Commerce 370 – Midterm Exam – Sep-Dec-2011 – Solutions Name: ______________________________________________________ Student ID: __________________________________________________ Section (circle one): M-W 2:30pm ; Tu-Th 11:00am ; Tu-Th 2:00pm Write your name and student ID at the top of this front page, and circle your section. Check the number of pages in the exam. You should have X pages. This is a 100-point exam with 7 questions. You have 2 hours to complete the exam. Carefully administer your time! No books or notes are permitted. You may use a non-programmable calculator.
Only exams written in ink will be eligible for formal re-grading. Please answer the questions in the space provided after the question. Write your answers clearly and legibly. Show all details of your work. A formula sheet is provided in the last page, but be aware that the formulas given may or may not be useful to solve the questions in this exam. Do not use formulas without carefully thinking whether they are useful in a particular problem. GOOD LUCK! ______________________________________________________________________________ Instructor use only:
Problem 1 ( 8 points): Problem 2 (18 points): Problem 3 (18 points): Problem 4 (18 points): Problem 5 (15 points): Problem 6 (13 points): Problem 7 (10 points): Total (of 100 points): 1 Question 1 (8 points) Answer the following two independent multiple choice questions. Clearly circle your answer. a) (4 points) A firm’s customers are cash constrained and can borrow from the bank at 18% per year. Other things equal (e. g. , assuming no changes in sales), if the firm changes the terms of credit it offers to its customers from “1/15 net 40” to “2/10 net 50”, then the firm’s Accounts Receivable Period will _______________.
A. decrease B. increase C. either increase or decrease D. stay the same E. none of the above Answer: A. With “1/15 net 40”, EAR = (1 + 1/99)365/25 – 1 = 15. 8% < 18%. So, before the change in credit policy, customers forego the discount and pay on day 40, i. e. , borrow from the firm at 15. 8% instead of from the bank at 18%. The ARP is 40 days. With the new credit policy “2/10 net 50”, EAR = (1 + 2/98)365/40 – 1 = 20. 2% > 18%. So customers will take the discount and pay on day 10, i. e. , borrow from the bank at 18% instead of from the firm at 20. 2%.
The ARP will drop to 10 days. FYI: This is similar to the discussion in Lecture 3 (Clarkson Lumber case) on Clarkson’s cost of payables financing and change in APP as he starts taking the discounts for early payment. b) (4 points) Suppose that all the assumptions required in the derivation of the formulas for the internal and the sustainable growth rates listed in class are valid. Also assume that a firm’s sales will grow at the internal growth rate (gi) next year, that the firm will not raise any external financing next year, and that the firm’s retention ratio (R) will be unchanged.
In this case, the growth rate of the firm’s equity for next year (gE) is equal to ___________________. A. gi B. ROE x R x gi C. ROA x R x (1+ gi) D. NI x R x gi E. ROE x R x (1+gi) F. none of the above Answer: E. By definition of a growth rate gE = ? E/E. But the firm does not issue stock, so ? E = ? RE, and with the assumptions ? RE = NI x R x (1+ gi). Since ROE=NI/E, gE = ? RE/E = ROE x R x (1+ gi). FYI: This is from Lecture 2 and associated practice questions, where we wrote the addition to retained earnings as ? RE = NI ? r ? 1+g), and said equity grows with RE if no equity is issued. 2 Question 2 (18 points) Purdy’ CEO is considering the complete elimination of trade credit from the firm’s operations, and switching to an “all cash transactions policy”: the firm would not give any credit to its customers and it would not take any credit from its suppliers. Assume that Purdy’s inventory turnover and sales will not be affected by the change in trade credit policy. a) (6 points) Write an equation for the change in Purdy’s operating cycle as a result of the new policy and enclose it in a box.
Then carefully explain whether the operating cycle will become shorter or longer and why. Show all details of your work. b) (12 points) Write an equation for the change in Purdy’s cash cycle as a result of the new policy and enclose it in a box. Then carefully explain whether the cash cycle will become shorter or longer and why. Show all details of your work. Solution OC = IP + ARP and CC = IP + ARP – APP; let sub “0” denote before and sub “1” after. a) Chg in OC = OC1 – OC0 = IP1 + ARP1 – IP0 – ARP0 The average inventory turnover does not change, so the inventory period does not change, and so IP1 = IP0.
