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Subjective Short Answer
1. Write the formula for finding the future value in n years of $x today.
2. Write the formula for finding the future value of $1,000 today in 10 years if the interest rate is 4 percent.
3. Anthony closes out his account in which he deposited $500 five years ago at an interest rate of 5%. Mark closes out his
account in which he deposited $500 ten years ago at an interest rate of 5%. Who had more in their account? About how
much more did he have?
4. Write the formula to find the present value of $x to be paid in n years.
5. Write the formula to find the present value of $750 to be paid in 5 years if the interest rate is 3 percent.
6. A payment of $10,000 is to be made in the future. The interest rate 3%. Is this payment worth more if it is paid in 5
years or 10 years? How much more is it worth?
7. Jack’s Lock and Key is considering remodeling. It estimates that the remodeling will cost $6,000 and that as a result
revenues will rise by $3,000 the first year, $2,500 the second year, $1,500 the third year and have no effect after then. If
the interest rate is 5%, should Jack’s remodel? Defend your answer by showing your work.
8. If the interest rate is 5 percent, then what is the present value of $2,000 to be received in three years?
9. If the interest rate is 8 percent, then what is the present value of $5,000 to be received in ten years?
10. If a savings account pays 7% interest, then according to the rule of 70 how long will it take for the account balance to
double?
11. If a savings account pays 3.5% interest, then according to the rule of 70 how long will it take for the account balance
to double?
12. Suppose you invest $10,000 at 7% interest to be withdrawn by your heirs in 100 years. According to the rule of 70,
approximately how much will your heirs be able to withdraw?
13. The nation of Zambonia experiences the same rate of population growth every year. If the population of Zambonia
doubles every 35 years, then what is the approximate annual rate of population growth?
14. Suppose you place $1,000 into a savings account that will pay you 4% interest per year. What will be the future value
of the savings account in 10 years?
15. Suppose you place $500 into a savings account that will pay you 6% interest per year. What will be the future value of
the savings account in 15 years?
16. Suppose the interest rate is 3% and that you are to receive three annual payments of $1,000, with the first payment
today, the second payment one year from now, and the third payment two years from now. What is the present value of
this stream of payments?
17. Suppose the interest rate is 5% and that you are to receive three annual payments of $10,000, with the first payment
one year from now, the second payment two years from now, and the third payment three years from now. What is the
present value of this stream of payments?
18. A company has an investment project that will cost $2 million today and yield a payoff of $3 million in 5 years. If the
interest rate is 7%, should the firm undertake the project? Show evidence to support your answer.
19. A company has an investment project that will cost $2 million today and yield a payoff of $3 million in 5 years. If the
interest rate is 9%, should the firm undertake the project? Show evidence to support your answer.
20. A company has an investment project that will cost $2 million today and yield a payoff of $3 million in 5 years. What
interest rate represents the cutoff between profitability and nonprofitability for this project?
21. Suppose your bank account pays a 4% interest rate. You are considering purchasing a share of stock in ABC
Corporation for $500. The stock will pay you a $10 dividend at the end of years 1, 2, and 3. You expect to be able to sell
the stock at the end of year 3 for $550. Is ABC a good investment? Provide evidence to support your answer.
22. Suppose your bank account pays a 5% interest rate. You are considering purchasing a share of stock in DH
Corporation for $250. The stock will pay you a $10 dividend at the end of years 1, 2, 3, 4, and 5. You expect to be able to
sell the stock at the end of year 5 for $300. Is DH a good investment? Provide evidence to support your answer.
23. Thompson Corporation is considering the purchase of a new piece of machinery. Thompson expects the new
machinery to increase its revenues by $70,000 at the end of year 1, $60,000 at the end of year 2, and $50,000 at the end of
year 3 at which point the machinery will have exhausted its useful life. If the interest rate is 4%, what is the most
Thompson should be willing to pay today for this piece of machinery?
24. List two ways a risk adverse person may attempt to reduce risks.
25. Describe the shape of the utility function of a risk averse person.
26. From the standpoint of the economy as a whole, the role of insurance is not to eliminate the risks inherent in life. Then
what is its purpose?
27. How does adverse selection affect the insurance market?
28. How does moral hazard matter in the market for insurance?
29. Bill gets medical insurance and then exercises less. Lilly has health concerns and so applies for medical insurance.
Identify each of these as moral hazard or adverse selection.
30. Can insurance be thought of as diversification? Defend your answer.
31. The objective of diversification is to reduce risk. How does a person diversify a stock portfolio? How is risk
measured?
