Business, Legal & Accounting Glossary
Present value refers to the future value of an asset that has been discounted back to its value in “today’s” dollars (or other economic unit).
Present value, often expressed as PV, is a financial term describing how much a given amount of money is worth in today’s terms, relative to the prevailing interest rate.
For example, you could have $100 today or $100 in one year. Naturally, to have $100 today is preferable than having it in one year. $100 one year from now at 5% interest rate is therefore only worth $95.23 today.
$100/1.05=$95.23
The present value of a future cash flow is the nominal amount of money to change hands at some future date, discounted to account for the time value of money. A given amount of money is always more valuable sooner than later since this enables one to take advantage of investment opportunities. Because of this present values are smaller than corresponding future values.
The simplest model of the time value of money is compound interest, which is in fact much simpler than simple interest. To someone who has the opportunity to invest an amount of money C for t years at a rate of interest of i% compounded annually, the present value of the receipt of C, t years in the future, is:
Ct = C · (1 + i)−t
The expression (1 + i)−t enters almost all calculations of present value. It represents the present value of 1. Many equations are expressed more concisely by making the substitution v = (1 + i)−1. Something worth 1 at time = t (years in the future) is worth vt at time = 0 (the present).
Present value is additive. The present value of a bundle of cash flows is the sum of each one’s present value.
Many financial arrangements (including bonds, other loans, leases, salaries, membership dues, annuities, straight-line depreciation charges) stipulate structured payment schedules, which is to say payment of the same amount at regular time intervals. The term annuity is often used in to refer to any such arrangement when discussing the calculation of present value, whether or not the arrangement is a retirement plan. The expressions for the present value of such payments amount to summations of geometric series.
A periodic amount receivable indefinitely is called perpetuity and is of mostly theoretical interest. A perpetuity receivable starting at the present time is called perpetuity due. If the frequency of payments equals the frequency of interest compounding, the present value of perpetuity due with payments of 1, is given by d−1, where d = 1 − (1 + i)−1, and is called the rate of discount. In this case, i is the interest rate per period, not necessarily per year. If the first payment is 1 period in the future, the annuity is a perpetuity immediate, and the present value is i−1.
A finite number (n) of periodic payments, receivable at times 1 through n, is an annuity immediate. Again assuming payment size of 1, its present value differs from the present value of the corresponding perpetuity immediate by an amount that is the present value of all the payments numbered n + 1 and above. The latter has a value of i−1 at time n, and vni − 1 at time 0. The present value of the annuity immediate is i−1 − vni−1, or i−1(1 − vn). An annuity due receivable at times 0 through n − 1 has a present value of d−1(1 − vn).
This entire discussion thus far makes some enormous assumptions:
For these and many other reasons, we consider the prediction of the future value to be an inexact science.
When we talk about present value, we are referring to the “reverse compounded” value, or discounted value as of today, of a future payment or stream of payments. To do this, we take that future value and discount it by an assumed rate to determine what it would be worth today if it earned that rate of return in the interim.
For instance, in the realm of investing for the future, you might want to know how much you would have to invest today, at a designated assumed rate of return, in order to end up with a set amount at some future point in time. As an example, if you wanted to have $10,000 available to you in 10 years’ time, and we assume it will grow at an average annual compound rate of 10%, you would have to invest approximately $3,850 today. So $3,850 is the present value of $10,000, earning 10% compounded annually over the next 10 years.
The present value method is also called the discounted cash flow method.
A different way to look at it: As James Early, now advisor of Motley Fool Income Investor, explained in a 2004 article, present value has to do with $100 now and $113 a year from now. If he offers you either $100 now or $100 a year from now what are you going to take? D’uh. $100 now. The present value of money has to do with how much he will need to offer 12 months hence to get you to consider waiting rather than taking the $100 and running.
You’ll take into account things like how much you could get if you put $100 into Treasuries for a year and how likely you think it is that James will show up a year from now with the promised money. In the article, James lays out the math of working the formula into the future.
One hundred units 1 year from now at 5% interest rate is today worth: {\rm Present\ value}=\frac{\rm future\ amount}{(1+{\rm interest\ rate})^{\rm term}}=\frac{\ 100}{1.05}=\ 95.23. So the present value of 100 units 1 year from now at 5% is 95.23 units. A different way of stating the formula –> PV = FV/((1+r)^n)); r = interest rate; n = number of periods. Alternative formula 1: Present Value = Future Value * ((1 + interest rate r)^(negative period n)). –> Restated: PV=FV*((1+r)^(-n)). Note: All of the above is in regards to a single lump sum amount. There is a separate formula to calculate PV of annuities. For present value of annuities, use this formula –> PV annuity = ((1-((1+r)^-n))/r) * (payment amount).
Discounted cash flow
Time value of money
Beta
Present value refers to the future value of an asset that has been discounted back to its value in “today’s” dollars (or other economic unit).
When we talk about present value, we are referring to the “reverse compounded” value, or discounted value as of today, of a future payment or stream of payments. To do this, we take that future value and discount it by an assumed rate to determine what it would be worth today if it earned that rate of return in the interim.
For instance, in the realm of investing for the future, you might want to know how much you would have to invest today, at a designated assumed rate of return, in order to end up with a set amount at some future point in time. As an example, if you wanted to have $10,000 available to you in 10 years’ time, and we assume it will grow at an average annual compound rate of 10%, you would have to invest approximately $3,850 today. So $3,850 is the present value of $10,000, earning 10% compounded annually over the next 10 years.
The present value method is also called the discounted cash flow method.
A different way to look at it: As James Early, explained in a 2004 article, present value has to do with $100 now and $113 a year from now. If he offers you either $100 now or $100 a year from now what are you going to take. D’uh. $100 now. The present value of money has to do with how much he will need to offer 12 months hence to get you to consider waiting rather than taking the $100 and running.
You’ll take into account things like how much you could get if you put $100 into Treasuries for a year and how likely you think it is that James will show up a year from now with the promised money.
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This glossary post was last updated: 30th November, 2021 | 0 Views.