Deck 6: Uncertainty, Default, and Risk

Question 1

A risk-free investment of $10,000 will return 8%. A risky $10,000 investment has a 50% chance of defaulting and returning only $3,000. What is the expected rate of return on the risky
Investment?

A)+5.40%
B)-0.54%
C)-31.00%
D)-46.00%

Answer 1

-31.00%

Question 2

An investor who is risk-neutral

A)would prefer to invest in only risk-free assets.
B)would be indifferent between investing her money in a savings account at 4% or investing in a bond that has a 50% chance of returning 8% and a 50% chance of returning 0%.
C)will take any fair bet.
D)Both B and C are true.

Answer 2

Both B and C are true.

Question 3

A risk-free investment of $10,000 will return 8%. A risky $10,000 investment has a 50% chance of defaulting and returning only $3,000. How much must the risky investment promise to
Return?

A)36.2%
B)86.0%
C)18.6%
D)37.2%

Answer 3

86.0%

Question 4

A project has the following possible outcomes: Calculate the expected value of this project.

A)$2,000
B)$4,000
C)$4,500
D)none of the above

Question 5

Which of the following is a random variable?

A)the price of a stock in one year
B)the actual price of a stock in one year
C)the known expected price of a stock in one year
D)the average price of a stock throughout a year

Question 6

The possible one-year returns for three different investments are as follows: The returns for each investment are equally likely to occur. Which investment's
returns would have the lowest standard deviation? Why? (Note: No calculations are
necessary.)

Question 7

Which of the following is an ordinary, non-random variable?

A)the price of a stock in one year
B)the actual price of a stock in one year
C)the known expected price of a stock in one year
D)both B and C are ordinary, non-random variables

Question 8

Which of the following statements is (are)true about risk aversion?

A)Risk-averse investors would be indifferent between investing in a risk-free investment that will earn 4% or a risky asset that has a 50% chance of earning 8% and a 50% chance of
Returning 0%.
B)Risk-averse investors should accept only fair bets.
C)The effective risk-aversion of a group of investors is less than the risk aversion of any single investor.
D)Both A and B are true.

Question 9

An investment will cost $100 today. You have estimated the following probability distribution for the value of the investment one year from now: Calculate the expected rate of return and the standard deviation of the returns for the 1-year
Holding period.

A)
B)
C)
D)

Question 10

A fair bet is

A)a bet for which the outcome is unknown by all participants.
B)a bet with a cost that is less than the expected value.
C)a bet with equally likely outcomes.
D)a bet for which the cost is exactly equal to the expected value.

Question 11

The price of a stock in one year has been assigned the following probability distribution: What is the expected price of the stock?

A)$24.16
B)$22.67
C)$21.40
D)$20.00

Question 12

What is the difference between the assumption of risk-neutrality and the assumption
of risk-aversion?

Question 13

An investment has the following possible values in one year: Calculate the expected value and the standard deviation of the future values for the investment.

A)
B)
C)
D)

Question 14

You have estimated a probability distribution for the value of an investment one year from now. Calculate the expected value and the standard deviation of the future values for the
Investment.

A)
B)
C)
D)

Question 15

The risk of an investment as measured by the standard deviation reflects

A)only how much lower than the expected value the actual outcome might be.
B)both how much lower or how much higher than the expected value the actual outcome might be.
C)how fair the bet is.
D)how random the variable being evaluated is.

Question 16

A project has the following possible outcomes: Calculate the expected value of the project at the end of the year.

A)$12,600
B)$12,667
C)$11,400
D)none of the above

Question 17

An investment of $20,000 today has the following possible outcomes: Calculate the expected rate of return of the investment and the variance and standard
deviation of the returns.

Question 18

An investment that is risk-free

A)has a standard deviation equal to its expected value.
B)is a fair bet.
C)has a variance of zero.
D)Both A and B are true.

Question 19

Which of the following is a measure of risk?

A)expected value
B)standard deviation
C)variance
D)Both B and C are measures of risk.

Question 20

An investment will cost $1,500 today. You have estimated the following probability distribution for the
Value of the investment one year from now: Calculate the expected rate of return and the standard deviation of the returns for the 1-year
Holding period.

