978-1260152616 Chapter 11 Solution Manual Part 1

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Chapter 11 – Time and Uncertainty

CHAPTER 11

TIME AND UNCERTAINTY

Chapter Overview

Some of life’s most important decisions involve weighing uncertain future

costs and benefits against costs and benefits today. In this chapter, we

looked at tools that can help with these decisions. Interest rates enable you

to compare apples to apples when you think about costs and benefits that

occur at di erent times. Expected value can help you think about what is the

best option given uncertainty. Managing risk through pooling or

diversification can allow you to avoid bearing the full cost of a worst-case

scenario if it happens.

Learning Objectives

LO 11.1: Explain why money is worth more now than in the future, and how

the interest rate represents this relationship.

LO 11.2: Calculate compounding over time with a given interest rate.

LO 11.3: Calculate the present value of a future sum.

LO 11.4: Evaluate the costs and benefits of a choice using expected value.

LO 11.5: Explain the behavior of individuals who are risk-averse or risk-

seeking.

LO 11.6: Explain how risk aversion makes a market for insurance possible.

LO 11.7: Explain the importance of pooling and diversification for managing

risk.

LO 11.8: Describe the challenges that adverse selection and moral hazard

pose for insurance.

Chapter Outline

OPENING STORY: IS COLLEGE WORTH IT?

Value over Time

Timing Matters (LO 11.1)

Interest Rates

Compounding (LO 11.2)

BOX FEATURE: REAL LIFE – THE RULE OF 70

Present Value (LO 11.3)

Risk and Uncertainty

What Is Risk?

Expected Value (LO 11.4)

Propensity for Risk (LO 11.5)

Insurance and Managing Risk

The Market for Insurance (LO 11.6)

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Chapter 11 – Time and Uncertainty

BOX FEATURE: FROM ANOTHER ANGLE – HOLE-IN-ONE INSURANCE?

Pooling and Diversifying Risk (LO 11.7)

BOX FEATURE: WHAT DO YOU THINK? – WHO SHOULD BEAR THE RISK THAT A

COLLEGE DEGREE

DOESN’T PAY OFF?

BOX FEATURE: FROM ANOTHER ANGLE – HINDSIGHT IS 20/20

Problems with Insurance (LO 11.8)

BOX FEATURE: WHAT DO YOU THINK? – SHOULD HEALTH INSURANCE INCLUDE

PREVENTIVE

CARE?

Beyond the Lecture

Class Activity: Present Value (LO 11.3)

Ask students to consider whether an individual who wins the lottery should

take a lump sum payment or take annual payments over time. To engage

students, have them indicate (perhaps using www.polleverywhere.com)

which option they would take if they won, and display the aggregate results

for the class. (Do this before reading the article or engaging in the below

activity.) You can also have students read this article about that very

question. You can make up numbers or use the numbers in the article.

1. Ask students to calculate the present value of taking the annual

payments, using either the numbers in the article or your own

numbers. Ask them how this compares to the lump-sum payment.

2. What factors should an individual consider when deciding between the

lump-sum payment and annual future payments?

3. Ask students to revisit their answer to the question of which option

they would take: Did their answer change?

Class Activity: Expected Value (LO 11.4)

Have students play Deal or No Deal to highlight the concept of expected

value. You can find a computerized version of the game here and instructions

for a handwritten version (created by John Sloman) here. While going

through this activity, students must choose whether to keep the banker’s

o er or continue with the game. You can even have students calculate

expected value along the way, to help them make their decisions. This

activity also provides insight into risk tolerance.

Class Activity: Expected Value (LO 11.4)

The Deal or No Deal activity detailed above us fun, but in order to get a true

picture of preferences and tolerance for risk, it may be even more exciting

for students to have a little skin in the game with real money. A day ahead

of time, tell the students to bring their wallets (and money!) to class. On the

day when you are playing games, you can use a spreadsheet and random

number generator to pick out a few students (who of course have the option

to decline to participate if they don’t like gambling).

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Chapter 11 – Time and Uncertainty

Games you can have students play include:

1. Pay for a coin Jip game. Heads wins money, tails gets nothing

2. Draw a card, face card wins

3. Roll a die

Students can figure out probability and expected value. Then, you can tweak

the games to make some of the expected values above or below the price to

play. If you’re wealthy enough, you can even have a game with a low

probability of winning but a high dollar top prize. Card games, coin games,

and dice games are easy since probability is straightforward.

Class Discussion: Expected Value (LO 11.4)

Consider showing a brief clip from the television show Storage Wars (just

about any clip will do; there are plenty on this YouTube channel). Have

students consider the following:

1. How do the buyers estimate the expected value of the units

purchased?

2. How risky is it to purchase the units?

3. What is the opportunity cost?

Class Discussion: Pooling and Diversifying Risk (LO 11.6)

In order to highlight the importance of diversification, have students examine

changes in the price of one stock relative to the entire stock market. It is

often entertaining for students to discuss the Wall Street Journal’s

investment dartboard contest, where reader’s pick a stock that they think

will do well (six readers are chosen) and darts are thrown to pick six random

stocks. This can be compared to the overall performance of the stock market.

You can find an article about the 2012 WSJ contest here.

