present value.

Related Finance Terms

  • Discount Rate
  • Future Value
  • Net Present Value (NPV)
  • Time Value of Money (TVM)

Sources for More Information

  • Investopedia
  • Corporate Finance Institute
  • Lumen Learning
  • Khan Academy

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Open Educational Resources

A brief guide to engineering financial calculations: present worth analysis.

Future values are a set of monetary values expressed in terms of the time at which each of the transaction occurs. Each amount is expressed in the value of the currency at that particular time, referred to as future dollars or more generally as “as-spent” dollars. 

\boldsymbol{i}

In Present Worth analysis, the focus is on the future. Any values from a time before the present time are ignored. These are called sunk costs. 

When MARR is used as the interest rate, then the NPV needs to be greater than zero to be accepted. (That’s why it is called a hurdle rate: the NPV has to be more than zero to clear the bar at MARR.) The Weighted Average Cost of Capital (WACC) is another hurdle rate that a company may use, which represents the cost of its financing and its overall level of investment risk. If the investment does not provide a return at that rate or better, then the company’s performance slips.   

Calculating the Present Market Value of a Bond

When assessing an investment, it is important to consider what its current market value, to determine whether it is still a worthwhile investment or it should be sold.

In the case of a bond, the investment has a fixed “coupon” rate, meaning that the same amount is paid at the end of each year for a specified number of years, as a percentage of the face value of the bond (the Principal). At the end of the final period, you also get the Principal back (the original amount).  The market interest rate is the discount rate that affects the future value of those amounts. 

In reality, the market interest rate changes all the time, but for our purposes for future value calculation we assume that it is constant, because we have no information to make us believe that the discount rate is going to be different from what it is right now.

\boldsymbol{P_{bond}}

Present Worth Analysis Using A Spreadsheet

Present Worth Analysis is most easily done using a spreadsheet program. The formulæ shown in the section above are useful for specific situations; but in reality, most cash flows are not as well behaved as the idealized series.

Calculation

\boldsymbol{P}

P = F x ( 1 + i ) – n

This formula is used to calculate the present value of each of the individual future values.

P = 100 x ( 1 + 0.03 ) -1   is

=B5*(1+$B$2)^(-A5).

Note that an absolute cell reference is used for the interest rate in cell $B$2.

The future values are entered in column B starting “today” in row 4, with the value one period later in row 5, etc.

The value in cell $C$6 calculates the present value at the end of year 2, which in this case is   P = 100 x ( 1 + 0.03 ) -2 , the formula in the cell is =B6*(1+$B$2)^(-A6). The value in cell $C$7 to calculate the present value at the end of year 3, or  P = 100 x ( 1 + 0.03 ) -3 , is =B7*(1+$B$2)^(-A7).

The NPV is simply the sum of the present values. In Excel, use the SUM( ) function. In this example the formula in cell $C$8 is

=SUM(C4:C7)

In this particular example, the NPV of the series happens to be the same as the Uniform Series Present Worth in the case of P =100 x (P/A, 3%, 3) .

Here is a tip for setting up a spreadsheet for NPV: Use an absolute reference for the interest rate. Remember that the convention for an absolute reference to a cell is to use dollar signs in front of the column (letter) and/or the row (number), $B$2 in this example. In this way, the present value is calculated by pointing directly to the cell that has the number that you use repeatedly, in this case, the interest rate. A common error can occur when setting up the spreadsheet by copying cells into another location that end up referring to the wrong cell. Check your calculation formulæ in the cells to make sure you are using the correct parameters from other cells.

Rate of Return

The internal rate of return (IRR) is the interest rate for which the sum of present values totals to zero. This is the rate of return at which the benefits of the investment are the same as its costs. If the IRR is greater than MARR, then it is a worthwhile investment.

If IRR is higher than MARR, then later future sums have more value at the MARR hurdle rate than at the IRR rate, which means that the investment will deliver value beyond what is demanded at the MARR.  If IRR is below MARR, then later future sums have less value at the MARR hurdle rate than at IRR rate, and so the investment will not deliver value required at MARR.

Calculation:

Tabulate a time series set of future values on a spreadsheet and calculate their individual present values using a first guess at the IRR interest rate. Calculate the Net Present Value of the series of Present Values. Then, use the Excel solver function to make this IRR Present Value total equal to zero by solving for the IRR interest rate, which is chosen by selecting the cell that contains the interest rate.

It is good practice to create an additional column in a spreadsheet for each present value case (e.g. MARR and IRR). You should question an IRR in the bazillions of percent; a common error is not putting the correct signs on costs or benefits.

