Present Value (PV)

Present Value (PV) Formula | Example | Calculator | Analysis

What is Present Value?

Definition: Present value is also known as discounted value. The financial formula calculates the worth of the received amount on a future that is in today’s dollars.

Based on the time value of the money principle this concept work. It dictates that the worth of today’s 1 dollar is more than the worth of tomorrow’s one dollar. The worth of today dollar is more than the worth of tomorrow dollars because of the three-component which are interest, inflation, and opportunity cost.

Present Value (PV) Formula

Accumulated Present Value formula

Present Value Formula can be calculated by dividing the one-period cash flow by the one plus return to the nth power. This formula is looking confused but simple to solve and calculate present value formula.

  • C1 = Cashflow from 1period
  • r = Rate of return
  • n = Number of period

The above equation uses the annual interest. So the rate and the number of periods are in years. For the calculation of semi-annual interest, you need to divide the numbers in half.

For the future value of a lump-sum payment, the PV formula is reformated as

  • FV = Future value of cash received at the later date
  • r = Rate of return
  • n = Numbers of period

Analysis

How to use present value formula? Here is the analysis. For the evaluation of potential investment and the measurement of return on the current project, investors and creditors use the present value calculator. In the PV time value of the money is the important concept because through this investors measure the worth of investment return today and whether there are better options available.

If we take the example of the lottery it allows the 2 options of the payment form. The winner can receive the smaller lump sum today or a winner can receive equal payment from the full amount of the rest of his life.

For the expansion of the project and investing in other projects management of any company use this theory. Management uses the net present value formula to estimate whether the potential project is worth pursuing and whether the company will make money on the deal or not.

Examples of net present value formula

This example example of present value formula help you to understand well. Tim has a shop of machines. Tim wants to expand his shop with new equipment. H needs a 100,000 dollars loan to buy the new machinery. He secures the zero interest, and zero principal loans with a single balloon payment of 150,000 dollars. Actually, how much interest-paying by Tim.

Now we calculate the interest, which Tim pay with the balloon loan. The time for the loan is 10 years so we need to figure out, what the PV of 150,000 dollars is lump sum from now.

 

From the above result, it is clear that the present value of balloon payment is 57,831.49 dollars. It means that if today Tim invested 57,000 dollars at 10% interest. He would have enough to pay off these loans when it is due. As an interest, he pays 93,000 dollars.

The above example is the assumption of the single payment in future. Continuous annuity payment is different from this.

PV of an Annuity

If we go back to the example of the lottery. Let us assume that Jerry won 1,000,000 dollars in the state lottery. There or 2 choices for Jerry from the lottery commission. He can either collect 425,000 dollars now or receive 50,000 dollars per year for the next 20 years. Assuming the interest rate of 10% which is the best choice.

Based on the time value of money, both choices are the same in the PV annuity formula calculation. With payment option he received (50,000 x 20 = 1,000,000) dollars. Interest rate discounts these payments overtime of 426,000 dollars approximately.

Most of the winners of the lottery choose lump sum payments.

Present Value Tables

To compute these numbers people typically use the PV calculator. To compute these numbers people can also use the present value table. For the calculation of the discount rate, these charts are used in the PV calculation. So for the calculation of PV, there is no need for complicated equations.

In the below table on the x-axis interest rate is listed and the number of periods is listed at the y-axis and multiply by payment.

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