(mining engineering) The sum of money which, if expended on a mine for purchase, development, and equipment, would produce over the life of the mine a return of the original investment plus a commensurate profit.
Present value
| Sci-Tech Dictionary: present value |
(′prez·ənt ′val·yü)
| 5min Related Video: Present value |
| Investment Dictionary: Present Value - PV |
The amount that a future sum of money is worth today given a specified rate of return.
Investopedia Says:
This sounds a bit confusing, but it really isn't. An investment that earns 10% per year and can be redeemed for $1,000 in five years would have a present value of $620. In other words, $620 today is worth $1,000 in five years.
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Find out why time really is money by learning to calculate present and future value. Understanding The Time Value Of Money
Valuing firms in this sector can seem like a black art, but there is a systematic way to pin a price on potential. Using DCF In Biotech Valuation
Learn the natural log and exponential functions used to calculate this value. Continuously Compound Interest
| Business Dictionary: Present Value (Worth) |
Today's value of a future payment, or stream of payments, discounted at some appropriate compound interest, or discount, rate; also called time value of money. The present value method, also called the Discounted Cash Flow method, is widely used in corporate finance to evaluate a proposed capital investment project or to measure the expected return. In security investments, the method is used to determine how much money should be invested today to result in a certain sum at a future time. Present-value calculations are facilitated by present-value tables, which are compound interest tables in reverse.
| Real Estate Dictionary: Present Value |
The equivalent lump-sum value today of expected future Cash Flow calculated according to a specific discount rate. See Net Present Value.
Example: Susan expects to receive $100 at the end of 2 years. If her Opportunity Cost is 5%, her prospective receipt has a present value of $90.70.
| Accounting Dictionary: Present Value |
Current worth of future sums of money. The process of calculating present value, or discounting, is actually the opposite of finding the compounded future value. Recall from Future Value that Fn = P(1 + i)n. Therefore, P = Fn/ [(l + i)n] = Fn[1/(1 + i)n] = PVIF(i,n) where PVIF(i,n) is the present value of $1 and is given in table 3 in back of book.
For example, assume Mr. B has been given an opportunity to receive $20,000 six years from now. If he can earn 10% on his investment, what is the most he should pay for this opportunity? To answer this question we need to find the present worth of $20,000 to be received six years from now. The PVIF(10%, 6 years) is in table 3-0.564. Therefore,
P = $20,000(0.564) = $11,280
This means that Mr. B could be indifferent to the choice between receiving $11,280 now or $20,000 six years from now since the amounts are time equivalent at 10%.
| Small Business Encyclopedia: Present Value |
Present value (PV) is an accounting term that measures how money money needs to be invested today in over to finance future business initiatives, projects, and obligations. In order to determine the present value of future costs, accountants use formulas based on the time value of money. These formulas features variables such as the length of time involved and the prevailing interest rate. In other words, the present value of an amount to be received in the future is the discounted face value considering the length of time the receipt is deferred and the required rate of return (or appropriate discount rate under the circumstances). Present value is the result of the time value of money concept, which recognizes that today's dollar is worth more than the same dollar received at a future point in time.
The standard formula for calculating the present value of a series of future receipts is:
PV = cash flow 1 / (1 + interest rate) 1 + cash flow 2 / (1 + interest rate) 2 + … + cash flow n / (1 + interest rate)n
Where cash flows 1 to n are the future receipts, the interest rate is the discount rate appropriate for the stated period, and n is the number of periods over which future receipts occur.
The interest, or discount, rate used in PV calculations is a key element in determining the PV. This importance is emphasized when the future amounts occur over an extended period of time, due to the power of compounding. For example, the final payment on a 30-year loan at 7 percent interest would be worth approximately 13.1 percent of its face amount on a present value basis at the date of loan origin [1/ (1 + .07)30]. By contrast, the 30th payment on a loan with a 9 percent interest rate would be worth only 7.5 percent [1/(1 + .09)30] of its face amount in present value terms at the origin. This example shows the power of compounding when time periods are long.
The discount rate used in a given circumstance must compensate the lender of funds for three elements of return:
Inflation. In order to remain even in terms of buying power, the return of money at a future date must be appended by the Consumer Price Index rate. In other words, if a person lends an amount of money adequate to buy a loaf of bread at t=0, he will require repayment at t=1 of the original amount plus the fraction of that amount representing the CPI increase over the period. That way he will be able to buy the same loaf of bread at t=1.
Time value of money (TVM). In addition to keeping pace with inflation, the investor or lender has a natural inclination for consumption sooner rather than later. The cost of compensating for this aspect of human nature has been found to be about 1 to 2 percent per year.
Risk. In addition to postponing the preferred immediate consumption and having to reimburse for inflation's erosion of buying power, many types of investment involve a risk of default. Compensating for this element of required return can be the most expense of the elements under consideration.
Further Reading:
Baroum, Sami M., and James H. Patterson. "The Development of Cash Flow Weight Procedures for Maximizing the Net Present Value of a Project." Journal of Operations Management. September 1996.