Solving for i of a Cash Flow Series by Interpolation Using Interest Tables

Incremental IRR

Incremental IRR (IIRR) is used for an investment that is being considered as an alternative to another investment. The investment with the lower capital cost is considered to be the base case. The cash flow of the higher-capital-cost alternative (in future dollars) is subtracted from the cash flow of the base investment (also in future dollars) to give the incremental cash flow. The IIRR is then found using an iterative solution (such as Solver in Excel) for the series of present values of the incremental cash flow that gives an NPV of $0. If the IIRR is greater than MARR, then the higher capital cost alternative should be selected, because it adds enough extra value to be worthwhile. In fact, if the IIRR is greater than the IRR of the base investment, then the incremental investment adds more value to the investment on a relative basis than the base investment does.

Other Analysis Techniques

Benefit-Cost Analysis

The Benefit-Cost ratio compares the Present Worth of the benefits of an investment PW benefits , and the Present Worth of the costs PW costs

BCR = PW benefits / PW costs

If BCR < 1, then the benefits are less than the costs, and so the investment is not worthwhile.

Incremental Benefit-Cost Analysis

Incremental Benefit-Cost analysis compares increasing costly alternatives.

  • For each option, calculate the PW of its benefits the PW of its costs, and its Benefit to cost ratio. Reject any option that has a BCR < 1.
  • Arrange the remaining options in ascending order of costs.
  • Then calculate the incremental BCR between cases, starting with the lowest two cost options. As analysis proceeds, reject any option that gives an incremental BCRs that is less than 1, and use the next higher cost option to calculate the incremental BCR.
  • Once all the valid incremental BCRs have been calculated, choose the option with the highest cost that still has an acceptable incremental BCR (that is, greater than 1). Note that the choice will not necessarily have the highest BCR.

Payback happens when an investment has paid for itself. The point at which the cumulative sum of values becomes positive is when payback occurs.

For engineering projects, the payback time is usually counted as the time from start-up (that is, the first period in which there is positive cash flow) to the point at which the sum of the series of time values goes positive, rather than counting from the beginning of the project itself. Payback usually happens in the middle of a period, but payback period is usually expressed as an integer: the end of that period minus beginning of start-up. For example, if an engineering project started at the beginning of year 1, started up sometime in year 4, and the sum of values went positive sometime in year 11, then the payback time is

11 – 4 = 7 years. Some people interpolate within a year to get more precision, but it’s not usually worth the extra effort, given the inherent uncertainties in such analyses.

Simple payback is found from the series of future values.

Discounted payback is found from the series of present values (the discounted values of the future sums).

Break-Even Analysis

Break-even analysis considers the effect of a parameter in an investment option on its equivalence to another investment option. The key is to express one investment option in terms of the variable to be solved and the equivalent value of the other option.

If the cash flow is simple, then it is often easiest to solve for a parameter directly using an interest formula and solving by interpolation from the interest tables. Of course, a spreadsheet can be used with the Solver function to find the value of the parameter.

Solving for n of a Cash Flow Series by Interpolation Using Interest Tables

What Is Included in the Cash Flow Series for an Investment Project

In evaluating an investment, only future costs are considered. The cash flow series should only include the incremental costs to do the project, and none of the costs associated with running the current business. For example, allocation of costs for head office overheads does not enter into a cash flow analysis, since no incremental money is spent. (The head office would run whether the project went ahead or not.) Providing an accounting reserve for future expenditures is a common accounting practice (recall that allowances are used to blend out expenditures); but cash flow forecasts use actual cash flows that are expected to occur, not allowances. Some projects may do preliminary project development work as part of regular business activities. These sunk costs would not be attributed to the project.

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Present Value of an Annuity

  • How It Works
  • Formula and Calculation

Annuity vs. Annuity Due

The bottom line.

  • Retirement Planning

Present Value of an Annuity: Meaning, Formula, and Example

Julia Kagan is a financial/consumer journalist and former senior editor, personal finance, of Investopedia.

define present worth (p)

Investopedia / Dennis Madamba

What Is the Present Value of an Annuity?

The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate . The higher the discount rate, the lower the present value of the annuity.

Present value (PV) is an important calculation that relies on the concept of the time value of money, whereby a dollar today is relatively more "valuable" in terms of its purchasing power than a dollar in the future.

Key Takeaways

  • The present value of an annuity refers to how much money would be needed today to fund a series of future annuity payments.
  • Because of the time value of money, a sum of money received today is worth more than the same sum at a future date.
  • You can use a present value calculation to determine whether you'll receive more money by taking a lump sum now or an annuity spread out over a number of years.

Understanding the Present Value of an Annuity

An annuity is a financial product that provides a stream of payments to an individual over a period of time, typically in the form of regular installments. Annuities can be either immediate or deferred, depending on when the payments begin. Immediate annuities start paying out right away, while deferred annuities have a delay before payments begin .

