Assignment #1_Spring24_Solutions

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Corporate Finance (BFIN 2036) Spring 2024 Problem Set #1 Solutions Classes 1-3: Analytical Problems Format: Turn in hard copy of Answers at beginning of Class #4 on 07-Feb-2024 . Special Instructions: This is an individual assignment meant to evaluate your understanding of concepts covered in the course. You are not to seek help from others (whether or not they are enrolled in this course); nor offer help to others. Content: • This 9-question, 100-point problem set (plus one extra credit question) in conjunction with the text and class discussion Assignment: This is the first of two problem sets for Corporate Finance. Your goal in working through these problems is threefold: 1. Ensure understanding of the topics covered so far this semester 2. Application of analytical skills to problems that may be stated in unfamiliar ways 3. Preparation for the Mid-Term and Final Exams You can solve these problems with a calculator or spreadsheets, but depending on the then-prevailing University status, the exams may be calculator-only. You should have facility with the solution process unaided by spreadsheets and their accompanying built-in formulas. Write directly on the sheets and show your work. Feel free to attach additional sheets if you like. Please print out single-sided .

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 1 Problem Set #1 Name: Answer Key

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 2 #1 Relationship Between Net Income and Retained Earnings (8 points) Given the following data about Regal Corporation: A. Develop an Income Statement. B. By how much will Retained Earnings in the Equity section of the Balance Sheet increase or decrease? Costs 146,940 Change in fixed assets 36,300 Other expenses 8,400 Depreciation expense 10,200 Sales 237,000 Interest expense 12,300 Taxes 21% Dividends 14,500 Income Statement Sales 237,000 $ Costs 146,940 Depreciation expense 10,200 Other expenses 8,400 EBIT 71,460 $ Interest expense 12,300 IBT 59,160 $ Taxes 12,424 Net income 46,736 $ Net income 46,736 $ Dividends 14,500 $ Addition to retained earnings 32,236 $

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 3 #2 A/R and Credit Policy (15 points) Calspect Corporation has annual sales of $37.0 million and all of its sales are credit sales, that is, all sales are made to customers who pay after receipt of an invoice following shipment. Calspect’s terms are “net 30 days ” and payments are made, on average, 1 6 days late. A. What are Calspect ’s A/R Days (DSO)? What is the average dollar investment in A/R? B. Calspect is seeking to accelerate its DSO by offering a discount for early payment. It offers to accept a 98.5% payment, 1.5% discount) if the invoice is paid in 10 days from shipment. Following the offer, 30% of the customers pay in 10 days and take the discount; while the other 70% pay as before. a. What is the new average investment in A/R? b. What is the new DSO? c. How much annual profit is Calspect foregoing? = $37,000,000 – ($25,900,000 + 10,933,500) = Foregone Profit = $166,500 d. If Calspect finances its A/R with 100% debt, and the interest rate is 8.3%, does offering the discount make financial sense? Investment Differential 1,099,356.16 $ Interest Savings = 91,246.56 $ 8.3% Foregone Profit = 166,500.00 $ Net position (75,253.44) $ Therefore, NO Net Terms 30 Average days past due 16 Annual credit Sales 37,000,000 $ DSO 46.00 Receivables turnover 7.9348 x Current Receivables Investment 4,663,013.70 $ New Days 46.00 10 Total New A/R 25,900,000 10,933,500 Turnover 7.9348 36.5000 A/R 3,264,109.59 $ 299,547.95 $ 3,563,658 $ New Investment in A/R New Days 46.00 10 Total New A/R 25,900,000 10,933,500 Turnover 7.9348 36.5000 A/R 3,264,109.59 $ 299,547.95 $ 3,563,658 $ New Investment in A/R 35.155 New DSO

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 4 #3 Assessing Leverage and Returns (8 points) There are two firms whose performance is summarized below: D =Debt TA=Total Assets ROA=Return on Assets A. What is the ROE (Return on Equity) of each firm, assuming that Debt + Equity = Total Assets? B. To what level (to the nearest whole percent) must the Firm B “D/TA” rise or fall for Firm B to earn the same ROE as Firm A? Firm A D/TA 14% ROA 9.25% Firm B D/TA 43% ROA 7.21% Firm A ROE (NI / Total Assets) ÷ (1-Percentage Debt) = NI ÷ Equity Firm B ROE (NI / Total Assets) ÷ (1-Percentage Debt) = NI ÷ Equity Firm A ROE 10.76% Firm B ROE 12.65% If Firm A ROE = 10.76% then (1-Percentage Debt) =(NI / Total Assets) ÷ (NI ÷ Equity) and Percentage Debt = 1 - [(Firm B ROA) ÷ (Firm A ROE)] so 33% or the new Firm B D/TA required to earn an ROE equal to Firm A