Brealey, Richard A., and Stewart C. Myers. Principles of Corporate Finance. McGraw Hill, 1991.
Finch, J. Howard, and John G. Fulmer. "Evaluating Ongoing Projects and Divisions." Managerial Finance. September 1997.
Pindyck, Robert S., and Daniel L. Rubinfeld. Microeconomics. Macmillan, 1992.
| Wikipedia: Present value |
Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful "like to like" basis.
Contents |
Background
If offered a choice between $100 today or $100 in one year ceteris paribus, a rational person will choose $100 today. This is described by economists as Time Preference.[citation needed] Time Preference can be measured by auctioning off a risk free security - like a US Treasury bill. If a $100 note, payable in one year, sells for $80, then the present value of $100 one year in the future is $80. This is because you can invest your money today in a bank account or any other (safe) investment that will return you interest.[clarification needed]
An investor who has some money has two options: to spend it right now or to save it. But the financial compensation for saving it (and not spending it) is that the money value will accrue through the interest that he will receive from a borrower (the bank account on which he has the money deposited).
Therefore, to evaluate the real value of an amount of money today after a given period of time, economic agents compound the amount of money at a given (interest) rate. Most actuarial calculations use the risk-free interest rate which corresponds the minimum guaranteed rate provided by your bank's saving account for example. If you want to compare your change in purchasing power, then, you should use the real interest rate (nominal interest rate minus inflation rate).
The operation of evaluating a present value into the future value is called a capitalization (how much $100 today are worth in 5 years?). The reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much $100 that I will receive in 5 years—at a lottery for example—are worth today?).
It follows that if one has to choose between receiving $100 today and $100 in one year, the rational decision is to cash the $100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least $105 in one year so that two options are equivalent (either receiving $100 today or receiving $105 in one year). This is because if you cash $100 today and deposit in your savings account, you will have $105 in one year.
Calculation
The most commonly applied model of the time value of money is compound interest. To someone who can lend or borrow for 
years at an interest rate 
per year (where interest of "5 percent" is expressed fully as 0.05), the present value of the receiving 
monetary units years in the future is:
This is also found from the formula for the future value with negative time.
The purchasing power in today's money of an amount C of money, t years into the future, can be computed with the same formula, where in this case i is an assumed future inflation rate.
The expression 
enters almost all calculations of present value. Where the interest rate is expected to be different over the term of the investment, different values for may be included; an investment over a two year period would then have PV of:
Technical details
Present value is additive. The present value of a bundle of cash flows is the sum of each one's present value.
In fact, the present value of a cashflow at a constant interest rate is mathematically the same as the Laplace transform of that cashflow evaluated with the transform variable (usually denoted "s") equal to the interest rate. For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the mathematics of continuous functions can be used as an approximation.
Choice of interest rate
The interest rate used is the risk-free interest rate. If there are no risks involved in the project, the expected rate of return from the project must equal or exceed this rate of return or it would be better to invest the capital in these risk free assets. If there are risks involved in an investment this can be reflected through the use of a risk premium. The risk premium required can be found by comparing the project with the rate of return required from other projects with similar risks. Thus it is possible for investors to take account of any uncertainty involved in various investments.
Annuities, perpetuities and other common forms
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 to refer to any such arrangement when discussing calculation of present value. The expressions for the present value of such payments are summations of geometric series.
A cash flow stream with a limited number (n) of periodic payments (C), receivable at times 1 through n, is an annuity. Future payments are discounted by the periodic rate of interest (i). The present value of this ordinary annuity is determined with this formula:[1]
![PV \,=\,\frac{C}{i}\cdot[1-\frac{1}{\left(1+i\right)^n}]](http://wpcontent.answers.com/math/3/f/5/3f5ee1d6ee77bc54f36862f83adea03d.png)
A periodic amount receivable indefinitely is called a perpetuity, although few such instruments exist. The present value of a perpetuity can be calculated by taking the limit of the above formula as n approaches infinity. The bracketed term reduces to one leaving:
The first formula is found from subtracting from the latter result the present value of a perpetuity delayed n periods.
These calculations must be applied carefully, as there are underlying assumptions:
- That it is not necessary to account for price inflation, or alternatively, that the cost of inflation is incorporated into the interest rate.
- That the likelihood of receiving the payments is high — or, alternatively, that the default risk is incorporated into the interest rate.
See time value of money for further discussion.
See also
References
- ^ Smart, Scott (2008). Corporate Finance. Stamford: Thomson Learning. p. 86. ISBN 184480562X.
External links
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
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Mentioned in
- Npv
- Future Value (finance term)
- Present Value Tables (insurance term)
- Earning Power (in accounting)
- Net Present Value (NPV) (in accounting)
- indicating instrument (engineering)
- Net Present Value Method (in accounting)
- Discount Rate
- Present Value of Annuity Due (insurance term)
- Present Value of Annuity Immediate (insurance term)
- Time Value of Money
- Income Stream (business term)
- Capitalization Rate (finance term)
- Discount Value (insurance term)