Because of the time value of money , money received today is worth more than the same amount of money in the future because it can be invested in the meantime. By the same logic, $5,000 received today is worth more than the same amount spread over five annual installments of $1,000 each.

Present value is an important concept for annuities because it allows individuals to compare the value of receiving a series of payments in the future to the value of receiving a lump sum payment today. By calculating the present value of an annuity, individuals can determine whether it is more beneficial for them to receive a lump sum payment or to receive an annuity spread out over a number of years. This can be particularly important when making financial decisions, such as whether to take a lump sum payment from a pension plan or to receive a series of payments from an annuity.

The pension provider will determine the commuted value of the payment due to the beneficiary. They do this to ensure they are able to meet future payment obligations.

Present value calculations can also be used to compare the relative value of different annuity options, such as annuities with different payment amounts or different payment schedules.

Present Value and the Discount Rate

The discount rate is a key factor in calculating the present value of an annuity. The discount rate is an assumed rate of return or interest rate that is used to determine the present value of future payments.

The discount rate reflects the time value of money, which means that a dollar today is worth more than a dollar in the future because it can be invested and potentially earn a return. The higher the discount rate, the lower the present value of the annuity, because the future payments are discounted more heavily. Conversely, a lower discount rate results in a higher present value for the annuity, because the future payments are discounted less heavily.

In general, the discount rate used to calculate the present value of an annuity should reflect the individual's opportunity cost of capital, or the return they could expect to earn by investing in other financial instruments. For example, if an individual could earn a 5% return by investing in a high-quality corporate bond, they might use a 5% discount rate when calculating the present value of an annuity. The smallest discount rate used in these calculations is the risk-free rate of return . U.S. Treasury bonds are generally considered to be the closest thing to a risk-free investment, so their return is often used for this purpose.

It's important to note that the discount rate used in the present value calculation is not the same as the interest rate that may be applied to the payments in the annuity. The discount rate reflects the time value of money, while the interest rate applied to the annuity payments reflects the cost of borrowing or the return earned on the investment.

The opposite of present value is future value (FV) . The FV of money is also calculated using a discount rate, but extends into the future.

Formula and Calculation of the Present Value of an Annuity

The formula for the present value of an ordinary annuity, is below. An ordinary annuity pays interest at the end of a particular period, rather than at the beginning:

P = PMT × 1 − ( 1 ( 1 + r ) n ) r where: P = Present value of an annuity stream PMT = Dollar amount of each annuity payment r = Interest rate (also known as discount rate) n = Number of periods in which payments will be made \begin{aligned} &\text{P} = \text{PMT} \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) }{ r } \\ &\textbf{where:} \\ &\text{P} = \text{Present value of an annuity stream} \\ &\text{PMT} = \text{Dollar amount of each annuity payment} \\ &r = \text{Interest rate (also known as discount rate)} \\ &n = \text{Number of periods in which payments will be made} \\ \end{aligned} ​ P = PMT × r 1 − ( ( 1 + r ) n 1 ​ ) ​ where: P = Present value of an annuity stream PMT = Dollar amount of each annuity payment r = Interest rate (also known as discount rate) n = Number of periods in which payments will be made ​

Example of the Present Value of an Annuity

Assume a person has the opportunity to receive an ordinary annuity that pays $50,000 per year for the next 25 years, with a 6% discount rate, or take a $650,000 lump-sum payment. Which is the better option? Using the above formula, the present value of the annuity is:

Present value = $ 50 , 000 × 1 − ( 1 ( 1 + 0.06 ) 25 ) 0.06 = $ 639 , 168 \begin{aligned} \text{Present value} &= \$50,000 \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + 0.06 ) ^ {25} } \Big ) }{ 0.06 } \\ &= \$639,168 \\ \end{aligned} Present value ​ = $ 5 0 , 0 0 0 × 0 . 0 6 1 − ( ( 1 + 0 . 0 6 ) 2 5 1 ​ ) ​ = $ 6 3 9 , 1 6 8 ​

Given this information, the annuity is worth $10,832 less on a time-adjusted basis, so the person would come out ahead by choosing the lump-sum payment over the annuity.

