Present Value Factor Formula

Present Value Factor Formula (Table of Contents)

• Present Value Factor Formula
• Present Value Factor Calculator
• Present Value Factor Formula in Excel (With Excel Template)

Present Value Factor Formula

Present Value Factor Formula:

• r = Rate of Return
• n = Number of Years/Periods

Present Value Factor Formula is used to calculate a present value of all the future value to be received. It works on the concept of time value money. 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.

Derivation of Present Value Factor Formula

Where,

• PV = Present Value
• FV = Future Value
• r = Rate of Return
• n = Number of Years/Periods

Example of Present Value Factor Formula

Company Z has sold goods to Company M for Rs. 5000. Company M gave an offer to Company Z that either Company M pays Rs. 5000 immediately or pay Rs. 5500 after two years. Discounting rate is 8%.

Now, in order to understand which of either deal is better i.e. whether Company Z should take Rs. 5000 today or Rs. 5500 after two years, we need to calculate a present value of Rs. 5500 on the current interest rate and then compare it with Rs. 5000, if the present value of Rs. 5500 is higher than Rs. 5000, then it is better for Company Z to take money after two years otherwise take Rs. 5000 today.

• PV = FV * [ 1 / (1+r)ⁿ ]
• PV = 5500 * [ 1 / (1+8%) ² ]
• PV = Rs. 4715

As present value of Rs. 5500 after two years is lower than Rs. 5000, it is better for Company Z to take Rs. 5000 today.

Explanation of PV Factor Formula

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. The concept of present value is useful in making a decision by assessing the present value of future cash flow. Given a situation where you have to decide whether to receive or pay any amount of sum today or in future, assessing present value of future cash flows helps in taking effective decisions by comparing today’s cash flow with a present value of future cash flow.

Present Value of Future Cash Flow is nothing but the intrinsic value of the Cash Flow due to be received in the future. It is a representative amount which states that instead of waiting for the Future Cash Flows if you want the amount today, then how much would you receive. Obviously, the present value of the future cash flows is lower than the future cash flows in an absolute sense as it is based on the concept of Time Value of Money. As per the concept of time value of money, money received today would be of higher value compared to money received in future as money received today can be reinvested to earn interest on it. Also, money received today reduces any risk of uncertainty. In short, longer the time in receiving money lower will be its current value.

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. 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. Discounting rate is very similar to interest rate i.e. if you invest in a government security, then interest rates are low as it is considered to be risk-free, similarly interest rate of FD are higher than government security because of higher risk than government security, and similarly in corporate deposits of different companies of different credit rating.

Hence, the discounting rate of a risky investment will be higher, as it denotes that the investor expects a higher return on the risky investment.

Significance and Use of Present Value Factor Formula

The concept of present value is very useful for making decisions based on capital budgeting techniques or for arriving at a correct valuation of an investment. Hence, it is important for those who are involved in decision making based on capital budgeting, calculating valuations of investments, companies, etc.

Present Value Factor Formula also acts as a base for other complex formulas for more complex decision making like internal rate of return, discounted payback, net present value, etc. It is also helpful in day to day life of a person, for example, to understand the present value of a home loan EMI or the present value of fixed return investment etc.

Present Value Factor Calculator

You can use the following Present Value Factor Calculator

Present Value Factor Formula in Excel (With Excel Template)

In this example, we have tried to calculate a present value of the Home Loan EMI using the PV factor formula. As illustrated b, we have assumed an annual interest rate of 10%, and the monthly EMI Installment for 30 years. Installment amount assumed is Rs. 50,000.

In order to calculate present value, using the PV Factor formula in excel, we need to understand components of the formula. Following are the components of the PV 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.
• Kindly note, that rate used has to be for a period, in our example, we have assumed an interest rate of 10% per annum, however, cash outflow in the form of EMI will happen on a monthly basis, hence we divided 10% by 12 to arrive at a monthly rate i.e. rate per period.
• NPER: NPER is the total number of payments. In our example, we have multiplied 30 years by 12 months each year to arrive at the total number of payments.
• PMT: PMT stands for payment per period. In our example, Rs. 50,000 EMI has to be paid on a monthly basis which is paid per period.
• FV: FV stands for Future Value of Annuity. It means Value to be received at the end of the period. It is optional to provide input for ‘FV’ and if left blank it is considered to be 0.
• Type: Type helps to determine whether payment will begin at the start or end of the period. If you type ‘0’, payment will be considered at the end of the period while for ‘1’ it considers payments to be made at the start of the period. It is also optional to provide input for ‘type’ and if left blank it is considered to be 0.

Now, in order to calculate, present value in excel, Use PV Factor Formula i.e PV(rate, nper, pmt, fv, type)

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