number 6 attached below , there is also the solution at the end..but just to explain to me how to do this type of problems for the exam

thanks

CORPORATE FINANCE AND FINANCIAL INSTITUTIONS II part REVIEW QUESTIONS & SOLUTION GUIDELINES Problem 1 What are the CFFA, the OCF, the cash flow to creditors and the cash flow to shareholders for company Alfa? Problem 2 Using 2009 data from Question 1 derive the Du Pont Identity. Problem 3 Using the data from Question 1 calculate the days' sales in receivables, the ones in inventory and the ones in payables. Problem 4 You've got only the income statement of Q1. You know that days' sales in receivables are 20, in inventory 40 and in payables 30. Calculate the final value of Accounts receivable, Inventory and Accounts payable. 1 Problem 5 Assuming the revenues will grow up 10% and the company operates at full capacity calculate the pro forma IS and BS assuming the plug variable is dividends. How many dividends will the company pay? Problem 6 Assuming the revenues will grow up 10%, the company operates at full capacity, the payout ratio will be 50%, the accounts payable are the only spontaneous liabilities, calculate the pro forma IS and BS assuming the plug variable is long term debt. Problem 7 Assets = 2000 Sales = 2500 Net income = 150 Spontaneous Liabilities = 300 Sales are expected to increase by 20% Pay-out ratio = 40% Calculate the external financing needed. Problem 8 Company Alfa has the following figures: Assets = 2000; Sales = 2500; NI = 150; Equity = 800; Pay-out ratio = 40%. Determine the current Sustainable growth rate. If the desired growth rate is 17%, how much should be the profit margin? Is it a reasonable number? 2 Problem 9 You have 100000 and you want to buy an apartment in four years. The expected cost will be 125000. What interest rate must be earned to be able to buy the apartment? Problem 10 The stated annual rate is 4%, compounded quarterly. What is the Effective Annual Rate? Problem 11 You own a land where next year cash flow is 5000. You expect the cash flows increase 2% per year. You receive an offer to buy the land at 100000. The relevant interest rate is 6%. Should you accept to sell the land at 100000? Problem 12 You save 5000 euro per year and invest them in a pension scheme. You expect to earn an annual net return of 5% for 35 years. How much will you have when you retire? Problem 13 Morena's Driving School's 2011 statement of financial position showed non-current assets of 4.4 million. One year later, the 2012 statement of financial position showed non-current assets of 4.74 million. The company's 2012 income statement showed a depreciation expense of 637,000. What was Morena's net capital spending for 2012? Problem 14 A firm has net revenues of 6,815 million (including net non-cash expenses). Net non-cash expenses (including depreciation) were 2,415 million. Cash outflows from investing activities (including capital expenditures) were 2,400 million. The firm paid a total cash dividend of 1,480 million and net interest expense was 3,560 million. What was the firm's net cash flow? Problem 15 A bond has these features: Face Value=100; annual coupon=4%, coupon frequency= semi-annual; yield-to-maturity=6%; Maturity=5 years. Calculate the current value of this bond. Problem 16 A bond has these features: Face Value=100; annual coupon=3%, coupon frequency= annual; current price=98; Maturity=3 years. Choose the right YTM among the following ones: 3.55%, 3.71%; 3.92%; 4.03%. Problem 17 Consider a stock with the following features: Div1=5; Div2=5.5, then, dividends will grow at 2% per annum. The required return is 9%. What is the stock price at time zero? Problem 18 Stock A. Price = 10; Next year's Expected dividend = 0.7; required return = 11%. Stock B. Price = 16; Next year's Expected dividend = 0.6; required return = 9%. Which stock has the higher upside potential for its dividend? 3 Problem 19 Stock A: Current Price = 6; next year dividend = 0.5; dividend growth rate = 2.2%. Stock B: Current Price = 8; next year dividend = 0.45; dividend growth rate = 2.3%. If the stocks have got the same risk, which do you buy (and why). Would your choice change if B were riskier than A? Problem 20 A company has Net Income = 40, Assets = 300, Debt 140. It plans to pay 40% of earnings. How much will earnings grow over the coming year? If the company wants the earnings grow at 10% per year how much should be the payout ratio? Problem 21 N share outstanding = 200,000; Earnings = 1,000,000; Required return = 8% The next year the company invests 1,000,000, projecting to increase earnings by 90,000 each year. Calculate the fair price for the stock. Problem 22 Why and when the payback period and the average accounting