An ordinary annuity makes payments at the end of each time period, while an annuity due makes them at the beginning. All else being equal, the annuity due will be worth more in the present. In the case of an annuity due, since payments are made at the beginning of each period, the formula is slightly different. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):

P = PMT × 1 − ( 1 ( 1 + r ) n ) r × ( 1 + r ) \begin{aligned} &\text{P} = \text{PMT} \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) }{ r } \times ( 1 + r ) \\ \end{aligned} ​ P = PMT × r 1 − ( ( 1 + r ) n 1 ​ ) ​ × ( 1 + r ) ​

So, if the example above referred to an annuity due, rather than an ordinary annuity, its value would be as follows:

Present value = $ 50 , 000 × 1 − ( 1 ( 1 + 0.06 ) 25 ) 0.06 × ( 1 + . 06 ) = $ 677 , 518 \begin{aligned} \text{Present value} &= \$50,000 \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + 0.06 ) ^ {25} } \Big ) }{ 0.06 } \times ( 1 + .06 ) \\ &= \$677,518 \\ \end{aligned} Present value ​ = $50 , 000 × 0.06 1 − ( ( 1 + 0.06 ) 25 1 ​ ) ​ × ( 1 + .06 ) = $677 , 518 ​

In this case, the person should choose the annuity due option because it is worth $27,518 more than the $650,000 lump sum.

Why Is Future Value (FV) Important to investors?

Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. It is important to investors as they can use it to estimate how much an investment made today will be worth in the future. This would aid them in making sound investment decisions based on their anticipated needs. However, external economic factors, such as inflation, can adversely affect the future value of the asset by eroding its value.

How Does Ordinary Annuity Differ From Annuity Due?

An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. An example of an ordinary annuity includes loans, such as mortgages. The payment for an annuity due is made at the beginning of each period. A common example of an annuity due payment is rent. This variance in when the payments are made results in different present and future value calculations.

What Is the Formula for the Present Value of an Ordinary Annuity?

The formula for the present value of an ordinary annuity is:

P = PMT × 1 − ( 1 ( 1 + r ) n ) r where: P = Present value of an annuity stream PMT = Dollar amount of each annuity payment r = Interest rate (also known as discount rate) n = Number of periods in which payments will be made \begin{aligned} &\text{P} = \text{PMT} \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) }{ r } \\ &\textbf{where:} \\ &\text{P} = \text{Present value of an annuity stream} \\ &\text{PMT} = \text{Dollar amount of each annuity payment} \\ &r = \text{Interest rate (also known as discount rate)} \\ &n = \text{Number of periods in which payments will be made} \\ \end{aligned} ​ P = PMT × r 1 − ( ( 1 + r ) n 1 ​ ) ​ where: P = Present value of an annuity stream PMT = Dollar amount of each annuity payment r = Interest rate (also known as discount rate) n = Number of periods in which payments will be made ​

What Is the Formula for the Present Value of an Annuity Due?

With an annuity due, in which payments are made at the beginning of each period, the formula is slightly different than that of an ordinary annuity. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):

P = PMT × 1 − ( 1 ( 1 + r ) n ) r × ( 1 + r ) \begin{aligned} &\text{P} = \text{PMT} \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) }{ r } \times ( 1 + r ) \\ \end{aligned} ​ P = PMT × r 1 − ( ( 1 + r ) n 1 ​ ) ​ × ( 1 + r ) ​

The present value (PV) of an annuity is the current value of future payments from an annuity, given a specified rate of return or discount rate. It is calculated using a formula that takes into account the time value of money and the discount rate, which is an assumed rate of return or interest rate over the same duration as the payments. The present value of an annuity can be used to determine whether it is more beneficial to receive a lump sum payment or an annuity spread out over a number of years.

Cornell Law School, Legal Information Institute. " 26 CFR § 25.2512-5 - Valuation of Annuities, Unitrust Interests, Interests for Life or Term of Years, and Remainder or Reversionary Interests ."

Rice University, OpenStax. " Principles of Finance: 8.2 Annuities ."

TreasuryDirect. " Treasury Bonds ."

George Brown College. " Formula Sheet for Financial Mathematics ." Page 2.

Wai-sum Chan and Yiu-kuen Tse. “ Financial Mathematics for Actuaries (Third Edition) ,” Pages 40-43. World Scientific Publishing Company, 2021.

George Brown College. " Formula Sheet for Financial Mathematics ." Page 3.

Rahman, Mohammad. " Time Value of Money: A Case Study on Its Concept and Its Application in Real Life Problems ." International Journal of Research in Finance and Management , vol. 1, no. 1, 2018, pp. 18-23.

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  • What Is a Fixed Annuity? Uses in Investing, Pros, and Cons 9 of 35
  • Immediate Payment Annuity: What it is, How it Works 10 of 35
  • Indexed Annuity: Definition, How It Works, Yields, and Caps 11 of 35
  • Individual Retirement Annuity: What it is, How it Works 12 of 35
  • Joint and Survivor Annuity: Key Takeaways 13 of 35
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  • Future Value of an Annuity: What Is It, Formula, and Calculation 17 of 35
  • Calculating Present and Future Value of Annuities 18 of 35
  • Annuity Table: Overview, Examples, and Formulas 19 of 35
  • Present Value Interest Factor of Annuity (PVIFA) Formula, Tables 20 of 35
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What is the Present Value of an Annuity?

