Corporate Finance, 4e (Berk / DeMarzo)
Chapter 3 Financial Decision Making and the Law of One Price
3.1 Valuing Decisions
1) Due to a pre-existing contract, Recycle America Inc. has the opportunity to acquire 10,000 pounds of
scrap aluminum and 2500 pounds of scrap lead for $10,750. If the current market price for scrap
aluminum is $0.83 per pound and the current market price for lead is $1.06 per pound, then the added
benefit (cost) to you if you acquire this metal is:
A) ($200)
B) $200
C) ($1925)
D) $1925
2) Which of the following statements regarding the valuing of costs and benefits is NOT correct?
A) The first step in evaluating a project is to identify its costs and benefits.
B) In the absence of competitive markets, we can use one–sided prices to determine exact cash values.
C) Competitive market prices allow us to calculate the value of a decision without worrying about the
tastes or opinions of the decision maker.
D) Because competitive markets exist for most commodities and financial assets, we can use them to
determine cash values and evaluate decisions in most situations.
3) Recycle America Inc. has the opportunity to trade 8000 pounds of plastic pellets made from recycled
soda bottles for 5000 pounds of aluminum cans. If the current market price of scrap aluminum is $0.83
per pound and the current market price for plastic pellets is $0.57 per pound, then the added benefit
(cost) of making this trade is:
A) ($410)
B) $410
C) ($780)
D) $780
Use the information for the question(s) below.
Alaska North Slope Crude Oil (ANS)
$71.75/Bbl
West Texas Intermediate Crude Oil (WTI)
$73.06/Bbl
As an oil refiner, you are able to produce $76 worth of unleaded gasoline from one barrel of Alaska
North Slope (ANS) crude oil. Because of its lower sulfur content, you can produce $77 worth of
unleaded gasoline from one barrel of West Texas Intermediate (WTI) crude.
4) Another oil refiner is offering to trade you 10,150 Bbls of Alaska North Slope (ANS) crude oil for
10,000 Bbls of West Texas Intermediate (WTI) crude oil. Assuming you currently have 10,000 Bbls of
WTI crude, the added benefit (cost) to you if you take the trade is closest to:
A) ($1400)
B) $1400
C) ($3908)
D) $3908
5) Assuming you currently have 10,000 Bbls of WTI crude, the added benefit (cost) to you if you were to
sell the 10,000 Bbls of WTI crude and use the proceeds to purchase and refine ANS crude is closest to:
A) ($1400)
B) $1400
C) ($3908)
D) $3908
6) Assuming you just purchased 10,000 Bbls of WTI crude at the current market price, the added benefit
(cost) to you if you were to refine this crude oil and sell the unleaded gasoline is closest to:
A) $730,600
B) $39,400
C) $770,000
D) -$39,400
7) Another oil refiner is offering to trade you 10,150 Bbls of Alaska North Slope (ANS) crude oil for
10,000 Bbls of West Texas Intermediate (WTI) crude oil. Assuming you just purchased 10,000 Bbls of
WTI crude at the current market price, the added benefit (cost) to you if you take the trade is closest to:
A) $730,600
B) $771,400
C) $40,800
D) $43,308
8) Assuming you currently have 10,000 Bbls of WTI crude, the added benefits to you if you were to sell
the 10,000 Bbls of WTI crude and use the proceeds to purchase and refine ANS crude is closest to:
A) $730,600
B) $770,000
C) $40,800
D) $43,308
9) Another oil refiner is offering to trade you 10,150 Bbls of Alaska North Slope (ANS) crude oil for
10,000 Bbls of West Texas Intermediate (WTI) crude oil. Assuming you currently have 10,000 Bbls of
WTI crude, what should you do?
A) Sell 10,000 Bbls WTI crude on the market and use the proceeds to purchase and refine ANS crude.
B) Do nothing, refine the 10,000 Bbls of WTI crude.