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 5 #4 Calculating Cash Flows (12 points) Balance Sheet 2023 2024 2023 2024 Assets Liabilities and equity Cash 58 $ 31 $ Current liabilities 56 $ 106 $ Other current assets 222 259 Long-term debt 102 112 Net fixed assets 236 198 Stockholder's equity 358 270 Total assets 516 $ 488 $ Total liabilities and equity 516 $ 488 $ Income Statement 2023 2024 Revenue 557 $ 573 $ Expenses 371 375 Depreciation 75 81 Net income 111 $ 117 $ Dividends 40 $ 35 $ Given this simplified set of financial statements, calculate the following: --Cash Flow from Operations Operations Net income 117 $ Depreciation 81 Change in other current assets (37) Accounts payable 50 Total cash flow from operations 211 $ --Cash Flow from Investing Activities Investing activities Acquisition of fixed assets (43) $ Total cash flow from investing activities (43) $ --Cash Flow from Financing Activities Financing activities Proceeds of long-term debt 10 Issuance of Equity (170) Dividends (35) Total cash flow from financing activities (195) $ --Calculated Change in Cash (Sum of prior three totals) (27) $ --Actual Balance Sheet Change in Cash from 2023 to 2024 → $31 - 58 = $(27)

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 6 Change in cash (on balance sheet) (27) $

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 7 #5 Option Pricing (10 points) An associate has re-typed the quotes for options of Zazoo Corporation and left this on your desk. You look it over, and then are able to answer the following questions. a) Are the call options “in the money” or “out of the money”? What is the intrinsic value (i.e., value realizable today) of one of these call options? • Call Options are “ Out of the Money” since the exercise price is above the realizable market price. • Intrinsic Value is $ 0; but they may still have “time value.” b) Are the put options “in the money” or “out of the money”? What is the intrinsic value (i.e., value realizable today) of one of these put options? • Put Options are “ In the Money” since the exercise price is a above the realizable market price. • Intrinsic value is $4.50; Buy the shares in the open market for $78 and then exercise the Put Option for $82.50 c) You suspect that there are typos in the table above since two of the options are clearly mispriced. Which ones are mispriced and why? The April Put and the December Call are mispriced. • The April Put is mispriced because it is selling for less than its intrinsic value. You could buy the April Put for $3.80, exercise it by paying $78 for the stock in the open market and then putting the share to the put seller for $82.50, grossing $4.50 and giving rise to a risk-free profit of $0.70. • The December Call is priced below the October Call. One could buy the December Call for $2.05 and simultaneously sell the October Call for $2.35 today, pocketing $0.30 and having no exposure to the underlying stock, being able to exactly offset the short position in the October stock with the long position in the December stock. Calls Puts ZZOO Quote Strike Price Expiration Volume Last Volume Last 78.00 82.50 Apr 230 0.70 160 3.80 78.00 82.50 Jul 170 1.00 127 4.95 78.00 82.50 Oct 139 2.35 43 5.19 78.00 82.50 Dec 60 2.05 11 6.03 Option Calls Puts ZZOO Quote Strike Price Expiration Volume Last Volume Last 78.00 82.50 Apr 230 0.70 160 3.80 78.00 82.50 Jul 170 1.00 127 4.95 78.00 82.50 Oct 139 2.35 43 5.19 78.00 82.50 Dec 60 2.05 11 6.03 Option

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 8 #6 Decision Tree (8 points) Latoya Taylor was a creative person. Her friends were always telling her that her product ideas were great and that she should try to actually produce them. One wintry weekend, she came up with an idea she dubbed “Bouncy Pen,” a pen that, when tossed on the table, bounced back (with some practice) to the writer’s hand. Determined that this was likely to be a big hit among students, she made scores of inquiries with novelty manufacturers to gauge their interest. Finally, UServe Industries saw her demonstration with a mock-up of Bouncy Pen at a new products expo. Because several other firms seemed interested, UServe offered to buy the idea on the spot from Latoya for either $35,000 up front or 15% of the profits. Once it acquired the rights from Latoya, UServe had to make several decisions. • First, was the idea itself any good? There is a 90% chance that the Userve marketing staff would decide that this was a bad product idea. (Naturally, if UServe decides it’s a bad idea, they will never manufacture it and there will be no profits.) • Next, UServe must decide whether they have the capital to add a new product line. Since UServe has been on shaky ground lately, there is 3 5% chance they wouldn’t manufacture Bouncy Pen even if it were deemed a good idea. • Finally, if UServe produces the pen, there is a 40% chance that it will be a hit with consumers and produce cash flows with a present value of $8.0 million. If it isn’t a consumer favorite (if it doesn’t sell well), there will be no profit (PV =0). A. Should Latoya take the $35,000 up front or 15% of profits? (Build a decision tree to help you to decide.) B. Does your answer change if you are subsequently told that Latoya is already fabulously wealthy? Probably. Latoya would be in no immediate need of the $35,000 and she might attribute option value to the project in addition to the NPV shown above. We have no means of quantifying the option (not enough information provided), but she might imply some time and volatility to UServe’s deliberations that would translate into option value that could significantly exceed the relatively small value difference shown between the two choices. Value if idea is good and there is a big following 2,080,000 $ Value if idea is good, it is produced, and there is a big following 208,000 $ 15% of profits if idea is good, there is a big audience, and the idea is good 31,200 $ Big Following 40% 8,000,000 $ 65% Product Sells 10% Make product Idea is good Product Bombs Investigate Idea 35% 60% Small following Don't Produce No profit Idea is bad No profit 90% Don't Produce No profit The inventor should take the cash upfront.

