What is Present Value?
Present value (PV) is the current value of a future stream of cash flows, discounted at a certain interest rate. PV analysis is used to compare different investment options, evaluate the profitability of a project, or determine the fair price of an asset.
How to Calculate PV in Excel?
Excel has a built-in function to calculate PV, which is:
=PV(rate, nper, pmt, [fv], [type])
The arguments for the PV function are:
- rate: the interest rate per period
- nper: the number of payment periods
- pmt: the amount paid each period (if omitted, it is assumed to be 0 and fv must be included)
- fv: the future value of the investment (if omitted, it is assumed to be 0 and pmt must be included)
- type: when payments are made (0 or omitted for end of period, 1 for beginning of period)
Note that any money paid out (outflows) should be entered as negative numbers, and money received (inflows) as positive numbers.
Example: Calculating PV of a Single Cash Flow
Suppose you want to invest $10,000 today and expect to receive $15,000 in 5 years. The annual interest rate is 8%. What is the present value of this investment?
To calculate the PV using Excel, you can use the following formula:
=PV(0.08, 5, 0, 15000)
The result is $10,206.48, which means that investing $10,000 today is equivalent to receiving $15,000 in 5 years, given an 8% interest rate.
Alternatively, you can use the basic PV formula:
=15000/(1+0.08)^5
The result is the same: $10,206.48.
Example: Calculating PV of a Series of Cash Flows (Annuity)
Suppose you want to buy a car that costs $25,000. You can pay in 5 equal annual installments of $6,000, starting from next year. The annual interest rate is 10%. What is the present value of this payment plan?
To calculate the PV using Excel, you can use the following formula:
=PV(0.1, 5, -6000)
The result is $22,789.25, which means that paying $6,000 per year for 5 years is equivalent to paying $22,789.25 today, given a 10% interest rate.
Example: Calculating PV of a Perpetuity
Suppose you want to buy a bond that pays $100 every year, forever. The annual interest rate is 5%. What is the present value of this bond?
To calculate the PV using Excel, you can use the following formula:
=PV(0.05, , 100)
The result is $2,000, which means that buying the bond for $2,000 today is equivalent to receiving $100 every year, forever, given a 5% interest rate.