A)
B)
C)
D)

Question 21

What kind of risk is captured in bond ratings? I. liquidity risk
II. interest rate risk
III. default risk

A)III only
B)II and III only
C)I and II only
D)I, II, and III

Question 22

A risk-free investment of $50,000 offers an annual return of 6%. A risky investment of $50,000 has a 40% probability of default, in which case it will pay only $25,000.
Refer to the information above. What is the expected rate of return on the risky investment?

A)+8.4%
B)-22.0%
C)-16.4%
D)+7.8%

Question 23

You want to borrow $20,000 for one year. Your bank believes that there is a 96% probability that you will be able to repay the loan with interest, a 3% probability that you will be able to repay only $15,000, and a 1% probability that you will repay nothing. The risk-free rate is 6%.
Refer to the information above. What return must you promise to pay the bank in order for it to earn the risk-free rate if its assumptions about your ability to repay are accurate?

A)12.76%
B)9.32%
C)10.04%
D)none of the above

Question 24

A type of investment that gives investors the ability to invest in only one aspect of a bond--e.g., time element or default element is called a

A)collateralized obligation (CO).
B)callable bond.
C)contingent payoff swap (CPS).
D)credit default swap (CDS).

Question 25

You want to borrow $20,000 for one year. Your bank believes that there is a 96% probability that you will be able to repay the loan with interest, a 3% probability that you will be able to repay only $15,000, and a 1% probability that you will repay nothing. The risk-free rate is 6%.
Refer to the information above. What default premium and time premium must this loan offer the banker?

A)default premium = 6.00%; time premium = 6.76%
B)default premium = 6.76%; time premium = 6.00%
C)default premium = 2.07%; time premium = 6.00%
D)default premium = 6.00%; time premium = 2.07%

Question 26

You have an investment opportunity with the following state-contingent payoffs:
Refer to the information above. What is the expected value of this investment?

A)$49,500
B)$49,333
C)$53,500
D)$56,000

Question 27

A risk-free investment of $50,000 offers an annual return of 6%. A risky investment of $50,000 has a 40% probability of default, in which case it will pay only $25,000.
Refer to the information above. What return must the risky investment promise?

A)8.1%
B)43.3%
C)71.7%
D)62.0%

Question 28

Will a bond that allows the borrower to repay the loan early have a higher or a lower
promised interest rate than an identical bond that does not allow early repayment?
Why?

Question 29

All else equal, which of the following bonds would you expect to offer the highest promised rate of
Return?

A)BBB bond
B)A+ bond
C)AAA bond
D)BB+ bond

Question 30

A bond with which of the following credit ratings would be considered investment grade? I. AA
II. A
III. BBB
IV. BB

A)I and II only
B)I, II, and III only
C)I only
D)All of the above are investment-grade bonds.

Question 31

A risk-free investment of $50,000 offers an annual return of 6%. A risky investment of $50,000 has a 40% probability of default, in which case it will pay only $25,000.
Refer to the information above. What default premium must the risky investment offer?

A)43.3%
B)33.3%
C)37.3%
D)52.0%

Question 32

The premium on a bond that compensates you for your potential inability to sell the bond in the future is the

A)liquidity premium.
B)default premium.
C)time premium.
D)risk premium.

Question 33

In a risk-neutral world, the realized default premium to be expected on a loan

A)will be greater than the expected rate of return.
B)will be equal to zero.
C)will equal the promised return minus the time premium.
D)Both B and C are true.

Question 34

You want to borrow $20,000 for one year. Your bank believes that there is a 96% probability that you will be able to repay the loan with interest, a 3% probability that you will be able to repay only $15,000, and a 1% probability that you will repay nothing. The risk-free rate is 6%.
Refer to the information above. If the bank agrees to lend you the money at the risk-free rate of 6%, what will the bank's expected return be?

A)+5.76%
B)+4.01%
C)+5.01%
D)-1.75%

Question 35

All else equal, which of the following bonds would you expect to sell for the highest price?

