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The Modern Firm II - All Relevant Questions, and Answers.
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The Modern Firm II - All Relevant Questions, and Answers©2022
,Chapter 3 – pages 59-70
Exemplary Questions (not in the book)
1.
• Suppose a jewelry manufacturer has the opportunity to trade 10 ounces of gold and receive 20
ounces of palladium today. The current market price for palladium is $600 per ounce and for
gold of $1,500 per ounce. Should the jewelry manufacturer do the trade?
• Solution:
– To compare the costs and benefits, we first need to convert them to a common unit.
– If the current market price for palladium is $600 per ounce, then the 20 ounces of
palladium we receive has a cash value of:
o (20 ounces of palladium) X ($600/ounce) = $12,000
– The 10 ounces of gold we give up has a cash value of:
o (10 ounces of gold) X ($1,500/ounce) = $15,000 today
– Therefore, the jeweler’s opportunity has a benefit of $12,000 today and a cost of $15,000
today. In this case, the net value of the project today is:
o $12,000 – $15,000 = –$3,000
– Because it is negative, the costs exceed the benefits and the jeweler should reject the trade.
2.
• Problem
– Your car recently broke down and it needs $2,000 in repairs. But today is your lucky
day because you have just won a contest where the prize is either a new motorcycle,
with a MSRP of $15,000, or $10,000 in cash. You do not have a motorcycle license,
nor do you plan on getting one. You estimate you could sell the motorcycle for
$12,000. Which prize should you choose?
• Solution
– Competitive markets, not your personal preferences (or the MSRP of the motorcycle),
are relevant here: One Motorcycle with a market value of $12,000 or $10,000 cash.
Instead of taking the cash, you should accept the motorcycle, sell it for $12,000, use
$2,000 to pay for your car repairs, and still have $10,000 left over.
3.
• Problem
– You are offered the following investment opportunity: In exchange for $40,000 today,
you will receive 2,500 shares of stock in the Ford Motor Company and 10,000 euros
today. The current market price for Ford stock is $9 per share and the current
exchange rate is $1.50 per €. Should you take this opportunity? Would your decision
change if you believed the value of the euro would rise over the next month?
• Solution
– The costs and benefits must be converted to their cash values. Assuming competitive
market prices:
2,500 shares × $9/share = $22,500
€10,000 × $1.50/ € = $15,000
The net value of the opportunity is $22,500 + $15,000 - $40,000 = -$2,500, we should not take
it. This value depends only on the current market prices for Ford and the euro. Our personal
opinion about the future prospects of the euro and Ford does not alter the value the decision
today.
,4.
• Problem
– The cost of replacing a fleet of company trucks with more energy efficient vehicles
was $100 million in 2012.
– The cost is estimated to rise by 8.5% in 2013.
– If the interest rate was 4%, what was the cost of a delay in terms of dollars in 2012?
• Solution
– If the project were delayed, its cost in 2013 would be:
• $100 million × (1.085) = $108.5 million
– Compare this amount to the cost of $100 million in 2012 using the interest rate of 4%:
• $108.5 million ÷ 1.04 = $104.33 million in 2012 dollars.
– The cost of a delay of one year would be:
• $104.33 million – $100 million = $4.33 million in 2009 dollars.
Problems and Solutions from book:
3-1. Honda Motor Company is considering offering a $2000 rebate on its minivan, lowering the
vehicle’s price from $30,000 to $28,000. The marketing group estimates that this rebate will
increase sales over the next year from 40,000 to 55,000 vehicles. Suppose Honda’s profit margin
with the rebate is $6000 per vehicle. If the change in sales is the only consequence of this decision,
what are its costs and benefits? Is it a good idea?
The benefit of the rebate is that Honda will sell more vehicles and earn a profit on each additional
vehicle sold:
Benefit = Profit of $6,000 per vehicle × 15,000 additional vehicles sold = $90 million.