Also, if the firm ceases to give credit to customers, then ARP1=0. Thus: Chg in OC = IP0 – IP0 – ARP0 = – ARP0 Hence, the operating cycle will be unambiguously shorter by a number of days equal to the prior accounts receivable period. Note in passing that OC1 = IP0. b) Chg in CC = CC1 – CC0 = IP1 + ARP1 – APP1 – IP0 – ARP0 + APP0 But note that (i) IP1 = IP0 (inventory turnover does not change); (ii) ARP1=0 (firm ceases to give credit to customers); and iii) APP1 = 0 (the firm now always pays cash for its purchases).
So: Chg in CC = IP0 – IP0 – ARP0 + APP0 = APP0 – ARP0 Whether the cash cycle is shorter or longer is uncertain. Specifically, if APP0 < ARP0 it will be shorter if APP0 > ARP0 it will be longer if APP0 = ARP0 it will not change FYI: This is from Lecture 1 and associated practice questions, where we discussed how the OC and CC might change in various situations, and is similar to a question on the practice midterm. 3
Question 3 (18 points) Consider a firm whose balance sheet and income statement for 2011 are: Balance Sheet in year 2011 Current Assets (CA) Current Liabilities (CL) Cash Accounts Payable Accounts Receivable Accrued Expenses Inventories Other Short-Term Obligations Other Current Assets Long-Term Debt (LTD) Net PPE (NPPE) Common Stock (S) Retained Earnings (RE) Total Assets Total Liabilities & Equity Income Statement in year 2011 Sales (S) Costs (C) Earnings before interest and taxes (EBIT) Depreciation (Dep) Interest (I) Taxable Income (TI) Taxes (T) Net Income (NI) Dividends Paid (Div) Addition to Retained Earnings (?
RE) a) (12 points) Using the notation above, derive an expression for the change in the firm’s cash position between years 2010 and 2011 (? Cash). Enclose your final expression in a box. Carefully explain and show each of your steps. Answers with no formal derivation will be given no credit. b) (6 points) Suppose that during 2011 the firm raised $500 in a common stock issue, but it retired $400 of its debt outstanding. In addition, suppose that accounts receivable decreased by $100 between 2010 and 2011, while accrued expenses decreased by $150, other short-term obligations increased by $50, and the level of inventory fell by $200.
There were no other changes in any current liability or current asset items. Finally, net income was -$250, and depreciation was $50. What was the “Cash Flow from Operating Activities” in 2011 reported in the Statement of Cash Flows? Enclose your final answer in a box. Carefully explain your answer. 4 Solution a) From the balance sheet in year 2011 we get the following identity: Cash = LTD + S + RE + CL – CA (excl. cash) – NPPE Apply ? operator or subtract equation for Cash in 2010 from the equation for Cash in 2011 to get: ? Cash = ? LTD + ? S + ?
RE + ? CL – ? CA (excl. cash) – ? NPPE Note: ? RE = NI – Div = NI – Div + Dep – Dep = OCF – Div – Dep, where OCF = NI + Dep. So we get: ? Cash = ? LTD + ? S + ? CL – ? CA (excl. cash) – ? NPPE – Dep + OCF – Div Note: ? GPPE = ? NPPE + Dep So we get: ? Cash = ? LTD + ? S + ? CL – ? CA (excl. cash) – ? GPPE + OCF – Div b) CF from operating activities = OCF + ? CL – ? CA (excl. cash) = -$250 + $50 – $150 + $50 – (-$100 – $200) = -$250 + $50 -$150 + $50 +$100 + $200 = $0 Note: OCF=NI+Dep ; issuing / repurchasing equity does not affect the CF from Oper.
Activities FYI: This is from Lecture 1, where we derived the change in cash from the balance sheet and income statement, and then identified the CF from operating activities. Also from the associated practice questions which require the calculation of these things. The practice midterm contains a somewhat related question based on the equation for ? Cash. 5 Question 4 (18 points) Surf Vancouver, an all-equity financed producer of surfing equipment, achieved record sales in 2011. In early 2012, the firm is analyzing its growth strategy for the year 2012.