32. At about what number of companies does the reduction in risk from adding stocks of more companies to a portfolio do
little to reduce risk?
33. Until recently, shares of stock accounted for 40 percent of Jimmy’s savings. A few days ago, Jimmy sold some bonds
and bought some additional shares of stock. Now shares of stock account for 70 percent of Jimmy’s savings. How did this
change affect Jimmy’s expected retun on his savings? How did it affect the risks he faces?
34. Should a person who is risk averse hold a portfolio with no stock and only bonds?
Explain.
35. You are a financial advisor and a client tells you he is concerned about the amount of risk in his portfolio. Assuming
your client hasn’t already done them, what two things can you suggest to reduce your client’s risk? What additional
information about reducing risk should you provide?
36. Your boss asks you to do fundamental analysis of a corporation. What value is she asking for and how would you
estimate this value?
37. Refer to Scenario 27-1. Use the following diagram to graph Lisa’s utility function for .
38. Refer to Scenario 27-1. Is Lisa risk averse? Explain.
39. Refer to Scenario 27-1. Suppose Lisa is faced with a choice between two options. With option A Lisa receives a
guaranteed $9 million. With option B Lisa faces a lottery that pays $4 million with probability 0.4 and pays $16 million
with probability 0.6. Given Lisa’s utility function, will she prefer option A or option B? Provide evidence to support your
answer.
40. Refer to Scenario 27-1. Suppose Lisa is faced with a choice between two options. With option A Lisa receives a
guaranteed $9 million. With option B Lisa faces a lottery that pays $16 million with probability P and pays $4 million
with probability (1-P). Given Lisa’s utility function, how high does P need to be before Lisa will prefer option B?
41. Refer to Scenario 27-2. Use the following diagram to graph Dave’s utility function for .
42. Refer to Scenario 27-2. Is Dave risk averse? Explain.
43. Refer to Scenario 27-2. Suppose Dave is faced with a choice between two options. With option A Dave receives a
guaranteed $2 million. With option B Dave faces a lottery that pays $0 with probability 0.8 and pays $10 million with
probability 0.2. Given Dave’s utility function, will he prefer option A or option B? Provide evidence to support your
answer.
44. Refer to Scenario 27-2. Suppose Dave is faced with a choice between two options. With option A Dave receives a
guaranteed $2 million. With option B Dave faces a lottery that pays $10 million with probability P and pays $0 with
probability (1-P). Given Dave’s utility function, how high does P need to be before he will prefer option B over option A?
45. Define the efficient markets hypothesis.
46. According to the efficient markets hypothesis, what changes the price of a share of a corporation’s stock? Make up an
example.
47. If a friend tells you that he is certain a stock price will rise based on information he heard on television or saw on the
Internet, should you be skeptical? Explain.
48. What does “random walk” mean? According to the efficient markets hypothesis, should stock prices follow a random
walk?
49. What is meant by an asset bubble?
50. Why might someone be willing to pay more than the fundamental value for a stock?
51. Suppose the Johnson Corporation releases an earnings report that beats the market’s expectations. What does the
efficient markets hypothesis predict will happen to Johnson’s stock price.
52. Suppose the McCormick Corporation releases an earnings report that fails to meet the market’s expectations. What
does the efficient markets hypothesis predict will happen to McCormick’s stock price?
53. Demonstrate that whether you would prefer to have $225 today or wait five years for $300 depends on the interest
rate. Show your work.
54. As the interest rate increases, what happens to the present value of a future payment? Explain why changes in the
interest rate will lead to changes in the quantity of loanable funds demanded and investment spending.
55. Write the rule of 70. Suppose that your great-great-grandmother put $50 in a savings account 100 years ago and the
account is now worth $1,600. Use the rule of 70 to determine about what interest rate she earned.
56. Give an example of adverse selection and an example of moral hazard using homeowners insurance.
57. What's the difference between firm-specific risk and market risk? Will diversification eliminate one or both? Explain.
58. List three different ways that a risk-averse person can reduce financial risk.
59. Discuss the statistical evidence concerning the efficient markets hypothesis.
60. In the 1990s, several stocks had very, very high price to earnings ratios. These stocks appeared overvalued to many
observers. What might the people who bought them have been thinking?
61. Give two conditions that are important to the efficient market theory. List one implication of the efficient market
theory.
62. Draw graphs showing the following three relationships.
1. The relation between utility and wealth for a risk averse consumer.
2. The relation between standard deviation and the number of stocks in a portfolio.
3. The relation between return and risk.