C) Trade the 10,000 Bbls WTI crude with the other refiner and refine the 10,150 Bbls of ANS crude.
D) Trade the 10,000 Bbls WTI crude with the other refiner and then sell the 10,150 Bbls of ANS crude.
10) By evaluating cost and benefits using competitive market prices, we can determine whether a
decision will make the firm and its investors wealthier. This central concept is called:
A) the Law of One Price.
B) the Present Value.
C) the Valuation Principle.
D) the Internal Rate of Return.
Use the information for the question(s) below.
Low-Grade Copper Ore
$640 per Ton
High-Grade Copper Ore
$940 per Ton
Coloma Cooper Incorporated is able to produce $640 worth of copper from one ton of low–grade copper
ore. Because of its higher copper content, Coloma can produce $940 worth of copper from one ton of
high-grade copper ore.
11) A mining company is offering to trade you 7250 tons of low-grade copper ore for 5000 tons of high-
grade copper ore. Assuming you currently have 5000 tons of high-grade ore, what should you do?
12) A company that manufactures copper piping is offering to trade you 5925 tons of low–grade copper
ore for 4000 tons of high-grade copper ore. Assuming you currently have 4000 tons of high-grade ore,
what are the total benefits and added benefits of taking the trade?
3.2 Interest Rates and the Time Value of Money
1) If the risk-free rate of interest (rf) is 3.5%, then you should be indifferent between receiving $1000 in
one-year or:
A) $965.00 today.
B) $966.18 today.
C) $1000.00 today.
D) $1035.00 today.
2) Suppose you have $1000 today and the risk-free rate of interest (rf) is 3.5%. The equivalent value in
one year is closest to:
A) $965.00 today.
B) $966.18 today.
C) $1000.00 today.
D) $1035.00 today.
3) A project that you are considering today is expected to provide benefits worth $168,000 in one year.
If the risk-free rate of interest (rf) is 4.5%, then the value of the benefits of this project today are closest
to:
A) $160,440
B) $160,766
C) $168,000
D) $175,560
4) Which of the following statements is INCORRECT?
A) In general, money today is worth more than money in one year.
B) We define the risk-free interest rate, rf for a given period as the interest rate at which money can be
borrowed or lent without risk over that period.
C) We refer to (1 – rf) as the interest rate factor for risk-free cash flows.
D) For most financial decisions, costs and benefits occur at different points in time.
5) If the risk-free rate of interest (rf) is 6%, then you should be indifferent between receiving $250 in one
year or
A) $235.85 today.
B) $250.00 today.
C) $265.00 today.
D) None of the above
6) If the risk-free rate of interest (rf) is 6%, then you should be indifferent between receiving $250 today
or
A) $235.85 in one year.
B) $250.00 in one year.
C) $265.00 in one year.
D) None of the above
7) A project you are considering is expected to provide benefits worth $225,000 in one year. If the risk–
free rate of interest (rf) is 8%, then the value of the benefits of this project today are closest to:
A) $190,333
B) $208,333
C) $225,000
D) $243,000
8) Suppose you have $500 today and the risk-free interest rate (rf) is 5%. The equivalent value in one
year is closest to:
A) $475
B) $476
C) $500
D) $525
9) Suppose you will receive $500 in one year and the risk-free interest rate (rf) is 5%. The equivalent
value today is closest to:
A) $475
B) $476
C) $500
D) $525
10) When we express the value of a cash flow or series of cash flows in terms of dollars today, we call it
the ________ of the investment. If we express it in terms of dollars in the future, we call it the ________.
A) present value; future value
B) future value; present value
C) ordinary annuity; annuity due
D) discount factor; discount rate
11) If we use future value rather than present value to decide whether to make an investment:
A) we will make a bad decision, since the future value will always be higher if the discount rate is
positive.
B) we will make a bad decision, since the future value will always be lower if the discount rate is
positive.
C) we will make the same decision using either future value or present value.
D) There is not enough information given to answer the question.
