Problem Set 1-2
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Course
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Subject
Finance
Date
Feb 20, 2024
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Problem Set I
Fin 638: Corporate Finance
Due Friday, February 11
Please submit neatly handwritten or typed answers.
Create a single pdf file and submit
electronically through Canvas or in class. Show your steps or reasoning. Do not just write
numbers. For example, avoid answers like 100
×
1
.
05
2
. A better answer would be PV = 100,
r = 5%, n = 2 =
⇒
FV
= 100
×
1
.
05
2
.
1
Corporation, Financial Markets
Problem 1.1.
See the Economist article about short selling from
https://www.economist.
com/finance-and-economics/2023/11/30/short-sellers-are-endangered-that-is-bad-
news-for-markets
or through library
https://stevens.idm.oclc.org/login?url=https:
//www.proquest.com/magazines/short-sellers-are-endangered-that-is-bad-news/docview/
2895218054/se-2
.
(a) According to the article, what were the effects of a short-sales ban in six European
countries?
(b) What do you think? Should short-selling be banned or suppressed?
Problem 1.2.
See the Wall Street Journal article about selling of shareholder voting rights
from
https://www.wsj.com/finance/stocks/buy-my-vote-a-startup-is-letting-shareholders-
sell-their-proxies-122f0eb9
or through library
https://stevens.idm.oclc.org/login?
url=https://www.proquest.com/newspapers/votes-sale-startup-is-letting-shareholders-
sell/docview/2916896574/se-2
. The buyer and the seller in a transaction obviously are
trading because they think it is in their interest. But we are interested in exploring whether
such trading good for companies and markets.
(a) According to the article, “creating a market for proxy votes would enhance share-
holder democracy and ultimately make companies better-run”.
What do you think
that means?
(b) In the next sentence, the article mentions a risk of such trading. Again, discuss how
such trading can be harmful to companies or markets.
2
Financial Statements
Use the financial statements of Duck Corporation to answer the following questions.
1
Duck Corporation
Consolidated Balance Sheet
Year ended December 31 (in
millions)
Liabilities and
Assets
2022
2021
Stockholders’ equity
2022
2021
Current Assets
Current Liabilities
Cash
127.2
117.0
Accounts payable
175.2
147.0
Accounts receivable
111.0
79.2
Notes payable
21.0
19.2
Inventories
91.8
85.8
Current maturities of long-term debt
79.8
73.8
Other current assets
12.0
6.0
Other current liabilities
12.0
24.0
Total current assets
342.0
288.0
Total current liabilities
288.0
264.0
Long-term assets
Long-term Liabilities
Land
133.2
124.2
Long-term debt
479.4
337.8
Buildings
219.0
183.0
Capital lease obligations
Equipment
238.2
199.2
Total Debt
479.4
337.8
Less accumulated depreciation
(112.2)
(105.0)
Deferred taxes
45.6
44.4
Net property, plant, and
equipment
478.2
401.4
Other long-term liabilities
Goodwill
120.0
Total long-term liabilities
525.0
382.2
Other long-term assets
126.0
84.0
Total liabilities
813.0
646.2
Total long-term assets
724.2
485.4
Stockholders’ equity
253.2
127.2
Total liabilities and
Total Assets
1066.2
773.4
Stockholders’ equity
1066.2
773.4
Duck Corporation
Consolidated Income Statement
Year ended December 31 (in
millions)
2022
2021
Revenue
1220.2
1156.6
Cost of sales
(1000.4)
(963.8)
Gross profit
219.8
192.8
Selling, general, and
administrative expenses
(81.0)
(78.0)
Research and development
(49.2)
(45.6)
Depreciation and amortization
(7.2)
(6.6)
Operating income
82.4
62.6
Other income
Earnings before interest and taxes (EBIT)
82.4
62.6
Interest income (expense)
(50.2)
(31.6)
Pre-tax income
32.2
31.0
Taxes
(11.0)
(10.6)
Net income
21.2
20.4
Dividends paid
10.2
10.0
Price per share
32
30
Shares outstanding (millions)
12.0
8.0
Problem 2.1.
What is Duck’s net working capital at year-end 2022?
2
Problem 2.2.
What is Duck’s market-to-book ratio at year-end 2022?
Problem 2.3.
What is Duck’s operating margin in 2022?
Problem 2.4.
What is Duck’s accounts payable days in 2022? Assume there are 365 days
in a year and use accounts payable at year-end.
3
Financial Decision Making
Problem 3.1.
See the following images for prices of a pack of 6 notebooks and a pack of
3 notebooks from an online retailer. Is there an arbitrage opportunity here? Why or why
not? Recall that there is an arbitrage strategy if there is a strategy to profit without taking
any risk.
3
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Problem 3.2.
You have an investment opportunity in France that requires an investment
of
500,000 today and will produce a cash flow of
e
459000 in one year with no risk. Suppose
the risk-free rate of interest in France is 2% and the current competitive exchange rate is
1.10 to
e
1. What is the NPV of this project? Would you take the project?
4
4
Time Value of Money
Problem 4.1.
Joe has decided to save
10,000 each year for his retirement. His first saving
will be deposited into the bank one year from today and the last one at the time of his
retirement, 25 years from today. Joe expects his annual need after retirement to be
60,000.
He will start withdrawing
60,000 a year with first withdrawal 26 years from today.
The
interest rate is 8%. For how many years after retirement can Joe’s retirement savings support
his annual
60,000 need?
Problem 4.2.
Chloe took a 30-year mortgage for
250,000 ten years ago for her first house
purchase.
The mortgage payments are monthly with a fixed annual interest rate of 5%.
Chloe has just paid the mortgage installment due after 10 years.
The interest rates have
gone up and the current interest rate is 7% for similar mortgages of all maturities.
The
bank that provided the mortgage has offered Chloe a
25,000 cash rebate if Chloe prepays
the remaining balance on the mortgage immediately. What is the gain or less to Chloe by
prepaying the loan? Ignore any transaction costs.
Problem 4.3.
In the previous problem, Chloe will find the cash rebate on prepaying the
mortgage advantageous provided the current interest rate is sufficiently low. At what current
interest rate will Chloe be indifferent between accepting the prepayment offer and continuing
with the current loan?
Problem 4.4.
A stock will pay its first dividend of
0.25 after two years. The next dividend
will be
1.5 three years from today. After that annual dividends will increase at 6% a year
forever.
What is the price of the stock?
Investors require a return of 12% a year on the
stock.
5
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