# The present value factor

## Use of the Present Value Factor Formula

Rate – Rate is the interest rate or discounted rate used for discounting the future cash flow. As stated before, there can be a different rate for cash flow at different time period based on inflation and risk premium, but for simplicity purpose, we will use a single rate for discounting cash flows at different time intervals. A very important component in present value factor is the discounting rate. Discounting rate is the rate at which the value of future cash flow is determined. Discount rate depends on the risk-free rate and risk premium of an investment.

The time value of money (TVM) is a concept that is fundamental to financial theory. The concept states that a dollar today is worth more than a dollar tomorrow because you can get paid a rate of interest. The cash outflows at subsequent periods are discounted at the same rate of present value factor. The project claims to return the initial outlay, as well as some surplus (for example, interest, or future cash flows). An investor can decide which project to invest in by calculating each projects’ present value (using the same interest rate for each calculation) and then comparing them.

These calculations are used to make comparisons between cash flows that don’t occur at simultaneous times, since time dates must be consistent in order to make comparisons between values. The project with the highest present value, i.e. that is most valuable today, should be chosen. Because the PV of 1 table had the factors rounded to three decimal places, the answer ($85.70) differs slightly from the amount calculated using the PV formula ($85.73). In either case, what the answer tells us is that $100 at the end of two years is the equivalent of receiving approximately $85.70 today (at time period 0) if the time value of money is 8% per year compounded annually.

For example, when an individual takes out a bank loan, the individual is charged interest. Alternatively, when an individual deposits money into a bank, the money earns interest. In this case, the bank is the borrower of the funds and is responsible for crediting interest to the account holder.

The reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much will $100 received in 5 years—at a lottery for example—be worth today?). Present value calculations, and similarly future value calculations, are used to value loans, mortgages, annuities, sinking funds, perpetuities, bonds, and more.

Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of the borrowed funds (the present value) is less than the total amount of money paid to the lender. Suppose, if someone were to receive $1000 after 2 years, calculated with a rate of return of 5%.

Even, each cash flow stream can be discounted at a different discount rate, because of variation in expected inflation rate and risk premium, but for simplicity purpose, we generally prefer to use single discounting rate. Present Value Factor Formula is used to calculate a present value of all the future value to be received. Time value of money is the concept that says an amount received today is more valuable than the same amount received at a future date.

The concepts of present value and present value factors play an important role in investment valuation and capital budgeting. Say, the present value of future cash inflows exceeds the present cash outflow of $1000, then the machinery is worth investing, else it would serve better for Company S to invest the money in other more profitable avenues. Present value means today’s value of the cash flow to be received at a future point of time and present value factor formula is a tool/formula to calculate a present value of future cash flow.

## Present Value Interest Factor

The reverse operation—evaluating the present value of a future amount of money—is called discounting (how much will 100 received in five years be worth today?). Interest is the additional amount of money gained between the beginning and the end of a time period. Interest represents the time value of money, and can be thought of as rent that is required of a borrower in order to use money from a lender.

The present value interest factor is based on the key financial concept of the time value of money. That is, a sum of money today is worth more than the same sum will be in the future, because money has the potential to grow in value over a given period of time. Provided money can earn interest, any amount of money is worth more the sooner it is received. The operation of evaluating a present sum of money some time in the future is called a capitalization (how much will 100 today be worth in five years?).

Now, the term or number of periods and the rate of return can be used to calculate the PV factor for this sum of money with the help of the formula described above. The present value factor formula is based on the concept of time value of money.

- These two factors can then be used to calculate the present value factors for any given sum to be received on any given future date.
- This formula is centered on the idea of assessing if an ongoing investment can be encashed and utilized better to enhance the final outcome as compared to an original outcome that can be had with the current investment.

## Present Value Factor

A compounding period is the length of time that must transpire before interest is credited, or added to the total. For example, interest that is compounded annually is credited once a year, and the compounding period is one year.

The reason being the value of money appreciates over time provided the interest rates remain above zero. The two factors needed to calculate the present value factor are the time period and the discount rate. Present value factor is often available in the form of a table for ease of reference. This table usually provides the present value factors for various time periods and discount rate combinations. While using the present value tables provides an easy way to determine the present value factor, there is one limitation to it.

It is called so because it represents the rate at which the future value of money is ‘discounted’ to arrive at its present value. The present value interest factor of an annuity (PVIFA) is useful when deciding whether to take a lump-sum payment now or accept an annuity payment in future periods. Using estimated rates of return, you can compare the value of the annuity payments to the lump sum. The present value interest factor (PVIF) is a formula used to estimate the current worth of a sum of money that is to be received at some future date. PVIFs are often presented in the form of a table with values for different time periods and interest rate combinations.

The project with the smallest present value – the least initial outlay – will be chosen because it offers the same return as the other projects for the least amount of money. , of a stream of cash flows consists of discounting each cash flow to the present, using the present value factor and the appropriate number of compounding periods, and combining these values. The operation of evaluating a present value into the future value is called a capitalization (how much will $100 today be worth in 5 years?).

If a $100 note with a zero coupon, payable in one year, sells for $80 now, then $80 is the present value of the note that will be worth $100 a year from now. This is because money can be put in a bank account or any other (safe) investment that will return interest in the future. 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. Time value can be described with the simplified phrase, “A dollar today is worth more than a dollar tomorrow”. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day’s worth of interest, making the total accumulate to a value more than a dollar by tomorrow.

This formula is centered on the idea of assessing if an ongoing investment can be encashed and utilized better to enhance the final outcome as compared to an original outcome that can be had with the current investment. With a view to estimating what would be the current value of a certain sum to be received on a future date, we need two factors, namely, the time interval after which the sum is to be received and the rate of return for the same. These two factors can then be used to calculate the present value factors for any given sum to be received on any given future date. The discount rate or the interest rate, on the other hand, refers to the interest rate or the rate of return that an investment can earn in a particular time period.

Interest that is compounded quarterly is credited four times a year, and the compounding period is three months. A compounding period can be any length of time, but some common periods are annually, semiannually, quarterly, monthly, daily, and even continuously. If offered a choice between $100 today or $100 in one year, and there is a positive real interest rate throughout the year, ceteris paribus, a rational person will choose $100 today. Time preference can be measured by auctioning off a risk free security—like a US Treasury bill.

The concept of present value is useful in making a decision by assessing the present value of future cash flow. The Present Value Factor is an integral component in the calculation of the present value of money under the Discounted Cash Flow (DCF) model for determining the present value of future cash flows of an investment and is always less than one. Present value factor, also known as present value interest factor (PVIF) is a factor that is used to calculate the present value of money to be received at some future point in time. In other words, this factor helps us to determine whether cash received now is worth more, or less than when it is received later.

Time value of money is the idea that an amount received today is worth more than if the same amount was received at a future date. Any amount received today can be invested to earn additional monies. The Present Value Factor is based on the concept of the time value of money, which states that a dollar received today is more valuable than a dollar received in the future.

If you don’t have access to an electronic financial calculator or software, an easy way to calculate present value amounts is to use present value tables (PV tables). PV tables cannot provide the same level of accuracy as financial calculators or computer software because the factors used in the tables are rounded off to fewer decimal places. In addition, they usually contain a limited number of choices for interest rates and time periods. Despite this, present value tables remain popular in academic settings because they are easy to incorporate into a textbook. Because of their widespread use, we will use present value tables for solving our examples.