Home › Finance › Valuation Guides › What is the Present Value of an Annuity?

Definition:  The present value of an annuity is the amount of dollars today that a stream of equal future payments is worth. In other words, it’s the amount of money you would need to invest today in order to equate to the total of the annuity payments adjusted for the time value of money.

  • What Does Present Value of an Annuity Mean?

Summary Definition

What is the definition of present value annuity?  An annuity is a financial instrument that provides regular payments to the holder each period until the end of the contract. The present value of these payments is the amount that an investor would have to invest today at a given interest rate to equate to the total amount of payments in the future discounted by the same interest rate.

Annuities are split into two main categorized:  ordinary annuities  and annuities due. In ordinary annuities, the payment is received at the end of the time period. Annuities due, on the other hand, receive their payments at the beginning of each period. The present value of an annuity formula is calculated below for both types of annuities.

Present Value of an Annuity Example

Where: P = Present value of the annuity PMT = Money value of each annuity payment R = discount rate N = Number of periods / Number of payments made

Determining the present value of a stream of payments helps investors understand how much money they are actually receiving over time in today’s dollars and allows them to make informed investment decisions. This is a common calculation in most lottery winnings where the winner is usually offered the choice between being paid out a one-time lump sum or a series of payments over time. Most lottery winner typically choose the lump sum, so they can receive their winnings up front and invest them accordingly in the future.

Let’s look at an example.

Mr. Johnson is a 65 years old retired military veteran who has been funding his retirement account each month for the last 30 years and now he is finally able to start withdrawing funds. As part of the agreement, the retirement company is offering to pay him $30,000 the 1st of each year for the next 25 years, or a one-time payment of $500,000. He wants to know what the value of the $30,000 yearly payments is worth today to determine his best option.

Using the  present value  formula above, we can see that the annuity payments are worth about $400,000 today assuming an average interest rate of 6 percent. Thus, Mr. Johnson is better off taking the lump sum amount today and investing it himself.

Define Present Value of an Annuity:  PV of an Annuity means the dollar amount a stream of equal payments in the future is worth today.

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Compound Interest Formulas III

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5. Uniform Series Present-Worth Factor

The fifth group in Table 1-5 covers a set of problems that uniform series of equal investments, A, occurred at the end of each time period for n number of periods at the compound interest rate of i. In this case, the cumulated present value of all investments, P, needs to be calculated. In summary, P is unknown and A, i, and n are given parameters. And the problem can be noted as P / A i , n and displayed as:

Figure 1-6:  Uniform Series Present-Worth Factor, P / A i , n

If we replace substitute F in Equation 1-3 from Equation 1-2, we will have the present value as:

Equation 1-5 gives the cumulated present value, P, of all uniform series of equal investments, A, as P = A [ ( 1 + i ) n − 1 ] / [ i ( 1 + i ) n ] . And also can be noted as: P = A * P / A i , n .The factor   [ ( 1 + i ) n − 1 ] / [ i ( 1 + i ) n ]   is called the “uniform series present-worth factor” and is designated by P / A i , n . This factor is used to calculate the present sum, P that is equivalent to a uniform of equal end of period payments, A. Then P / A i , n =   A [ ( 1 + i ) n − 1 ] / [ i ( 1 + i ) n ]

Note that n is the number of time periods that equal series of payments occur.

Please review the following video, Uniform Series Present Worth Factor (Time 3:35).

PRESENTER: The fifth group covers the set of problems that P is a known parameter, A, i and n are given variables. In these problems, we have uniform series of equal investments, A, in the end of each time period, for n number of periods, at the compound interest rate of I.

And the problem asks you to calculate the accumulated present value of all investments, P. We can summarize these questions using the factor notation. P is the unknown variable, and should be on the left side. And A is the given, and should be written on the right side.

As explained before, Equation 1-3 returns the future value, F, from A, i and n. And Equation 1-2 calculates the future value, F, from present value, P, interest rates, i and n number of periods. So if we substitute F in Equation 1-3 from Equation 1-2, we will have this new equation-- 1-5. This equation gives us the accumulated present value of equal series payments, A, paid for n period, at interest rate of i.

Equation 1-5 can also be written according to factor notation. P equals A times the factor P over A. This factor is called Uniform Series Present-Worth Factor, which is used to calculate the presence on P that is equivalent to a uniform series of equal payments, end of the period payments, A.

For example, what would be the present value of 10 uniform investments of $2,000, invested at the end of each year, for interest rate of 12%, compounded annually? First, we draw the time line. Left hand side is a present time, time zero payment, which needs to be calculated. N equals 10, because there are 10 uniform investments.

