Table of Contents

## Present Value of Money

Present value of money represents the basic financial concept that states that same amount of money is worth more now than the value of money in future.

This is concept is also called **Time value of money.**

Reasons may include:

- Potential of earning (Amount of money can be invested right now at specific interest rate).
- Inflation (Purchasing power of the same amount of money will not be same in future)
- Physical / Financial risk involved in keep the money safe.

In economics and finance, present value (PV), also referred to as a present discounted value, is that the value of anticipated income stream intent on as of the date of valuation. The present value is typically but the longer-term value because money has interest-earning potential, a characteristic mentioned because the value of cash, except during times of zero- or negative interest rates, when the present value is going to be equal or quite the future value.

The time value can be described with the simplified phrase, “A dollar today is worth more than a dollar tomorrow”. Here, ‘worth more’ means its value is greater. A dollar today is worth quite a dollar tomorrow because the dollar is often invested and earn a day’s worth of interest, making the entire accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the cash for a time before paying it back. By letting the borrower have access to the cash, the lender has sacrificed the exchange value of this money and is reimbursed for it within the sort of interest. The initial amount of the borrowed funds (the present value) is a smaller amount than the entire amount of cash paid to the lender.

## Limitations of Using PV

### Present Value Formula

As stated earlier, calculating this value involves making an assumption that a rate of return could be earned on the funds over the time period. In our example, we checked out one investment over the course of 1 year. However, if a corporation is deciding to travel ahead with a series of projects that feature a different rate of return for every year and every project, the present value becomes less certain if those expected rates of return aren’t realistic.

It’s important to think about that in any investment decision, no rate of interest is guaranteed, and inflation can erode the speed of return on any investment.

**Alternative Formula:**

**Present Value Formula Derivation**

The future value (FV) of a present value (PV) sum that assembles interest at the rate over a single period of time is the present value plus the interest earned on that sum. The mathematical equation is:

For each period into the future, the assembled value rises by an additional factor (1 + i). Hence, the future value accumulated over, say 3 periods, is stated by:

Or Generally,

Similarly, We can solve

**Net Present Value:**

Net present value (NPV) is the value of your future money in today’s dollars. The concept is that a dollar today isn’t well worth the same amount as a dollar tomorrow.

The purchasing power of your money decreases over time with inflation and increases with deflation.

In addition, there is an implied interest value to the money over time that increases its value in the future and decreases (discounts) its value today relative to any future payment.

Since the worth of cash changes with time, all financial calculations must be delivered to a continuing date (usually today, thus the term “present” value) to form factual comparisons between competing investment substitutes.

Businesses use present value calculations for capital expenditures and routine business planning. Similarly, smart wealth builders run their finances like a business so they also use net present value for better family financial planning.