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 9 #7 Cash Management (12 points) You are assessing whether to use a lockbox system to accelerate your cash availability. With a lockbox, a bank assumes all the effort of receiving and posting the payments. The best offer from your banks is to process each transaction for $0.55/transaction plus an annual fixed fee of $25,000. You receive 220 payments per day (assume 365 business days per year) and the average payment is $2,750. Finally, you can earn a return on cash balances of 2% per year, or 0.0055% per day. By using the lockbox, you will have your payments credited to your bank account 5 days sooner. A. How much would you have to pay to the bank every year to use their lockbox system? B. How much would you increase your daily cash balances as a result of the lockbox? (Hint: DaysSaved x #DailyPayments x PaymentSize) C. What incremental interest income would you earn each year by using the lockbox? D. Does the lockbox proposal make sense? Why or why not? Since the interest income (Answer C) on the higher available cash balances is slightly below the amount paid to the bank (Answer A) for the lockbox system, the proposal seems unattractive. In fact, however, the bank proposal might still have made sense since certain other costs not accounted for in this analysis, like staff time to open and post payments, can now be saved since they are borne by the lockbox bank. 69,165.00 $ = Fixed Fee + (# Daily Payments * Days per year * Variable Fee) 3,025,000.00 $ = (Decrease in Payment Days * Avg. Pmt Value * # Daily Pmts) 60,500.00 $ = (Increased Daily Cash Balance * Daily Interest Rate *Days per Year)

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 10 #8 Call Option Pricing with Black Scholes (12 points) You are offered a call option to purchase stock at $58/share. The underlying shares are currently trading at $56/share. The risk-free rate of interest is 1.75%. The option matures in 6 months (0.50 years) and the standard deviation (σ) is 48%. (Recall that variance is standard deviation squared.) • What is the intrinsic value, if any, of this call option? • What is this option worth to you (i.e., what is its total value)? Intrinsic Value: $0.00 (Max of 0, $56.00 - $58.00) Total Option Value: Input Area: Current stock price 56 $ Exercise price 58 $ Risk-free rate 1.75% Expiration (months) 6 Standard deviation 48% Output Area: d 1 0.0921 d 2 (0.2473) N(d 1 ) 0.5367 N(d 2 ) 0.4023 Call 6.92 $ Input Area: Current stock price 56 (Cell E7) Exercise price 58 (Cell E8) Risk-free rate 1.75% (Cell E9) Expiration (months) 6 (Cell E10) Standard deviation 48% (Cell E11) Output Area: d 1 =((((LN($E$7/$E$8))+(($E$9+(POWER($E$11,2)/2))*($E$10/12))))/($E$11*SQRT(($E$10/12)))) d 2 =$E$17-$E$11*SQRT($E$10/12) N(d 1 ) =NORMSDIST(I17) N(d 2 ) =NORMSDIST(I18) Call =($E$7*$E$19)-(($E$8*EXP(-$E$9*($E$10/12))*$E$20))

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 11 #9 Capital Needs (15 points) PowerApp Corporation, a high-performance battery manufacturer, is experiencing strong growth in 2023 and is anticipating revenue growth in 2024 of 17%. Here is the 2023 financial picture: A. Develop an Income Statement for 2024. Assume that Pre-Tax Income Margin % remains the same as in 2023. Memo: Growth rate for Next Year 17% Income Statement Sales 62,807,000 $ Costs 60,180,000 Taxable income 2,627,000 $ Taxes 551,670 21% Net income 2,075,330 $ Memo: Dividends 1,405,500 $ Addition to retained earnings 669,830 Balance Sheet Assets Liabilities & Equity Current assets 7,200,000 $ Short-term debt 1,800,000 $ Fixed assets 15,300,000 Long-term debt 4,300,000 Common stock 1,300,000 $ Accumulated retained earnings 15,100,000 Total equity 16,400,000 $ External Funding Needed - $ Total assets 22,500,000 $ Total L&E 22,500,000 $ Income Statement Sales 73,484,190 $ Costs 70,410,600 Taxable income 3,073,590 $ Taxes 645,454 Net income 2,428,136 $

