Time value of money: determining its future value


If you were offered $ 100 today or $ 100 a year from now, which would you choose? Would you rather have $ 100,000 today or $ 1,000 a month for the rest of your life?

Net Present Value (NPV) provides an easy way to answer these types of financial questions. This calculation compares the money received in the future with an amount of money received today, taking into account time and interest. It is based on the time value of money (TVM) principle, which explains how time affects the monetary value of things.

The TVM calculation may seem complicated, but with some understanding of the NPV and how the calculation works, along with its basic variations, present value and future value, we can begin to use this formula in a common application.

Justification of the value of money in time

If you were offered $ 100 today or $ 100 a year from now, which would be the best option and why?

This question is the classic method in which the TVM concept is taught in virtually every business school in the United States. Most of the people who asked this question chose to take the money today. And they would be right, according to TVM, which argues that the money available today is worth more than the same amount in the future. But why? What are the advantages and, more importantly, the disadvantages of this decision?

There are three basic reasons to support the TVM theory. First, you can invest a dollar and earn interest over time, giving you potential earning power. Also, money is subject to inflation, which erodes the purchasing power of the currency over time, making it worth a lesser amount in the future. Finally, there is always the risk of not actually receiving the dollar in the future, whereas if you hold the dollar now, there is no risk of this happening (since the old bird in your hand is better than – goes the saying of the two in the bush). Obtaining an accurate estimate of the latter risk is not easy and is therefore more difficult to use accurately.

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Understand the time value of money

Illustrating net present value

Would you rather have $ 100,000 today or $ 1,000 a month for the rest of your life?

Most people have a vague idea which one you would take, but a net present value calculation can accurately tell you which one is better, from a financial point of view, assuming you know how long you will live and what interest rate you would earn if you took the $ 100,000.

The specific variations of the calculations of the value of money over time are:

  • Net present value (allows you to value a future payment stream in a lump sum today, as you can see in many lottery payments)
  • Present value (tells you the present value of a future sum of money)
  • Future value (gives you the future value of the cash you have now)

Let’s say someone asks you, which would you prefer: $ 100,000 today or $ 120,000 a year from now? The $ 100,000 is the “present value” and the $ 120,000 is the “future value” of your money. In this case, if the interest rate used in the calculation is 20%, there is no difference between the two.

Determining the time value of your money

There are five factors in a TVM calculation. They are:


1. Number of time periods involved (months, years)
2. Annual interest rate (or discount rate, as calculated)
3. Present value (what you currently have in your pocket)
4. Payments (if they exist; if not, the payments are equal to zero).
5. Future value (The dollar amount you will receive in the future. A standard mortgage will have zero future value because it pays off at the end of the term).

Calculate present and future value

Many people use a financial calculator to quickly solve TVM questions. By knowing how to use one, you could easily calculate a present sum of money in a future one, or vice versa. With four of the five components above in hand, the financial calculator can easily determine the missing factor.

But you can also calculate future value (FV) and present value (PV) by hand. For future value, the formula is:

Fv

=

PV

×

(

1

+

I

)

North

text {FV} = text {PV} times left (1 + i right) ^ n

Fv=PV×(1+I)North

And for the present value, the formula would be:

PV

=

Fv

/

(

1

+

I

)

North

where:

Fv

=

Future value of money

PV

=

Present value of money

I

=

Interest rate

North

=

Number of compounding periods per year

begin {aligned} & text {PV} = text {FV} / left (1 + i right) ^ n \ & textbf {where:} \ & text {FV} = text { Future value of money} \ & text {PV} = text {Present value of money} \ & text {i} = text {Interest rate} \ & text {n} = text { Number of compounding periods per year} \ end {aligned}

PV=Fv/(1+I)Northwhere:Fv=Future value of moneyPV=Present value of moneyI=Interest rateNorth=Number of compounding periods per year

Applying Net Present Value Calculations

Net present value calculations can also help you find answers for financial questions, like determining a mortgage payment or how much interest is being charged on that loan for short-term Christmas expenses. By using a net present value calculation, you can find out how much you need to invest each month to achieve your goal. For example, to save $ 1 million for retirement in 20 years, assuming a 12.2% annual return, you must save $ 984 per month.

Below is a list of the most common areas in which people use net present value calculations to help them make financial decisions.

  • Mortgage payments
  • Student loans
  • Savings for college
  • Home, car, or other major purchases
  • Credit cards
  • Money Management
  • Retirement planning
  • Investments
  • Financial planning (both business and personal)

The bottom line

Calculating the net present value and its changes are quick and easy ways to measure the effects of time and interest on a given sum of money, whether it is received now or in the future. The calculation is perfect for short and long term planning, budgeting or reference. When charting your financial future, keep these formulas in mind. (For related reading, see “Why Time Value of Money (TVM) Matters to Investors”).

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Mark Holland

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