3.3 Present Value and the NPV Decision Rule
1) Rearden Metal needs to order a new blast furnace that will be delivered in one year. The $1,000,000
price for the blast furnace is due in one year when the new furnace is installed. The blast furnace
manufacturer offers Rearden Metal a discount of $50,000 if they pay for the furnace now. If the interest
rate is 7%, then the NPV of paying for the furnace now is closest to:
A) ($15,421)
B) $15,421
C) ($46,729)
D) $46,729
Use the information below to answer the following question(s):
The owner of the Krusty Krab is considering selling his restaurant and retiring. An investor has offered
to buy the Krusty Krab for $350,000 whenever the owner is ready for retirement. The owner is
considering the following three alternatives:
1. Sell the restaurant now and retire.
2. Hire someone to manage the restaurant for the next year and retire. This will require the owner to
spend $50,000 now, but will generate $100,000 in profit next year. In one year the owner will sell the
restaurant for $350,000.
3. Scale back the restaurant’s hours and ease into retirement over the next year. This will require the
owner to spend $40,000 on expenses now, but will generate $75,000 in profit at the end of the year. In
one year the owner will sell the restaurant for $350,000.
2) If the interest rate is 7%, the NPV of alternative #1 is closest to:
A) $350,000
B) $357,000
C) $375,500
D) $400,000
3) If the interest rate is 7%, the NPV of alternative #2 is closest to:
A) $350,000
B) $357,196
C) $370,561
D) $401,121
4) If the interest rate is 7%, the NPV of alternative #3 is closest to:
A) $350,000
B) $357,196
C) $370,561
D) $401,121
5) If the interest rate is 7%, the alternative with the highest NPV is:
A) Alternative #1 with an NPV of approximately $350,000
B) Alternative #2 with an NPV of approximately $370,561
C) Alternative #3 with an NPV of approximately $357,196
D) Alternative #2 with an NPV of approximately $380,561
6) If the interest rate is 7%, the alternative with the lowest NPV is:
A) Alternative #1 with an NPV of approximately $350,000
B) Alternative #2 with an NPV of approximately $370,561
C) Alternative #3 with an NPV of approximately $357,196
D) Alternative #2 with an NPV of approximately $380,561
7) Which of the following statements regarding Net Present Value (NPV) is INCORRECT?
A) The NPV represents the value of the project in terms of cash today.
B) Good projects will have a positive NPV.
C) The NPV of a project is the difference between the present value of its benefits and the present value
of its costs.
D) When faced with a set of alternatives, choose the one with the lowest NPV in order to minimize the
present value of costs.
Use the following information to answer the question(s) below.
The owner of the Krusty Krab is considering selling his restaurant and retiring. An investor has offered
to buy the Krusty Krab for $350,000 whenever the owner is ready for retirement. The owner is
considering the following three alternatives:
1. Sell the restaurant now and retire.
2. Hire someone to manage the restaurant for the next year and retire. This will require the owner to
spend $50,000 now, but will generate $100,000 in profit next year. In one year the owner will sell the
restaurant.
3. Scale back the restaurant’s hours and ease into retirement over the next year. This will require the
owner to spend $40,000 on expenses now, but will generate $75,000 in profit at the end of the year. In
one year the owner will sell the restaurant.
8) If the discount rate is 15%, the alternative with the highest NPV is:
A) #1 with an NPV of approximately $350,000
B) #2 with an NPV of approximately $341,300
C) #3 with an NPV of approximately $329,570
D) #2 with an NPV of approximately $400,000
E) None of the above
9) If the discount rate is 15%, the alternative with the lowest NPV is:
A) #1 with an NPV of approximately $350,000
B) #2 with an NPV of approximately $341,300
C) #3 with an NPV of approximately $329,570
D) #2 with an NPV of approximately $400,000
E) None of the above
10) If the discount rate is 15%, then which alternative should the owner choose:
A) #1
B) #2
C) #3
D) either #1 or #2
E) either #1 or #3
11) Which of the following statements regarding the NPV decision rule is FALSE?