So we have 10 years. And above each year, we have $2,000, starting from year one to year 10. So A equals $2,000, n is 10, and interest rate is 12%. Using the factorization, P equals A, multiply the factor-- i is 12%, and n is 10. And the result.

So if you save $2,000 per year, at the end of each year for 10 years, starting from year one to year 10, the accumulated money is equal to $11,300 at present time. It has the same value as $11,300 at the present time.

Example 1-5:

Calculate the present value of 10 uniform investments of 2000 dollars to be invested at the end of each year for interest rate 12% per year compound annually.

So, A =$2000 n =10 i =12% P=?

Using Equation 1-5, we will have: P = A * P / A i , n = A [ ( 1 + i ) n − 1 ] / [ i ( 1 + i ) n ] P = A * P / A 12 % , 10 = 2000 * [ ( 1 + 0.12 ) 10 − 1 ] / [ 0.12 ( 1 + 0.12 ) 10 ] P = 2000 * 5.650223 = $ 11 , 300.45

Note that we use the factor P / A i , n when we have equal series of payments. i is the interest rate and n is the number of equal payments. There is an important assumption here, the first payment has to start from year 1 . In that case P / A i , n will return the equivalent present value of the equal payments.

Now let's consider the case that we have equal series of payments and the first payment doesn't start from year 1. In that case the factor P / A i , n will give us the equivalent single value of equal series of payments in the year before the first payment. However, we want the present value of them (at year 0). So, we need to multiply that with the factor P / F i , n and discount it to the present time (year 0).  

Note that there are 10 equal series of $2,000 payments. But the first payment is not in year 1. The factor P / A 12 % , 10 returns the equivalent value of these 10 payments to the year before the first payment, which is year 1.

However, we want the present value. So, we need to discount the value by one year to have the present value of 10 equal payments.

Example: Now consider the the following case that the first payment starts at year 3:

6.Capital-Recovery Factor

The sixth group in Table 1-5 belongs to set of problems that A is unknown and P, i, and n are given parameters. In this category, uniform series of an equal sum, A, is invested at the end of each time period for n periods at the compound interest rate of i. In this case, the cumulated present value of all investments, P, is given and A needs to be calculated. It can be noted as A / P i , n .

Figure 1-7: Capital-Recovery Factor, A / P i , n

Equation 1-5 can be rewritten for A (as unknown) to solve these problems:

Equation 1-6 determines the uniform series of equal investments, A, from cumulated present value, P, as A = P [ i ( 1 + i ) n ] / [ ( 1 + i ) n − 1 ] . The factor [ i ( 1 + i ) n ] / [ ( 1 + i ) n − 1 ] is called the “capital-recovery factor” and is designated by A/P i,n . This factor is used to calculate a uniform series of end of period payment, A that are equivalent to present single sum of money P.

Please watch the following video, Capital Recovery Factor (Time 3:37).

PRESENTER: The sixth group belongs to the set of problems that A is unknown and P, i, and n are given parameters. This category is similar to the fifth group, but P is given and A needs to be calculated. In this category of problems, we know the present value P, or accumulated present value of all payments. And we want to calculate the uniform series of equal sum A that are invested in the end of each time period for n periods at the compound interest rate of i.

So we have present value P, and we want to calculate equivalent A, given interest rate of i and number of periods n. The proper factor to summarize these questions is A over P, or A/P. A is the unknown variable, is on the left side, and P, given variable, on the right side.

Equation to calculate A is straightforward. We just need to rewrite the equation in 1-5 for A as unknown, and we will have equation 1-6 that calculates A from P, i, and n. If we write the equation 1-6 according to the factor notation, we will have factor A over P. The factor is called capital recovery factor and is used to calculate uniform sales of end of period payments A that are equivalent to present single sum of money P.

Let's work on this example. We want to know the uniform series of equal investment for five years at interest rate of 4% which are equivalent to $25,000 today. Let's say you want to buy a car today for $25,000, and you can finance the car for five years and 4% of interest rate per year, compounded annually. And you want to know how much you have to pay each year.

First, we draw the timeline. Left side is the present time, which we have $25,000. n equals 5, and above each year, starting from year one to year five, we have A that has to be calculated. For the factor, we have i equal 4% and n is five and the result, which tells us $25,000 at present time is equivalent to five uniform payments of $5,616 starting from year one to year five with 4% annual interest rate. Or $25,000 at present time has the same value of five uniform payments of $5,616 starting from year one to year five with 4% annual interest rate.

Example 1-6:

Calculate uniform series of equal investment for 5 years from present at an interest rate of 4% per year compound annually which are equivalent to 25,000 dollars today. (Assume you want to buy a car today for 25000 dollars and you can finance the car for 5 years with 4% of interest rate per year compound annually, how much you have to pay each year?)