A)A+ bond
B)BBB bond
C)AAA bond
D)BB+ bond

Question 36

You have an investment opportunity with the following state-contingent payoffs:
Refer to the information above. If the appropriate expected return is 12%, what is the investment's present value? Round your answer to the nearest dollar.

A)$47,768
B)$44,196
C)$51,786
D)none of the above

Question 37

Assume a 1-year Treasury security offers a risk-free rate of return of 6%. The B. Smith
Company wants to borrow $100,000 from its bank. The banker believes that B. Smith
has a 30% chance of defaulting on the loan, in which case the company will be able to
repay only $40,000. What must B. Smith promise to repay in order for the bank to buy
the loan? What is the default premium and the time premium, assuming a risk-neutral
world?

Question 38

A $10,000 investment that promises a 20% return is equally likely to return $0, $2,000, $15,000, or $20,000 next year. What is the expected return on this investment?

A)+23.3%
B)+20.0%
C)-7.5%
D)+9.3%

Question 39

A risk-free investment of $10,000 will return 8%. A risky $10,000 investment has a 50% chance of
Defaulting and returning only $3,000. What default premium must the risky investment offer?

A)10.6%
B)78.0%
C)36.0%
D)25.2%

Question 40

Explain the mechanics of a credit default swap.

Question 41

An investor is considering a short-term investment in a resort property on a Caribbean island. If the weather is reasonably stable over the next year, the value of the investment is expected to be $1.2 million; however, if this proves to be a heavy hurricane year, the value is expected to be $0.5 million. According to the experts, there is a 40% chance that this will be a year of many hurricanes.
Refer to the information above. If the appropriate expected rate of return is 15%, what is the maximum amount the investor should invest?

A)$800,000
B)$678,000
C)$1,043,479
D)$739,000

Question 42

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. Assume that the new opportunity will be financed with a $150,000 bank loan. What rate of return will the levered equity holder earn if the business
Pays off $500,000 in one year?

A)57.1%
B)52.2%
C)45.7%
D)13.6%

Question 43

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. Assume that the new opportunity will be financed with a $150,000 bank loan. What is the maximum amount of his own money that an owner should be
Willing to invest in this business?

A)$195,455
B)$345,455
C)$215,000
D)$230,000

Question 44

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. What is the expected value of this investment?

A)$380,000
B)$300,000
C)$220,000
D)none of the above

Question 45

A business opportunity has a 10% chance of being worth $25,000 next year if the
economy improves, a 30% chance of being worth $8,000 if the economy worsens, and a
60% chance of being worth $15,000 if the economy stays the same. Develop a
state-contingent payoff table and calculate the expected future value of the business
and the fair value of the business opportunity today if the appropriate cost of capital is
14%.

Question 46

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. This new opportunity will be financed with a $150,000 loan. What must the promised rate of return on the loan be? Round your answer to the nearest
Hundredth of a percent.

A)10.00%
B)13.00%
C)28.57%
D)14.29%

Question 47

An investor is considering a short-term investment in a resort property on a Caribbean island. If the weather is reasonably stable over the next year, the value of the investment is expected to be $1.2 million; however, if this proves to be a heavy hurricane year, the value is expected to be $0.5 million. According to the experts, there is a 40% chance that this will be a year of many hurricanes.
Refer to the information above. If this investment is purchased for its fair market value, what is the expected return if there is a heavy hurricane season? Round your answer to the nearest
Tenth of a percent.

A)-62.5%
B)-45.7%
C)-37.5%
D)-54.3%

Question 48

A non-recourse loan is one in which

A)the lender can force repayment of the loan at any time, and the borrower must comply.
B)the borrower pays the lender a premium that the lender may keep if the borrower defaults on the loan.
C)the lender is entitled to the proceeds from the sale of any asset collateralizing the loan, but cannot seize any of the other assets of the borrower.
D)the lender may put a lien on the other assets of the borrower requiring future payment if the proceeds from the sale of the asset collateralizing a loan is not enough to repay the loan
In full.

Question 49

Which of the following investments is the most risky?

A)taking a 50% equity position in a project and borrowing the rest of the cost
B)lending 100% of the money needed for a project
C)taking a 100% equity position in a project
D)taking a 10% equity position in a project and borrowing the rest of the cost

Question 50

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. The new opportunity will be financed with a $150,000 bank loan. What is the expected future payoff for the levered equity holder? Round your answer to
The nearest dollar.

