Finance Chapter 4 Homework Present Value Chart See Appendix A3 Pages

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Chapter 4

Time Value of Money

Chapter Overview

I. Introduction

II. Inflation

a. Inflation rate

b. Consumer price index

c. Rates of inflation (exhibits)

III. Risk

a. Deferred salaries: Team and player risk

b. Policies on deferred salaries

IV. Future value

a. Simple interest

b. Compound interest

V. Annuities and perpetuities

VI. Future value of an annuity

VII. Liquidity

Key Concepts

When reading this chapter, students should focus on the following key concepts:

1. How present value and future value concepts impact the financial operation of sport

organizations

2. How inflation, liquidity and risk impact the financial operations of sport

Quiz Questions

1. Which of the following refers to the purchasing power of a dollar?

a. Nominal value

b. Real value

2. In its policies regarding deferred salaries, which of the following leagues has stated that

deferred payments must be placed by the team in a league fund for administration and

future disbursement?

c. National Hockey League

d. National Football League

e. Major League Baseball

3. The owners of which franchise agreed to a perpetuity when they negotiated to fold their

team after the ABA and NBA merger.

a. New York Nets

e. St. Louis Spirits

4. Which of the following is today’s value of a future cash flow?

c. Future value

d. Present value

e. None of the above

5. What is a measure of risk or uncertainty of time?

a. Inflation rate

b. Interest rate

c. Business activity rate

6. Which of the following is calculated by investigating changes in the Consumer Price

Index (CPI)?

d. Development rate

e. Discount rate

7. A series of equal payments or receipts made at any interval of time is referred to as

which of the following?

a. Cash inflow

b. Cash outflow

c. Annuity

8. Which of the following is a single cash flow per year forever into the future?

a. Annuity

e. Infinite cash flow

Answers to Quiz Questions

Numbers in parentheses represent where, in the text, you’ll find this discussed.

1. b (p. 88)

2. d (p. 93)

Responses

1. Explain the concept of inflation. How does inflation affect saving and investing?

See pages 88–91. Inflation is the gradual increase in prices for goods and services. Any

investment must account for inflation when determining its “real” potential rate of

2. How does a preference for liquidity influence an individual or organization’s financial

decisions?

See pages 97–98 Liquidity is the ability to turn assets into cash. Liquidity is important, as

cash may be needed to pay for projected or unforeseen liabilities. Most financial

3. Explain the difference between simple and compound interest.

See pages 94–95 Simple interest pays interest on principal. Compound interest pays

interest on principal and interest.

4. What aspects of the time value of money must professional sport organizations and

athletes consider when negotiating contracts?

See pages 89–94. Players and teams must investigate the projected rate of inflation,

risks (such as significantly increased or decreased player performance), likelihood of

5. What mistake did the NBA make in its dealings with the owners of the St. Louis Spirits?

See page 96, Sidebar 4.C. The NBA signed a contract that granted the St. Louis Spirits’

owners rights to future cash flows from television contracts in perpetuity.

6. What are some advantages and disadvantages of deferring salaries (from both the

players’ and the team’s perspectives)?

See pages 93–94. Players may defer salary if they do not have a need for the money

immediately. They may also do this to potentially impact the timing of their tax

payments. In some cases, player agents have their clients defer salaries to “protect”

7. What concerns should a sport organization contemplate when negotiating future

payments from sponsorships or other long-term agreements?

See multiple pages discussing various aspects of Time Value of Money. The sport

organization should first evaluate the likelihood that the sponsor will be in business in

the future. Even some prominent organizations (e.g., Enron) have encountered financial

Responses

1. What is the real increase in value if $1,500 is invested for one year at 5% interest and

the rate of inflation during that time is 1.79%?

$1,500  .05 = $75

$1,500  .0179 = $26.85

2. A sport organization has a commitment from a sponsor for a $17,000 payment in three

years. What is the present value of that money if it is discounted at (a) 3%, (b) 5%, and

$17,000 in three years discounted at

a. 3% = $17,000  .9151 = $15,556.70

3. You are the financial manager for a recreation center that has signed an option to

purchase new elliptical machines for $22,000 in two years. If you have an investment

opportunity that guarantees 7% interest, how much must you invest to have the

necessary funds to purchase the elliptical machines?

4. An athlete signs a five-year endorsement deal with a prominent sponsor. Under this

deal, the athlete will receive $5,000 each year for the first three years and $6,500 each

year for the final two years. What is the present value of the total deal if the payments

are discounted 6%?

Add the present value of each year

1―$5,000  .9434 = $4,717.00

2―$5,000  .8900 = $4,450.00

5. What is the future value of $12,000 invested at 8% interest, compounded yearly for ten

Use the Future Value table; see Appendix A.1 on pages 454–455. (Note potential

rounding differences.)

6. If an investor commits $4,500 to an IRA each year for 30 years and receives 6% interest,

what will her total investment be worth at the end of the 30 years?

Use Future Value of an Annuity; see Appendix A.2 on pages 466–457. (Note

potential rounding differences.)

7. A bank offers customers the option of receiving interest compounded quarterly, semi–

annually, or annually. If the rate of interest is the same, which is the best option for the

customer?

8. What is the difference between $10,000 invested for ten years at 3% interest,

compounded yearly, and at 8% interest, compounded semi-annually?

To determine the 8% interest compounded semi-annually, take the 8% interest and

cut it in half and then take the 10 periods and double it. Future value factor would

be where 20 periods crosses with 4%.

Responses to Questions

The director of marketing of your organization asks for your advice regarding sponsorship

deals she is contemplating. She has to choose between the following: a 15-year sponsorship

1. Determine the present value of each year for each proposal, as well as the total present

value of each proposal.

2. Which proposal should the marketing director choose?

To complete the case, the first thing to do is determine the nominal value of each year in

each scenario.

Year Option 1 Year Option 2 Year Option 3

1 $100,000.00 1 $75,000.00 1 $45,000.00

2 $100,000.00 2 $78,750.00 2 $50,400.00

Then you must assign a present value factor (or factors if you want the students to do a

comparison). In this case, if you choose a 5% discount rate (a good one since students can

see how the interest and the discount rate counteract each other), the results will be:

Option 2 Option 3

Yearly Payment Factor Discounted $ Yearly Payment Factor Discounted $

$75,000.00 0.9524 $71,430.00 $45,000.00 0.9524 $42,858.00

In this case, the highest present value of the options is Option 2 as it is greater than Option

1 or Option 3.

If we change the discount rate to 10%, then adjustments must be made.

Option 1 can still be computed with the Present Value of an Annuity

Option 2 Option 3

Yearly Payment Factor Discounted $ Yearly Payment Factor Discounted $

$75,000.00 0.9091 $68,182.50 $45,000.00 0.9091 $40,909.50

$78,750.00 0.8264 $65,079.00 $50,400.00 0.8264 $41,650.56

In this case, Option 1 yields the highest return after applying a 10% discount rate.

In each scenario, choosing the option that yields the highest result is advisable. The

differences in the final results are dramatically impacted by the discount rate applied. This is

Additional Classroom/Exam Problems

1. What is the future value of $1000 invested that accumulates 4% interest for 5 years?

(compounded annually)

2. What is the future value of a yearly investment of $1000 that accumulates 4%

interest for 5 years?

3. Have students research player salaries in Major League Baseball or another North

American professional team sport (USA Today has an available database). Identify

players who have signed long-term contracts that are not providing salaries that

4. Explain why the Silna brothers decided to sell a significant portion of their NBA TV

perpetuity back to the NBA.

Students should discuss how the Silnas had investment issues that led to their

needing more cash for the short term than for the long term (see page 96). It