# The Time Value Of Money

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THE TIME VALUE OF MONEY

FOCUS

This chapter develops and applies time value formulas. The focus is on using time value concepts to solve business problems.

OUTLINE

I. OUTLINE OF APPROACH

A brief explanation of the fact that money promised in the future is worth less than money in hand today.

Four kinds of problems and using time lines.

II. AMOUNT PROBLEMS

A. The Future Value of an Amount

The expression relating future and present values of a single amount is developed in terms of the future value factor and the associated table.

Problem solving technique is introduced.

Applications include deferred payment terms as the equivalent of cash discounts and the opportunity cost rate.

Financial calculators are introduced and instruction is provided on their use in solving time value problems.

B. The Expression for The Present Value of an Amount

An alternate formulation emphasizing the present value in terms of the future value. More on technique.

III. ANNUITY PROBLEMS

A. Annuities

The concept of an annuity and its present and future values.

B. The Future Value of an Annuity - Developing a Formula

The FVA expression, factor and tables are developed.

C. The Future Value of an Annuity - Solving Problems

Problem solving technique, the sinking fund concept, using a financial calculator for annuity problems.

D. Compound Interest and Non-Annual Compounding

Compound interest concepts and how to handle non-annual compounding in problems. The EAR and APR.

E. The Present Value of an Annuity

The formula, factor, and table are developed.

Computer spreadsheet techniques for solving time value problems are introduced and explained.

F. The Present Value of an Annuity - Solving Problems

Applications include discounting a stream of payments, amortized loans and amortization schedules, and working with mortgages.

G. The Annuity Due

The concept and formula are developed and applied.

H. Perpetuities

The idea of a never-ending stream with a finite present value is developed intuitively.

Applications include the capitalization of earnings and preferred stock.

I. Multi-Part Problems

Dealing with situations in which the solutions to problems become inputs to other problems.

Visualizing and time lining complex problems.

J. Uneven Streams and Imbedded Annuities

Recognizing and dealing with annuities imbedded in uneven payment streams.

QUESTIONS

1. Why are time value concepts important in ordinary business dealings, especially those involving contracts?

ANSWER: Business contracts and agreements generally specify payments that are due at future times. If such payments are more than a few months into the future, the correct analysis of the value of the agreement depends on a recognition of the time value of money.

2. Why are time value concepts crucial in determining what a bond or a share of stock should be worth?

ANSWER: All securities derive their value solely from the future cash flows that come from owning them. The only way to value