A) Reject projects with a NPV of zero, as accepting them is equivalent to reducing firm value.
B) When faced with a set of alternatives, choose the one with the highest NPV.
C) Accept those projects with a positive NPV, as accepting them is equivalent to receiving their NPV in
cash today.
D) Reject those projects with a negative NPV.
12) Which of the following formulas regarding NPV is INCORRECT?
A) NPV + PV(benefits) = PV(Cost)
B) NPV + PV(costs) = PV(benefits)
C) NPV = PV(All project cash flows)
D) All of the above
13) You are offered an investment opportunity in which you will receive $23,750 today in exchange for
paying $25,000 in one year. Suppose the risk-free interest rate is 6% per year. Should you take this
project? The NPV for this project is closest to:
A) Yes; NPV = $165
B) No; NPV = $165
C) Yes; NPV = –$165
D) No; NPV = –$165
14) You are offered an investment opportunity in which you will receive $25,000 in one year in
exchange for paying $23,750 today. Suppose the risk-free interest rate is 6% per year. Should you take
this project? The NPV for this project is closest to:
A) Yes; NPV = $165
B) No; NPV = $165
C) Yes; NPV = –$165
D) No; NPV = –$165
15) You have an investment opportunity in Germany that requires an investment of $250,100 today and
will produce a cash flow of €208,650 in one year with no risk. Suppose the risk-free rate of interest in
Germany is 7% and the current competitive exchange rate is €0.78 to $1.00. What is the NPV of this
project? Would you take the project?
A) NPV = –$100; No
B) NPV = $100; Yes
C) NPV = $2358; Yes
D) NPV = $3650; Yes
16) You have an investment opportunity in Germany that requires an investment of $250,000 today and
will produce a cash flow of €208,650 in one year with no risk. Suppose the risk-free rate of interest in
Germany is 6% and the current competitive exchange rate is €0.78 to $1.00. What is the NPV of this
project? Would you take the project?
A) NPV = 0; No
B) NPV = –$2358; No
C) NPV = $2358; Yes
D) NPV = $13,650; Yes
Use the table for the question(s) below.
Project
Cash flow
today
Cash flow
in one year
Eenie
–10
15
Meenie
10
-8
Mighty
–15
20
Moe
10
–15
17) If the risk-free interest rate is 10%, then the NPV for Eenie is closest to:
A) -3.64
B) 2.73
C) 3.18
D) 3.64
18) If the risk-free interest rate is 10%, then the NPV for Moe is closest to:
A) -3.64
B) 2.73
C) 3.18
D) 3.64
19) If the risk-free interest rate is 10%, then of the four projects listed, if you could only invest in one
project, which one would you select?
A) Eenie
B) Meenie
C) Mighty
D) Moe
20) If the risk-free interest rate is 10%, then of the four projects listed, which project would you never
want to invest in?
A) Eenie
B) Meenie
C) Mighty
D) Moe
21) If the risk-free interest rate is 10%, then of the four projects listed, if could only invest in two of these
projects, which two projects would you select?
A) Mighty & Eenie
B) Mighty & Meenie
C) Eenie & Moe
D) Eenie & Meenie
22) You have an investment opportunity in the United Kingdom that requires an investment of $500,000
today and will produce a cash flow of £320,000 in one year with no risk. Suppose the risk-free rate of
interest in the U.K is 6% and the current competitive exchange rate is $1.70/£. What is the NPV of this
project? Would you take the project?
Use the table for the question(s) below.
Project
Cash flow
today
Cash flow
in one year
“alpha”
–18
23
“beta”
15
–12
“gamma”
15
–20
“delta”
–16
21
23) Assume that the risk-free interest rate is 10%. Rank each of the four projects from most desirable to
least desirable based upon NPV. Which project would you invest in first? Are there any projects that
you wouldn’t invest in?