©2011 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 5 Time Value of Money: The Basics

Chapter Overview

Time value of money is one of the most important concepts in finance. The basic premise of time value of money problems is that time impacts the value of a dollar. That is, a dollar received today is worth more than one received in the future. The principles of time value of money are used in a variety of applications in finance, including capital budgeting, capital structure, cost of capital, and working capital management decisions.

This chapter explores time value of money concepts as they apply to a lump sum or single cash flow. Future value is the value of a sum of money compounded at a given interest rate for a specific period of time. Present value is the current value of a sum of money to be received at a specified time in the future, given a stated rate of interest.

Chapter Outline

5.1 Using Timelines to Visualize Cash Flows

A. A timeline identifies the timing and amount of a stream of payments, along with the interest rate it earns.

B. Timelines are the first step in visualizing and solving time value of money problems.

5.2 Compounding and Future Value

A. Simple versus Compound Interest 1. Simple interest is the interest earned on the principal amount. 2. Compound interest is the interest earned on both the initial principal amount and on

reinvested interest from previous periods.

B. Future Value is the value of a current sum of money at a time in the future, given a specified compound interest rate. 1. The future value of an investment grows with the number of periods it is compounded; the

longer the time, the larger the future value. 2. The future value increases with the level of the rate of interest; the higher the interest rate,

the larger the future value.

C. Compounding principles can be applied to things other than money. 1. Compounding applies to anything that grows. 2. Examples include sales, population, inflation rates, etc.

Chapter 5 Time Value of Money: The Basics 15

©2011 Pearson Education, Inc. Publishing as Prentice Hall

5.3 Discounting and Present Value

A. Present value is the value today of a future cash flow. 1. The process of discounting involves determining the present value of an expected future

cash flow, given a specified rate of interest. 2. Present value decreases as the number of periods until the payment is received is increased. 3. Present value decreases as the interest rate increases.

B. Present value techniques can be used to solve problems for either the number of periods or interest rate to reach a future value.

5.4 Making Interest Rates Comparable

A. Annual Percentage Rate (APR) is the amount of interest rate paid or earned without compounding.

APR = Interest Rate per Period × Compounding Periods

B Effective Annual Rate (EAR) is the annual compounded rate that produces the same return as the nominal, or stated, rate.

EAR = (1 + Quoted Annual Rate/Compounding Periods per year)m − 1

C. Continuous Compounding occurs when the time intervals between when interest is paid is infinitely small.

Learning Objectives

5-1. Construct cash flow timelines to organize your analysis of time value of money problems

5-2. Understand compounding and calculate the future value of cash flows using mathematical formulas, a financial calculator, and an Excel spreadsheet.

5-3. Understand discounting and calculate the present value of cash flows using mathematical formulas, a financial calculator, and an Excel spreadsheet.

5-4. Understand how interest rates are quoted and know how to make them comparable.

Lecture Tips

1. Introduce Future Value by looking at a variety of examples: a. Population growth b. Weight change c. Salary over a lifetime d. Prices given a constant inflation rate

2. Use the Rule of 72 to explore how the growth rate significantly affects the time for a quantity to double. Vary the growth rate to see how doubling is affected for such examples as population, sales, prices, etc.

3. Use ads from various financial institutions showing interest rates on CDs to illustrate the concepts of APR and EAR.

16 Titman/Keown/Martin • Financial Management, Eleventh Edition

©2011 Pearson Education, Inc. Publishing as Prentice Hall

Questions for Further Class Discussion

1. What is the relationship between present value and future value?

2. Explain what is meant by continuous compounding? How can compounding occur continuously?

3. When you graduate from college, you are offered the choice between a job with a starting salary of $30,000 per year which grows annually at 6% or a job with a arting salary of $40,000 per year which grows annually at 4%. How would you determine which is the best job to take if you assume you will stay in this position for 5 years? At what growth rate would you be indifferent between the two positions?

End-of-Chapter Problem Complexity Rating

The end-of-chapter problems are sorted below, according to their level of complexity.

Simple Average Complex

1, 5, 17, 19-22, 29-30 6, 11, 13-16, 18, 23-24, 26, 27, 31-38

12, 25, 28

Spreadsheet Solutions in Excel

The following end-of-chapter problem solutions are available with Excel spreadsheets. These spreadsheets are available on the Instructor’s Resource Center at www.pearsonhighered.com. If you do not have a login and password for this Web site, contact your Pearson sales representative. Problems: 5-1—5-9, 5-11—5-18, 5-20—5-34, 5-37—5-38

Internet Resources

http://antwrp.gsfc.nasa.gov/htmltest/gifcity/e.5mil http://tr.im/fabcam www.kiplinger.com/tools/index.html www.dinkytown.net www.bankrate.com/calculators.aspx www.interest.com www.predatorylendingassociation.com www.responsiblelending.org/payday-lending www.responsiblelending.org/payday-lending/tools-resources/debttrap.html