Using Equation 1-6, we will have: A = P * A / P i , n = P [ i ( 1 + i ) n ] / [ ( 1 + i ) n − 1 ] A = P * A / P 4 % , 5 = 25 , 000 * [ 0.04 ( 1 + 0.04 ) 5 / [ ( 1 + 0.04 ) 5 − 1 ] ] A = 25 , 000 * 0.224627 = 5615.68

So, having $25,000 at the present time is equivalent to investing $5,615.68 each year (at the end of the year) for 5 years at annual compound interest rate of 4%.

Using these six techniques, we can solve more complicated questions.

Example 1-7:

Assume a person invests 1000 dollars in the first year, 1500 dollars in the second year, 1800 dollars in the third year, 1200 dollars in the fourth year and 2000 dollars in the fifth year. At an interest rate of 8%: 1) Calculate time zero lump sum settlement “P”. 2) Calculate end of year five lump sum settlement “F”, that is equivalent to receiving the end of the period payments. 3) Calculate five uniform series of equal payments "A", starting at year one, that is equivalent to above values.

1) Time zero lump sum settlement “P” equals the summation of present values:

2) End of year five lump sum settlement “F”, that is equivalent to receiving the end of the period payments equals the summation of future values:

Please note that in the factor subscript, n is the number of time period difference between F (the time that future value has to be calculated) and P(the time that the payment occurred). For example, 1800 payment occurs in year 3 but we need its future value in year 5 (2 year after) and time difference is 2 years. So, the proper factor would be: ( F / P 8 % , ( 5 − 3 ) )  or  ( F / P 8 % , 2 ) .

3) Uniform series of equal payments "A" can be calculated from either P or F : A   = 5884.03 * A / P 8 % , 5 = 5884.03   * 0.25046 = 1473.7 or A = 8645.58 * A / F 8 % , 5   = 8800.71 * 0.17046   = 1473.7

Example 1-8 : repeat your calculations for the following payments:

1) Time zero lump sum settlement “P” equals the summation of present values: P = 800 + 1000 * ( P / F 8 % , 1 ) + 1000 * ( P / F 8 % , 2 ) + 1600 * ( P / F 8 % , 3 ) + 1400 * ( P / F 8 % , 4 ) P = 800 + 1000 * 0.92593 + 1000 * 0.85734 + 1600 * 0.79383 + 1400 * 0.73503 P = 4882.44

2) End of year five lump sum settlement “F”, that is equivalent to receiving the end of the period payments equals the summation of future values: F = 800 * ( F / P 8 % , 5 ) + 1000 * ( F / P 8 % , 4 ) + 1000 * ( F / P 8 % , 3 ) + 1600 * ( F / P 8 % , 2 ) + 1400   * ( F / P 8 % , 1 ) F = 800   * 1.46933 + 1000 * 1.36049 + 1000 * 1.25971 + 1600 * 1.1664 + 1400 * 1.08 F = 7173.9

3) Uniform series of equal payments "A" can be calculated from either P or F: A = 4882.44 * A / P 8 % , 5 = 4882.44 * 0.25046 = 1222.84 or A = 7173.9 * A / F 8 % , 5 = 7173.9 * 0.17046 = 1222.84

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Single-Payment Present-Worth ( P / F )

The single-payment compound-amount formula (just discussed) calculates the unknown future value of some known present amount ( F given P ). The single-payment present-worth turns this around and calculates the unknown present value needed to return a known future value ( P given F ) at the interest rate and term. If you know that a certain interest rate is available and you know how much money you want to end up with over some period of time, this formula tells you how much to invest now. The generic cash-flow diagram for this situation is shown in Figure 5.5 .

Figure 5.5. The generic cash-flow diagram for single-payment present-worth (lender's view)

We'll use a variation of Bee Co. from above. This time, it's Evans ...

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define present worth (p)

IMAGES

  1. Present Value

    define present worth (p)

  2. What Is Present Value?

    define present worth (p)

  3. Chapter 5 present worth analysis -with examples

    define present worth (p)

  4. PPT

    define present worth (p)

  5. Chapter 5 present worth analysis -with examples

    define present worth (p)

  6. Chapter 5 present worth analysis -with examples

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COMMENTS

  1. Introduction to present value (video)

    Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, …

  2. Introduction to present value (video)

    Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash …

  3. What Is Present Value in Finance, and How Is It Calculated?

    Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher...

  4. Present Value

    Present value (PV) measures the current value of an amount of money - or a stream of cash flows - that is expected in the future. This value will differ from the cash flows' nominal value, since time itself affects value. Time represents distance from money, and distance creates risk, which offsets value.

  5. What Is Present Value (PV)?

    A real-world example Present value is a way of measuring the current value of future cash flows. It's a financial concept that has a broad range of applications, including real estate,...