A)$245,000
B)$195,455
C)$222,727
D)$215,000

Question 51

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. This new opportunity will be financed with a $150,000 commercial loan. What must the promised future payoff to the lender be? Round your answer
To the nearest dollar.

A)$380,000
B)$171,429
C)$345,455
D)$192,857

Question 52

You have an investment opportunity with the following state-contingent payoffs:
Refer to the information above. Assume this investment is purchased for its fair market value. What is its expected rate of return under the assumption of a worsened economy? Round your
Answer to the nearest tenth of a percent.

A)-49.5%
B)-46.7%
C)-43.4%
D)-56.6%

Question 53

An investor is considering a short-term investment in a resort property on a Caribbean island. If the weather is reasonably stable over the next year, the value of the investment is expected to be $1.2 million; however, if this proves to be a heavy hurricane year, the value is expected to be $0.5 million. According to the experts, there is a 40% chance that this will be a year of many hurricanes.
Refer to the information above. What is the expected future value of this investment?

A)$920,000
B)$780,000
C)$850,000
D)none of the above

Question 54

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. The new opportunity will be financed with a $150,000 bank loan. What rate of return will the levered equity holder earn if the business pays off only
$100,000? Round your answer to the nearest tenth of a percent.

A)-100.0%
B)-48.8%
C)-55.2%
D)This cannot be determined without knowing how much equity was invested in the business.

Question 55

What is meant by "limited liability" in the context of finance?

Question 56

You have an investment opportunity with the following state-contingent payoffs:
Refer to the information above. Assume this investment is purchased for its fair market value. What is its expected rate of return under the assumption of a stable economy? Round your
Answer to the nearest tenth of a percent.

A)+17.2%
B)+31.2%
C)-11.6%
D)+11.7%

Question 57

An investor is considering a short-term investment in a resort property on a Caribbean island. If the weather is reasonably stable over the next year, the value of the investment is expected to be $1.2 million; however, if this proves to be a heavy hurricane year, the value is expected to be $0.5 million. According to the experts, there is a 40% chance that this will be a year of many hurricanes.
Refer to the information above. If this investment is purchased for its fair market value, what is the expected return if the weather is stable? Round your answer to the nearest tenth of a
Percent.

A)41.2%
B)30.4%
C)62.4%
D)none of the above.

Question 58

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. What is the present value of this investment? Round your answer to the nearest dollar.

A)$454,545
B)$345,455
C)$200,000
D)$272,727

Question 59

A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
Refer to the information above. This new opportunity will be financed with a $150,000 loan. What will the lender's rate of return be if the business opportunity returns only $100,000 next
Year?

A)0.0%
B)-33.3%
C)+1.5%
D)none of the above

Question 60

You have an investment opportunity with the following state-contingent payoffs:
Refer to the information above. Assume this investment is purchased for its fair market value. What is its expected rate of return under the assumption of an improved economy? Round
Your answer to the nearest tenth of a percent.

A)47.1%
B)30.0%
C)12.1%
D)31.3%

Question 61

Parker Technologies has been established for the purpose of developing a new product that is expected to produce a one-time cash flow of $500,000 next year if the firm can beat the competition to the market with it. If not, the cash flow is expected to be only $200,000. Parker believes it has a 60% chance of being the first to the market with the product, and it wants to finance this undertaking with a $250,000 loan. The appropriate cost of capital is 15%.
Refer to the information above. Develop a state-contingent payoff table for the loan
and calculate the promised interest rate the loan must offer.

Question 62

Parker Technologies has been established for the purpose of developing a new product that is expected to produce a one-time cash flow of $500,000 next year if the firm can beat the competition to the market with it. If not, the cash flow is expected to be only $200,000. Parker believes it has a 60% chance of being the first to the market with the product, and it wants to finance this undertaking with a $250,000 loan. The appropriate cost of capital is 15%.
Refer to the information above. Develop a state-contingent payoff table for the levered
equity position. What is the maximum amount that Parker should be willing to invest
of its own money?