Problem Set 1-2

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Stevens Institute Of Technology *

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CORPORATE

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Finance

Date

Feb 20, 2024

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pdf

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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