TIME VALUE OF MONEY OVERVIEW

Why Does Money Have a Time Value?

Money has a time value.  This is because individuals have a preference for current consumption since they gain satisfaction from consuming goods and services. In order to convince an individual to postpone that consumption (and to save or invest the money), people are given some compensation.  That compensation usually comes in the form of an investment return or interest earnings.  Since a dollar that is saved or invested has to power to increase over time (if the earnings are reinvested), a dollar amount invested today becomes a greater dollar amount in the future.

For dollar amounts in the present, we use the term "Present Value" or the initials "PV".

For dollar amounts at some some point in the future, we use the term "Future Value" or the initials "FV".

 

Fundamental Relationships

The fundamental relationship is as follows:

For a specific dollar amount today (the present value or PV), the associated future value (FV) will be larger, given a positive rate of return (or a positive interest rate).

For a specific dollar amount at some point in the future (a future value or FV), the present value today (or PV) will be smaller, given a positive rate of return (or a positive interest rate).

If we consider $100 invested today (a PV) in an account that pays interest, that $100 will grow to a greater amount in the future.

If we consider a $100 dollar payment that is made 3 years from today (a FV), the associated  present value of that amount will be less than $100.

 

Importance of Stating Cash Flows in Present Value Terms

The fact that money has a time value means we must take this time value of money into consideration when we are making financial decisions.  We do this by restating money values through time with Time Value of Money Calculations.  This module teaches these calculations.  Once the methods of restating money values through time is mastered, they can be used for restating cash flows in such a way as to make them comparable in the financial decision making process.  By stating all future cash flows in terms of present values, we can compare them.  The calculation of present values is the foundation for many financial decision making processes including the area of capital budgeting.  

 

TVM Calculations

 

Time value of money calculations are used to shift dollar values through time.  They can be used to state future dollar flows in present value terms or to restate current dollars into future dollar values.  The calculations are the most powerful tool available for making financial and business decisions.  They allow numerous calculations related to the earning of interest, the earning of non-interest returns on investments, loan related problems, capital budgeting decision processes, insurance programming problems,  and almost any asset purchase decision.  They also provide the foundation for some of the most widely used valuation concepts and valuation models employed in finance.

 

There are just four fundamental time value of money calculations.  These four types of calculations provide the basis for most of the financial calculations preformed by financial managers. 

 

1.     Future Value of a Dollar calculation (FV$)

2.     Present Value of a Dollar calculation (PV$)

3.     Future Value of an Ordinary Annuity (FV ord ann)

4.     Present Value of an Ordinary Annuity (PV ord ann)

 

 

Relationship Between these Four Calculations

 

Once the the FV$ problem and the related equation is understood, it is found that the PV$ problem and its equation is just the opposite (the inverse) of the FV process.  Furthermore, the Annuity problems are shown to be nothing more than a series of the simpler FV and PV problems.

 

In reality, once the first and most fundamental type of time value calculation is mastered, all the calculations become simple.

 

 

Types of Financial Calculations Using TVM 

 

Even the most complicated financial modeling problems can be broken down into component parts and can be addressed with these four types of time value of money problems.  See the list below for examples.

 

 

Loan related problems:

 

All automobile loans, equipment loans, home mortgage loans, and credit card loans that require a periodic payment (such as a monthly payment) that contains both interest due and a payment on the loan principal are often called loan amortization problems.  They are, in reality, nothing more than PV of an Annuity problem. 

 

The types of questions answered with this calculation include:

 

 

Capital budgeting decisions and other business investments:

 

All business investment decisions should be based on Discounted Cash Flow (DCF) decision tools such as Net Present Value (NPV).  Once the incremental after-tax cash flows associated with an investment project are identified, the process of calculating the NPV is nothing more than a series of PV$ and PV of Annuity calculations.

 

The questions answered with capital budgeting decisions are:

 

 

Personal investment decisions:

 

Personal decisions to invest in securities such as bonds and stocks create the problem of how to decide what the security might be worth.  There are a number of different valuation methods that are used to determine what the economic value of the cash flows associated with an investment are.  These models rely on the PV$ calculations to arrive at these values.

 

The types of questions answered are:

 

 

Retirement planning:

 

Whether an individual is saving through a pension fund, IRA, Keogh Plan, or a life insurance policy, an understanding of how future wealth is created is essential for proper decision making. All retirement planning is based on FV$ and FV of Annuity problems.

 

The main questions answered are:

 

As you can see, the basis of many fundamental financial decisions is Time Value calculations.  The remainder of this TVM topic reviews basic time value concepts and calculations.