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Chapter 27

The Basic Tools of Finance

Educators


Problem 1

According to an old myth, Native Americans sold the island of Manhattan about 400 years ago for $\$$24. If they had invested this amount at an interest rate of 7 percent per year, how much, approximately, would they have today?

Kaylee M.
Numerade Educator

Problem 2

A company has an investment project that would cost $\$$10 million today and yield a payoff of $15 million in 4 years.

a. Should the firm undertake the project if the interest rate is 11 percent? 10 percent? 9 percent?
8 percent?

b. Can you figure out the exact cutoff for the interest rate between profitability and nonprofitability?

Kaylee M.
Numerade Educator

Problem 3

Bond A pays $\$$8,000 in 20 years. Bond B pays $\$$8,000 in 40 years. (To keep things simple, assume these are zero-coupon bonds, which means the $\$$8,000 is the only payment the bondholder receives.)

a. If the interest rate is 3.5 percent, what is the value of each bond today? Which bond is worth more? Why? ($Hint$: You can use a calculator, but the rule of 70 should make the calculation easy.)

b. If the interest rate increases to 7 percent, what is the value of each bond? Which bond has a larger $percentage$ change in value?

c. Based on the example above, complete the two blanks in this sentence: "The value of a bond
[rises/falls] when the interest rate increases, and bonds with a longer time to maturity are
[more/less] sensitive to changes in the interest rate."

Jesse N.
Numerade Educator

Problem 4

Your bank account pays an interest rate of 8 percent. You are considering buying a share of stock in XYZ Corporation for $\$$110. After 1, 2, and 3 years, it will pay a dividend of $\$$5. You expect to sell the stock after 3 years for $\$$120. Is XYZ a good investment? Support your answer with calculations.

Jesse N.
Numerade Educator

Problem 5

For each of the following kinds of insurance, give an example of behavior that can be called $moral hazard$ and another example of behavior that can be called $adverse selection$.

a. health insurance

b. car insurance

c. life insurance

Jesse N.
Numerade Educator

Problem 6

Which kind of stock would you expect to pay the higher average return: stock in an industry that is very sensitive to economic conditions ( such as an automaker) or stock in an industry that is relatively
insensitive to economic conditions (such as a water company)? Why?

Jesse N.
Numerade Educator

Problem 7

A company faces two kinds of risk. A firm-specific risk is that a competitor might enter its market and
take some of its customers. A market risk is that the economy might enter a recession, reducing sales.
Which of these two risks would more likely cause the company's shareholders to demand a higher return? Why?

Kaylee M.
Numerade Educator

Problem 8

When company executives buy and sell stock based on private information they obtain as part of their jobs, they are engaged in $insider \, trading$.

a. Give an example of inside information that might be useful for buying or selling stock.

b. Those who trade stocks based on inside information usually earn very high rates of return. Does this fact violate the efficient markets hypothesis?

c. Insider trading is illegal. Why do you suppose that is?

Jesse N.
Numerade Educator

Problem 9

Jamal has a utility function $U = W^{1/2}$, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $\$$4 million for sure, or (B) a gamble that pays $\$$1 million with probability 0.6 and $\$$9 million with probability 0.4.

a. Graph Jamal's utility function. Is he risk averse? Explain.

b. Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate
calculations. ($Hint$: The expected value of a random variable is the weighted average of the
possible outcomes, where the probabilities are the weights.)

c. Does A or B offer Jamal a higher expected utility? Again, show your calculations.

d. Should Jamal pick A or B? Why?

Jesse N.
Numerade Educator