  6. Present Value (PV): Definition, Formula & Calculation

    Beginning With p Present Value Present Value (PV): Definition, Formula & Calculation Updated: February 24, 2023 A dollar today is worth more than a dollar tomorrow. This is the classic phrase that is associated with the concept of the time value of money.

  7. What Is Present Value?

    Definition Present value is what a sum of money in the future is worth in today's dollars at a rate of interest. Definitions and Examples of Present Value The basic principle behind the time value of money is simple: One dollar today is worth more than one dollar you will receive in the future.

  8. Present value

    In economics and finance, present value ( PV ), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation.

  9. What is Present Value (PV)?

    Definition: Present value, also known as discounted value, is a financial calculation that measures the worth of a future amount of money or stream of payments in today's dollars adjusted for interest and inflation. In other words, it compares the buying power of one future dollar to purchasing power of one today. What Does Present Value Mean?

  10. Present Value (PV)

    You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest. Example: You can get 10% interest on your money. So $1,000 now can earn $1,000 x 10% = $100 in a year. Your $1,000 now can become $1,100 in a year's time. Present Value

  11. Introduction to present value (video)

    AboutTranscript. The video explains the concept of present value in finance. Present value helps compare money received today to money received in the future. To find present value, we discount future money using a discount rate (like 5%). This helps decide which option is better: getting money now or later.

  12. What Is Present Value & How Is It Calculated?

    The present value of money is a financial formula used primarily by accountants and economists to calculate the present-day value of a financial asset or assets that will be earned or...

  13. PRESENT VALUE definition

    noun [ C or U ] ukus(abbreviationPV); (alsopresent discounted value) ACCOUNTING the value today of an amount of money that you expect to receive in the future, considering the fact that a future payment is worth less than one received now: The gift, paid as an annuity, has a present value of $175 million.

  14. Present Value (PV)

    Present Value is a financial concept that represents the current worth of a sum of money or a series of cash flows expected to be received in the future. PV takes into account the time value of money, which assumes that a dollar received today is worth more than a dollar received in the future due to its potential earning capacity.

  15. Present value Definition & Meaning

    The meaning of PRESENT VALUE is the sum of money which if invested now at a given rate of compound interest will accumulate exactly to a specified amount at a specified future date.

  16. Present Value: An In-Depth Look at Today's Worth of Future Money

    Present Value Definition. Present value is the concept in finance that determines the current worth of a future sum of money or stream of cash flows given a specified rate of return. It contrasts future cash flows with their value today, factoring in the time value of money - the idea that money available now is worth more than the same ...

  17. Present Value Definition & Examples

    Present Value (PV) is a financial concept that describes the current value of a future sum of money or stream of cash flows. That means it is a way to measure the value of money today compared to a future date. To calculate the present value (PV), you need to know the future value (FV), the interest rate (r), and the number of periods until the ...

  18. Present Worth financial definition of Present Worth

    The amount of cash today that is equivalent in value to a payment, or to a stream of payments, to be received in the future. To determine the present value, each future cash flow is multiplied by a present value factor.

  19. Present Value

    Definition. Present value (PV) is a financial term that refers to the current worth of a future sum of money or stream of cash flows given a specific rate of return. It computes the value of future money in today's terms. The calculation helps determine what an investment or any amount of cash could be valued at today.

  20. Engineering at Alberta Courses » Present Worth Analysis

    Present values (PV) convert the set of future values to the equivalent set of present sums in terms of a single value of currency at a single point in time, referred to as "today's dollars." This conversion is done using (P|F,i,n), where is the discount rate (or interest rate or return rate). In Present Worth analysis, the focus is on the future.

  21. Present Value of an Annuity: Meaning, Formula, and Example

    The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate. The higher the discount rate, the lower the...

  22. What is the Present Value of an Annuity?

    An annuity is a financial instrument that provides regular payments to the holder each period until the end of the contract. The present value of these payments is the amount that an investor would have to invest today at a given interest rate to equate to the total amount of payments in the future discounted by the same interest rate.

  23. Compound Interest Formulas III

    5. Uniform Series Present-Worth Factor. The fifth group in Table 1-5 covers a set of problems that uniform series of equal investments, A, occurred at the end of each time period for n number of periods at the compound interest rate of i. In this case, the cumulated present value of all investments, P, needs to be calculated.

  24. Single-Payment Present-Worth (P/F)

    Single-Payment Present-Worth (P / F)The single-payment compound-amount formula (just discussed) calculates the unknown future value of some known present amount (F given P).The single-payment present-worth turns this around and calculates the unknown present value needed to return a known future value (P given F) at the interest rate and term.If you know that a certain interest rate is ...