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 12 B. Create a 2024 Balance Sheet with the following constraints: Assets-to-Sales ratio is same as 2023; Long-Term, Short-Term Debt, and dividends are unchanged at current dollar amounts. What is the amount of external funding required to support the 2024 operations? C. Management has just made an initial estimate that their plant (net Fixed Assets) has the capacity to support up to $75 million in sales without additions from the 2023 level. What is the new external funding required in 2024 now? D. On further review, management finally determines that plant additions of $1.2 million are required if Revenue equals or exceeds $65 million; and more additions are required for every increment of $4 million in Revenue over $65 million. (This means that no new Fixed Assets are needed for Revenue below $65 million; $1.2 million in additions are needed for Revenue of $65 million to $69 million; $2.4 million for $69 to $73 million in Revenue; and so on.) They have also decided to suspend (not pay) the dividend in 2024. All the other assumptions remain as in Part B above. What is the 2024 external financing need now? Balance Sheet Assets Liabilities & Equity Current assets 8,424,000 $ Short-term debt 1,800,000 $ Fixed assets 17,901,000 $ Long-term debt 4,300,000 Common stock 1,300,000 $ Accumulated retained earnings 16,122,636 Total equity 17,422,636 $ External Funding Needed 2,802,364 $ Total assets 26,325,000 $ Total L&E 26,325,000 $ Balance Sheet Assets Liabilities & Equity Current assets 8,424,000 $ Short-term debt 1,800,000 $ Fixed assets 15,300,000 $ Long-term debt 4,300,000 Common stock 1,300,000 $ Accumulated retained earnings 16,122,636 Total equity 17,422,636 $ External Funding Needed 201,364 $ Total assets 23,724,000 $ Total L&E 23,724,000 $ Balance Sheet Assets Liabilities & Equity Current assets 8,424,000 $ Short-term debt 1,800,000 $ Fixed assets 18,900,000 $ Long-term debt 4,300,000 Common stock 1,300,000 $ Accumulated retained earnings 17,528,136 Total equity 18,828,136 $ External Funding Needed 2,395,864 $ Total assets 27,324,000 $ Total L&E 27,324,000 $

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 13 #10 Extra Credit (5 points) Your pharmaceutical distribution company, Apex Drug, is bidding for a start-up drug company that has patents covering a new drug therapy for colitis. Your finance team has looked at the company, which has no revenue (the drug is still in FDA trials and is not yet approved for sale). They have estimated future sales, investment, profits, and cash flow. They then determined that the likelihood of realizing these cash flows was low (no certainty of FDA approval) and calculated a risk-adjusted Net Present Value of $30 million. That means that you could bid up to $30 million; any bid higher than that would destroy shareholder value, according to the Apex Discounted Cash Flow model. When you relay this conclusion to your investment banker, she is startled. “Other bids are coming in over $100 million! Your bid is far too low. You have no chance of winning.” You know that the other bidders have essentially similar operating models (potential synergies) and financial characteristics (discount rates, capital structures, etc.). In the end, you submit a bid for $30 million, and quickly learn that the start-up was sold for $150 million to one of your closest rivals, Low Country Pharmaceutical. You know that the management at Low Country is rational and analytical; and they have a reputation for being conscientious stewards of corporate resources. What possible explanation might there be for Low Country’s seemingly outrageous bid? (Note: Answer must be 150 words or fewer.) We are assured that Low Country is not an irrational actor making an emotional investing decision that ignores its own financial analysis. An NPV analysis of the start-up would surely give a low value because the risks are so high and the likelihood of achieving positive cash is so low. But Low Country probably took an additional step: Looking at the start-up as a real option on a very large payoff. This option has considerable value since the therapy market for this disease is large and potentially profitable. The option today is fa r “out of the money” since there isn’t even a product. But there is a high potential payoff, the amount of the payoff is volatile, and there is still considerable time before the actual outcome is known. Each of these elements can contribute to “option value” in a way that the bidders other than Acme appreciated. (This is not to say that companies do not consistently over pay for acquisitions. Two-thirds of acquisitions are failures, mostly because the price offered is too high. And management is treading on thin ice when it says that it paid more than anyone else because of “unquantifiable strategic benefits.” If, however, management can make an honest and rigorous option value assessment, it may reasonably pay more than the outcome of the DCF might otherwise indicate.)