Clicker Questions

There are three main purposes to clicker questions. First, they are a great

way to do a quick and instant “on demand” test of student understanding of

the material. You can cover material, and instantly get feedback on student

comprehension. You can see whether you need to explain certain topics

again, or move on to the next subject. Second, they are a great method to

break up the class and take a moment away from lecture. It gets the

students actively involved. Finally, certain clicker questions can be framed in

a “discussion” manner, in which you can invite students to talk about the

possible right answer with their peers. You can instruct students to convince

their classmate of a right or wrong answer.

1. Suppose you could take a prize of $100,000 today or $110,000 one year

from now. What can we say about people who take the money today? [LO

11.1]

A. They are very patient and willing to wait for gratification

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Chapter 11 – Time and Uncertainty

B. They must think they can get better than a 10% annual return on the

money by investing it themselves

C . The person believes having the money today is of greater benefit even

though they could wait and get more money next year

D. The person is scared of the future

Feedback: Students could discuss that [B] could be correct, but we’re not

certain what the person would do with the money. Chances are they

wouldn’t invest, but spend it instead, or perhaps pay o debt. Even answer

[D] could be argued under certain circumstances to be correct, if the fear in

the future is regarding high inJation, rendering future money less valuable.

2. The rule of 70 tells us an estimate of… [LO 11.2]

A. How much money we should save each year to retire at age 70

B. What interest rate we need to make saving money more desirable than

spending it

C. How much money we can save over time by spending just 70% of each

dollar we earn.

D . How long it will take to double an investment with a certain interest rate

Feedback: You can roughly estimate that an investment will double in 70/r

years, where r is the annual interest rate. This also assumes compounding.

3. If a coin is Jipped heads, you earn $20. If the coin is Jipped tails, you earn

$8. What is the expected value of this game? [LO 11.4]

A. $8

Feedback: The sum of each (probability)*(payo ).

4. If a coin is Jipped heads, you earn $100. If the coin is Jipped tails, you

earn nothing. The price to play this game is $60. Billy chooses to play.

What can we most likely say about Billy? [LO 11.5]

A. Billy is risk-averse

Feedback: The expected value of the game is just $50, but he’s willing to

pay $60 for the chance to win the $100. A risk-averse person would not play

this game. For a risk-averse person to play, the price to play would have be

some amount below $50.

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Chapter 11 – Time and Uncertainty

5. How are insurance companies able to operate at a profit, when they are

subject to large costs if a consumer files a claim? [LO 11.6]

D. It is extremely rare that a consumer will file a claim

Feedback: Not everyone will have a car accident. Thus, the insurance

company can pool risky drives and safer drivers into the same insurance

pool. Higher-risk people are generally charged higher premiums for

insurance as well.

Solutions to End-of-Chapter Questions and Problems

Review Questions

1. Anna is indi erent between receiving $200 today and $230 in a month.

What does this imply about her opportunity cost in the coming month? How

much interest would Anna need to charge to lend $200 for the month in

order to break even? [LO 11.1]

Answer: If Anna is indi erent between receiving $200 today or $230 in a

month, it means that her opportunity cost in the coming month is $30.

2. Colton has a choice between $100 today and $150 in three months. Farah

has a choice between $100 today and $125 in three months. Colton chooses

$100 today. Farah chooses $125 in three months. Explain why Farah is the

one who delays payment even though Colton stands to earn more by

waiting. [LO 11.1]

Answer: Colton and Farah di er in their opportunity costs. Colton has a

stronger preference for cash in hand. He would require more than $50 to

3. Suppose your aunt invests $2,000 for you. You are not allowed to have the

money until the original amount doubles. Your aunt’s investment earns 10

percent, compounded annually. Give a rough estimate of how long it will take

before you can access the money your aunt invested for you. [LO 11.2]

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4. You are considering taking out a two-year loan of $1,000 from a bank, on

which you can pay either compound yearly interest of 1 percent or a Jat rate

of 2 percent for the whole two-year period. Which option is a better deal, and

why? [LO 11.2]

Answer: The Jat rate of 2 percent is the better deal. If you pay the Jat

rate of 2 percent, you will wind up paying $20 in interest on your loan.

5. Suppose you know that an investment will earn a positive return in the

future. Why is it important to know the present value of the investment? [LO

11.3]

Answer: It’s important to know the present value of the investment so

that you can compare the costs and benefits of the investment in today’s

6. Suppose you are selling a piece of furniture to a friend who can’t a ord to

pay you upfront but o ers to pay you in monthly installments for the next

year. What information do you need to calculate the present value of this

o er? (Hint: Think about the formula for present value.) [LO 11.3]

Answer: The formula for present value is given as PV = FV / (1 + r)n.

7. A pharmaceutical company is considering investing in the development of

a new drug. The company stands to make a lot of profit if the drug is

successful. However, there is some risk that the drug will not be approved by

government regulators. If this happens, the company will lose its entire

investment. Advise the company how to take this risk into account as

managers evaluate whether to invest. [LO 11.4]

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Answer: The pharmaceutical company could use expected value to

assess the investment. Expected value takes risk into account. To

8. You have a big exam tomorrow. You were planning to study tonight, but

your friend has tickets to a concert and has invited you to join her. You would

be willing to accept a B on the exam in order to go to the concert. You

estimate that if you don’t study you have a 35 percent chance of scoring a

90, a 35 percent chance of scoring an 80 (the score required to earn a B), a

25 percent chance of earning a 75, and a 5 percent chance of earning a 60.

Will you go to the concert? Explain why or why not. [LO 11.4]

Answer: The expected value of your score if you don’t study is 81.25,

which is enough for a B. If you make your decision based on expected

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