The income statement for 2011 and balance sheet for December 2011 are given below. Surf Vancouver Inc. Income Statement for 2011 Sales Costs Taxable Income Taxes Net Income Dividends $200,000 160,000 40,000 13,600 $26,400 $8,800 Surf Vancouver Inc. Balance Sheet at December 2011 Current Assets Cash Accounts receivable Inventory Sub-total Net PPE Total Assets 26,000 39,000 45,000 110,000 122,000 232,000 Current Liabilities Accounts payable Sub-total Stock Retained earnings Total Equity Total Liabilities and Equity 52,000 52,000 120,000 60,000 180,000 232,000 ) (6 points) The firm plans to increase its annual sales by 20% in 2012, with no changes in its dividend payout ratio or the management of its current assets and current liabilities with respect to 2011. The firm operated at full capacity in 2011 and its fixed assets do not depreciate. What is firm’s external financing need in 2012? Enclose the number in a box. Carefully explain. b) (12 points) Assume now that the firm cannot issue any debt in 2012, but it can issue $5,000 in new common stock. The firm has to maintain its dividend payout ratio and will not change the management of its current assets and current liabilities.
The firm operated at full capacity in 2011 and its fixed assets do not depreciate. What is the maximum growth rate (gM) the firm can achieve in 2012? Enclose the number in a box. Carefully explain. 6 Solution a) Surf Vancouver Inc. Pro-Forma Income Statement for 2012 Sales Costs Taxable Income Taxes Net Income Dividends Addition to Retained Earnings: 31,680 – 10,560 = 21,120. Surf Vancouver Inc. Pro-Forma Balance Sheet at December 2012 Current Assets Cash Accounts receivable Inventory Sub-total Net PPE Total Assets $ Chg.
Current Liabilities 31,200 5,200 Accounts payable 46,800 7,800 Sub-total 54,000 9,000 132,000 22,000 Stock 146,400 24,400 Retained earnings Total Equity 278,400 46,400 Total Liab. + Equity $ Chg. 62,400 10,400 62,400 10,400 120,000 0 81,120 21,120 201,120 21,120 263,520 31,520 240,000 192,000 48,000 16,320 31,680 10,560 EFN = 46,400-31,520 = 14,880 Alternatively, a very short way to do it is to realize that in this case everything grows at 20%: EFN = growth in assets – addition to RE – increase in AP EFN = 232,000 x . 2 – (26,400 – 8,800) x 1. 2 – 52,000 x . 2 = 14,880 b) Let g be the growth rate.
Assume dividend policy stays at R=2/3. You can raise $5,000 in new equity, but cannot borrow, and AP grow with sales. EFN = growth in assets – addition to retained earnings – increase to AP = Assets2011 x g – (2/3) x NI2011 x (1+g) – AP2011 x g To figure out the maximum growth rate that the firm can achieve with internal funds and some equity issuance, fix the EFN=5,000 and solve for gM. 232,000 x gM – (2/3) x 26,400 x (1+gM) -52,000 x gM = 5,000 232,000 x gM – (2/3) x 26,400 x gM – 52,000 x gM = (2/3) x 26,400 + 5,000 162,400 x gM = 22,600, solving yields gM = 13. 9% < 20%. 7
FYI: This is from Lecture 2 and its practice questions, where we calculated EFN using pro-forma BS and IS, and discussed how the amount of external financing you can raise determines the maximum growth rate possible. Note also that part b) is similar to what we did in class to derive gi. The question is also similar to that in the practice midterm. Question 5 (15 points) Almar Corp. is planning its sales growth for next year. The COO explains he wants to increase sales by 10% next year, a rate which, given the firm’s dividend payout of 1/3 of net income and current return on assets, is below its internal growth rate.
The CFO cautions that the firm is currently at its target (book) debt-to-equity ratio and that it should maintain this ratio next year. Discuss a possible financial strategy to minimize the change in the debt-to-equity ratio next year, while growing at 10% and keeping the same dividend payout ratio. Carefully justify your answer. Solution Since the COO wants to grow at less than the internal growth rate, the firm can fund all the growth with internal funds and it will still create a surplus of internal funds.