The cost of the rebate is that Honda will make less on the vehicles it would have sold:
Cost = Loss of $2,000 per vehicle × 40,000 vehicles that would have sold without rebate = $80 million.
Thus, Benefit – Cost = $90 million – $80 million = $10 million, and offering the rebate looks attractive.
(Alternatively, we could view it in terms of total, rather than incremental, profits. The benefit as
$6000/vehicle × 55,000 sold = $330 million, and the cost is $8,000/vehicle × 40,000 sold = $320
million.) 40*30=120 vs. 55*28=1540
3-2. You are an international shrimp trader. A food producer in the Czech Republic offers to pay you
2 million Czech koruna today in exchange for a year’s supply of frozen shrimp. Your Thai
supplier will provide you with the same supply for 3 million Thai baht today. If the current
competitive market exchange rates are 25.50 koruna per dollar and 41.25 baht per dollar, what is
the value of this deal?
Czech buyer’s offer = 2,000,000 CZK / (25.50 CZK/USD) = 78,431.37 USD.
Thai supplier’s offer = 3,000,000 THB / (41.25 THB/USD) = 72,727.27 USD.
The value of the deal is $78,431 – 72,727 = $5704 today.
3-3. Suppose the current market price of corn is $3.75 per bushel. Your firm has a technology that can
convert 1 bushel of corn to 3 gallons of ethanol. If the cost of conversion is $1.60 per bushel, at
what market price of ethanol does conversion become attractive?
The price in which ethanol becomes attractive is ($3.75 + $1.60 / bushel of corn) / (3 gallons of ethanol
/ bushel of corn) = $1.78 per gallon of ethanol.
, 3-4.* Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company
stock. Whichever one you choose will be awarded today. The stock is currently trading for $63
per share.
a. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus
should you choose? What is its value?
b. Suppose that if you receive the stock bonus, you are required to hold it for at least one year.
What can you say about the value of the stock bonus now? What will your decision depend
on?
a. Stock bonus = 100 × $63 = $6,300
Cash bonus = $5,000
Since you can sell (or buy) the stock for $6,300 in cash today, its value is $6,300 which is better
than the cash bonus.
b. Because you could buy the stock today for $6,300 if you wanted to, the value of the stock bonus
cannot be more than $6,300. But if you are not allowed to sell the company’s stock for the next
year, its value to you could be less than $6,300. Its value will depend on what you expect the stock
to be worth in one year, as well as how you feel about the risk involved. You might decide that it is
better to take the $5,000 in cash than wait for the uncertain value of the stock in one year.
3-5. You have decided to take your daughter skiing in Utah. The best price you have been able to find
for a roundtrip air ticket is $359. You notice that you have 20,000 frequent flier miles that are
about to expire, but you need 25,000 miles to get her a free ticket. The airline offers to sell you
5000 additional miles for $0.03 per mile.
a. Suppose that if you don’t use the miles for your daughter’s ticket they will become worthless.
What should you do?
b. What additional information would your decision depend on if the miles were not expiring?
Why?
a. The price of the ticket if you purchase it is $359. The price if you purchase the miles is $0.03 x
5000=$150. So you should purchase the miles.
b. In part a, the existing miles are worthless if you don’t use them. They are not worthless now, so
you must add in the cost of using them. Because there is no competitive market price for these
miles (you can purchase at 3¢ but not sell for that price) the decision will depend on how much you
value the existing miles (which will depend on your likelihood of using them in the future).
3-6.* Suppose the risk-free interest rate is 4%.
a. Having $200 today is equivalent to having what amount in one year?
b. Having $200 in one year is equivalent to having what amount today?
c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when
you need the money? Why or why not?
a. Having $200 today is equivalent to having 200 × 1.04 = $208 in one year.
b. Having $200 in one year is equivalent to having .04 = $192.31 today.
c. Because money today is worth more than money in the future, $200 today is preferred to $200 in
one year. This answer is correct even if you don’t need the money today, because by investing the
$200 you receive today at the current interest rate, you will have more than $200 in one year (given
positive interest rates, of course).
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