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What is the present value or PV?

Let us start with the definition first, the present value or PV can be defined as the current value of the future money whether payable or receivable as the maybe. PV is also known as Present worth (PW), the underlying idea is based on the concept of time preference of money which says that people prefer to receive money than in future so to compensate this lower preference, there should be an extra incentive attached to the future value, this incentive is called interest, in other words, the only difference between present value and future value is interest. For making present value calculations, the two most important things to know are

  1.  Discount rate(externanl link to calc site) 
  2.  Future cashflows
Present Value (PV)- how to calculate it, Present value calculator, PV FORMULA
The present value of money

How the Present Value (PV) is calculated?

The Present value formula or Present value equation is given as follows:
 
  Case 1: Formula for Present value of a single future cash flow
 

where
F = Future cashflows or Future value of cashflow
i  = Discount rate or interest rate (per period) or rate of return
n = number of  periods
 
  Case 2: Formula to calculate present value of an annuity

Where,
 A = cashflows of an annuity per period
 i  = Discount rate or interest rate (per period) or rate of return

 n = number of  periods
These formulae show the following 
  • PV has an inverse relation with the discount rate, as the discount rate rises, Present value falls
  • In the case of single cash flows, “n” inversely affects PV however in case of annuity formula “n” is directly related to the present value.
  • do it your self and verify your calculation with our free Present value calculator
What is the interpretation of the present value?
As we have discussed above, Present value is based on the concept of time preference of money in which future value is compensated for its lower preference, this compensation amount is what is called interest or returns so in short present value is always lower than the future value(FV) or future worth(FW).
For example, if A lends $100 to B for a year and at the end of the year A receives $110 from B, then it means that B is paying the interest of $10 for compensating A for sacrificing his or her current consumption. here $110 is the future value and $100 is the present value.
Discount rate or interest rate or rate of return
The interest rate or rate of return is simply the interest expressed as a percentage of present value, in the above example interest rate is 10%.  it is called the discount rate because it is used to discount the future cash flows. In practice, it is not easy to determine the discount rate because it has an inherent subjectivity, 
Factors affecting the discount rate.
Opportunity cost: it is simply the return loss, which could have been earned on the next best alternative if the money was not invested in the current alternative.
Crux: higher the opportunity cost = higher the discount rate = lower the present value 

Inflation: Inflation is a macroeconomic phenomenon which is responsible for price rise, as a result, the real value of money is eroded. To make the adjustment for inflation in the present value, the discount rate is reduced by the inflation rate, the resulting rate is called the real interest rate, which is given by
Real interest rate = (1+ Im)/(1+ f) – 1
Where
Im = market interest rate
f = inflation rate
Crux: higher the inflation = lower the discount rate = higher the present value 
The intuitive explanation for this can be, to bear the future shock inflation, we need to put extra amount now as cushion.
NOTE THAT ONLY EXPECTED INFLATION IS CONSIDERED WHILE ADJUSTING THE DISCOUNT RATE
Risk factors: there are multiple risks which are considered while determining the discount rate, some of those are:
(1)Credit default risk: risk related to the payment of cash flows by the borrower to the lender.

(2) market risk: risk of market volatility
(3) liquidity risk: shows how frequently the instrument is traded
(4) maturity risk: the time at which the capital will be blocked
A risk premium is added for each type of risk
CRUX: higher the risk factors = higher the risk premium = higher the discount rate = lower the present value.

 Utility
The concept of the time value of money especially the present value is used in every corner of finance, be it security valuation, capital budgeting decisions, derivative pricing, mortgage calculations, loan calculations retirement savings and it is also used to calculate net present value (NPV)
NPV = PV of all cash inflows – PV of all cashflows
Present value vs Future value 
The only mathematical difference between present value and future value is the interest amount in short
Present value = future value – interest
The interest here is the compound interest. 

Examples of present value 

Let say a person wants to invest in a fixed deposit which will provide an assured return of 8%, now
Question 1: how much he or she needs to put in the deposit to get $100000 in 10 years’ time.
Here we need to use the formula for the present value of single cashflow which is
PV = $100000/1.08^10 = $46319
Question 2: how much he or she should put in the deposit account to get $10000 each year.
Here we will use Formula for the present value of annuity 
PV = $10000(1- 1.08^-10)/.08 = $67101

Practice question 
Take the above figures and calculate how much the person needs to put in the deposit account now to get $5000 every year and $50000 at the end of 10 years, try it yourself, you can verify your answer with free present value calculator.
present value calculator for annuity


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