At the same time, the accumulation of retained earnings next year will increase stockholders’ equity (which is retained earnings plus common stock) and will thus reduce D/E, unless we do something to minimize this change. The most natural thing to do is to use the surplus funds to buy back some common stock, which will tend to neutralize the positive effect on stockholders’ equity associated with increased retained earnings. In addition, if this is not enough, then you could also issue some debt (which increases the numerator of the D/E) and use some of these funds to buy back more equity.
FYI: This is from Lecture 2 and associated practice questions, where we discussed the impact on the book D/E of different growth strategies and possible corrective measures. The practice midterm also contained a similar question. Question 6 (13 points) It is estimated that in 2012 a firm will have sales of $80 million, net income of -$50 million, interest payments of $10 million, dividend payments of $8 million, a capital cost allowance of $5 million, an increase in current assets of $6 million, an increase in current liabilities f $3 million, capital expenditures of $7 million, and it will issue $100 million in new debt. The firm’s tax rate is 40%. a) (9 points) What is the firm’s estimated Free Cash Flow (FCF) in 2012? Show your work. b) (4 points) What is the firm’s estimated Earnings Before Interest and Taxes (EBIT) in 2012? Show your work. 8 Solution a) FCF = (S – C) ? (1 – ? C ) + ? C ? CCA – ? NWC – CapEx , but need to start from NI, so must use: FCF = NI + Interest ? (1 – ? C ) + CCA – ? NWC – CapEx FCF = -50M + 10Mx(1-. 4) + 5M – [6M-3M] – 7M = -49M b) NI = (EBIT – Interest) ? 1 – ? C) , so -50M = (EBIT – 10M) x (1 – . 4) ; solving gives EBIT = -73. 33M FYI: This is from Lecture 5, which explains the different ways to recover the FCF from pro-forma financial statements, and the associated practice questions. The practice midterm also contained a similar question, where we recovered the FCF using the three approaches. Question 7 (10 points) Kohlberg, Kravis, and Roberts (KKR) is considering the acquisition of Sinux, a private company which reported earnings of $10 million in 2010.
Sinux operates in the chemical products industry, where there are two publicly traded firms of similar size. These are Telex, which has a market value of equity of $500 million and reported earnings of $8 million in 2010 and Rarex, which has a market value of equity of $600 million and reported earnings of $12 million in the same year. Provide KKR with a quick estimate of the market value of Sinux’s equity. Carefully explain.
Solution Use price-earnings (PE) ratios from similar publicly-traded firms to estimate the market value of Sinux’s equity, under the assumption that the stock market correctly prices existing public firms and that those firms are similar to Sinux. Specifically, let ES by Sinux’s equity value which we want to estimate. We could write its (unknown) PE ratio as: PES = ES / NIS = ES / 10M. So we get ES = PES x 10M. If we knew PES then we can estimate ES. We estimate PES as the average of the PEs of similar publicly-traded firms: Telex’s PE = 500M/8M = 62. and Rarex’s PE = 600M/12M = 50. The average PE of similar traded firms is 56. 25 and thus ES = 56. 25 x 10M = $562. 5M. Note: PE = equity value / NI = [equity value / #shrs] / [NI / $shrs] = share price / EPS. FYI: This comes from Lecture 1, where we discussed how to use the PE ratios of comparable firms in the valuation of private companies. 9 FORMULA SHEET Operating Cycle = Inventory Period + Accounts Receivable Period Cash Cycle = Operating Cycle – Accounts Payable Period EFN = Increase in assets – Addition to RE – Increase in AP ROA ?
R 1 ? ROA ? R ROE ? R 1 ? ROE ? R gi ? g* ? CAPM: E ? rS ? ? r f ? ? S ? E ? rM ? ? r f ? PV of Perpetuity ? C r PV of growing perpetuity ? C r? g ?1 ? ?r ? ? 1 Annuity Factor ? A(r , t ) ? ?1 ? ? (1 ? r )t ? The PV of the perpetual CCA tax shield adjusted for tax shields lost if the asset is sold in year n at a value of S is: CdTC [1 ? .5r] SdTC 1 ? ? PV of perpetual CCA tax shield ? ? ? r ? d ? (1 ? r) ? r ? d ? (1 ? r) n WACC = (E/V) ? rE + (P/V) ? rP + (D/V) ? rD ? (1-TC) Formulas for Z-score and O-score are not needed 10