return should be used in practice? Problem 23 What are the decision rules for accepting an investment under the IRR approach? Problem 24 You are considering the following two mutually exclusive projects. The Required rate of return is 12% for A and 14% for B. Calculate the Profitability index for the projects and decide what you should undertake. A CF time 0 = - 70 CF time 1 = 25 CF time 2 = 31 CF time 3 = 38 B CF time 0 = - 85 CF time 1 = 15 CF time 2 = 20 CF time 3 = 90 Problem 25 Exercise plc has the following mutually exclusive projects. Year Project A () Project B () 0 -28,000 -13,100 1 7,980 9,825 2 11,200 4,780 3 15,960 395 Suppose Exercise's payback period cut-off is 2 years. Which of these two projects should be chosen? Calculate the NPV of both the projects. Assume the discount rate is 12 per cent. Suppose Excercise uses the NPV rule to rank these two projects. Which project should be chosen? 4 Problem 26 ABC company operates in the US market. Comparables companies have an average beta of 0.8. ABC has a market capitalization of equity of 11.93 billion and it has no debt. Determine the expected return on the ABC's shares if the expected return on the FTSE 100 is 12 per cent and the risk free rate is 3 per cent. Problem 27 You are analysing two mutually exclusive projects with the following cash flows: T 0 1 2 3 4 Project 1 -$4,000,000 $2,000,000 $1,500,000 $1,250,000 $1,000,000 Project 2 $-4,000,000 $1,000,000 $1,500,000 $1,700,000 $2,400,000 a. Estimate the NPV of each project assuming a cost of capital of 10%. Which is the best project? b. Estimate the IRR for each project. What is the better project? Problem 28.a You have to pick between 3 mutually exclusive projects with the following cash flows: T A B C 0 -$10,000 $5,000 -$15,000 1 $8,000 $5,000 $10,000 2 $7,000 -$8,000 $10,000 The cost of capital is 12%. a. What project would you pick using the NPV rule? b. Which project would you pick using the IRR rule? c. How would you explain the differences between the two results? Problem 28.b Barring the case of multiple IRRs, is it possible for the NPV of a project to be positive while the IRR is less than the discount rate? Explain. Problem 29 You know a company has a ratio D/E = 0.8 and the beta equity is 1.1. Calculate the beta asset. If the financial structure change and D/E = 1.2, how much will be beta asset and beta equity? Problem 30 A company has a D/E ratio of 0.5, the cost of debt of 12%, the cost of equity of 15%, the corporate tax rate of 32%. The company is considering taking an investment costing 30 mln that is expected to generate cost savings of 7 mln for the next 7 years. Should the company undertake the project? 5 Problem 31 The ABC company's equity has a beta of 1.3. If the risk free rate is 4.5% and the expected return on the market is 12%, what is its cost of equity capital? Problem 32 The XYZ firm has a market value of equity of 15.77 billion and total debt of 1.21 billion. The cost of equity capital is 19.96% and the cost of debt is 5%. If the company has a marginal tax rate of 24%, what is its WACC? Problem 33 A company has a target D/E ratio of 0.80. Its WACC is 10.5% and the tax rate is 35%. a. If the cost of equity is 15%, what is the pre-tax cost of debt? b. If instead the after tax cost of debt is 6.4%, what is the cost of equity? 6 SOLUTION GUIDELINES Problem 1 EBIT = 140000 EBITDA = 190000 Operating Cash Flow = 190000 - Taxes = 150100 NWC0 = 9000 ; NWC1 = 7000 Change in NWC = - 2000 NCS = 190000 - 170000 + 50000 + 5000 ( \"-\" if gains) = 75000 CFFA = 150100 - (-2000) - 75000 = 77100 Cash Flow to creditors (+ = net inflow, - = net outflow) = 30000 - 25000 - 2000 = +3000 Cash Flow to shareholders (+ = net inflow, - = net outflow) = (42000 - 40000) - (93100 - 125000 - 114000) = - 80100 Problem 2 DU Pont Identity = 0.1825 x 2.0238 x 1.509 = 0.5575 Problem 3 Days' sales in receivables = 22000/510000 x 365 = 15.75 Days in inventories = 29000/180000 x 365 = 58.81 Days in payables = 43000/(180000 + 140000) x 365 = 49.05 Problem 4 Accounts receivable = 20/365 x 510000 = 27945 Inventory = 40/365 x 180000 = 19726 Accounts payable = 30/365 x (180000 + 140000) = 26301 Problem 5 7 Change in RE = 8000 Dividends = 41910 - 8000 = 33910 Problem 6 Dividends = 0.5 x 41910 = 20955 New Retained Earnings = 80000 + 20955 = 100955 8 Problem 7 (2000/2500 - 300/2500) x 2500 x 0.2 - 150/2500 x 2500 x (1 + 0.2) x (1 - 0.4) = 232 Problem 8 ROE = 150/800 = 18.75% SGR = 18.75x(1 - 0.4) / (1 - 18.75 x (1 - 0.4)) = 12.68% The ROE must be = 0.17/((1+0.17) x (1-0.4)) = 24.22% ROE = PM x TAT x EM = 24.22% PM = 0.2422/( TAT x EM ) = 0.2422 / ((2500/2000) x (2000/800)) = 7.75% The current PM is 6%, so ...... Problem 9 100000 x (1 + r)4 = 125000 r = (125000/100000)1/4 - 1 = 5.74% Problem 10 EAR = (1 + 0.04/4)4 - 1 = 4.06% Probelm 11 9 5000/(0.06 - 0.02) = 125000 So you should ...... Problem 12 1 (1 0.05) 35 Future value = 5000 x (1 + 0.05) x = 5000 x 5.516 x 16.374 = 451601 0.05 35 Problem 13 Net capital spending = NCAend- NCAbeg + Depreciation Morena's Driving School Year million Non-current assets 2011 4.4 Non-current assets 2012 4.74 Net non-current assets Add: Depreciation 0.34 0.637 Net capital spending 0.977 Problem 14 Net cash flow 1,790 Statement of Cash Flow Net Revenues Net Non-Cash Expenses Cash Flow From Activities Cash Flow From Activities Dividends Interest Cash Flow From Activities Net Cash Flow million 6,815 2,415 Operating million 9,230 Investing -2,400 -1,480 -3,560 Financing -5,040 1,790 Problem 15 First step. Calculate the value of the annuity. Find the stated annual rate = ((1 + 0.06)1/2 - 1) x 2 = 5.91% 10 Annuity = 1 (1 0.0591/2) 2*5 = 8.55 0.0591/2 Second step. Present value of coupons = 2 x 8.55 = 17.10 Third step. Present value of face value 100 x (1 + 0.06)-5 = 74.73 Fourth step. Present value of bond = 74.73 + 17.10 = 91.82 Problem 16 98 = 3 3 103 1 2 (1 YtM ) (1 YtM ) (1 YtM ) 3 When YtM is 3.55% price = 98.46 When YtM is 3.71% price = 98.02 When YtM is 3.92% price = 97.44 When YtM is 4.03% price = 97.14 3.71% is the correct YtM. Problem 17 First step 5 5.5 4.59 + 4.53 = 9.22 1 0.09 (1 0.09) 2 Second step 5.5 * (1 0.02) P2 = = 78.57 0.09 0.02 Third step Price = 9.22 + 78.57/(1+0.09)2 = 9.22 + 66.13 = 75.35 Problem 18 Rearranging the DGM formula g = R - D1/P0 A: g = 0.11 - 0.7/10 = 4% 11 B: g = 0.09 - 0.6/16 = 5.25% B is the stock with higher potential for dividends. Problem 19 Rearranging the DGM formula: R = D1/P0 + g R (A) = 0.5/6 + 0.022 = 10.53% R(B) = 0.45/8 + 0.023 = 7.95% Since they have the same risk one should prefer A. The choice is the same if B is riskier. If A is riskier one can't decide without further information. Problem 20 The company's equity is 160, and therefore ROE is 40/160 = 25%. The retention Ratio is 60%. G = 60% * 25% = 15%. If G = 10% the retention ratio must be = 10%/25% = 40%. Therefore the payout ratio must be 60%. Problem 21 We follow the NPVGO approach. EPS = 1,000,000 / 200,000 = 5. Price as a cash cow = EPS / 0.08 = 62.5 Value of the investment = - 1,000,000 + 90,000 / 0.08 = -1,000,000 + 1,125,000 = 125,000 It must be discounted to 0. NPVGO = 125,000 / 1.08 = 115,740 NPVGOPS = 115,740 / 200,000 = 0.58 New price = 62.5 + 0.58 = 63.08 Problem 22 Suggestion. (It must be further developed) Payback = small scale investments AAR = because investors, media and shareholders pay attention to accounting figures and to the overall profitability of the company 12 Problem 23 Suggestion. (It must be further developed) Usually Required return IRR Problem 24 PV of cash flows after initial investment for A = 22.32 + 24.713 + 27.047 = 74.08. PI = 1.058 PV of cash flows after initial investment for B = 13.158 + 15.389 + 6.747 = 89.29. PI = 1.050 B has a smaller PI but this methods doesn't work for mutually exclusive projects. In fact, NPV A = 4.08, whereas NPV B = 4,29. Therefore you should undertake B. Problem 25 a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. PROJECT A: Cumulative cash flows Year 1 = 7,980 = 7,980 Cumulative cash flows Year 2 = 7,980 +11,200 = 19,180 Cumulative cash flows Year 3 = 7,980 + 11,200 + 15,960 = 35,140 > 28,000 PROJECT B Cumulative cash flows Year 1 = 9,825 = 9,825 Cumulative cash flows Year 2 = 9,825 + 4,780 = 14,605 > 13,100 The payback period is less than the 2 year cut-off and so project B would be accepted. Companies can calculate a more precise value using fractional years. To calculate the fractional payback period, find the fraction of year 2's cash flows that is needed for the company to have cumulative undiscounted cash flows of 13,100. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cash flow of year 2. b. Discount each project's cash flows at 12 per cent. Choose the project with the highest NPV. NPV (A)= -586.42 NPV (B) = NPV = -235.94 The firm should choose neither project since both have negative NPVs Problem 26 Expected Return on Shares: R = RF + * (R - RF) = 0.03 + 0.8*(0.12 - 0.03). Problem 27 a. The NPV for Project 1 is $680,008 while for Project B is $ 1,065,228. b. The IRR of Project 1 is 18.71% while for project 2 is 20.19%. Project 2 is still better. 13 c. NPV assumes that you can reinvest at 10%; IRR assumes reinvestment at IRR. Problem 28.a a. B is the best project on a NPV basis b. A is the best project on a IRR basis. c. The reasons can be partially attributed to differences in scale, and difference in reinvestment rate assumptions. The strange pattern of cash flows on B also throws off the IRR rule. The IRR rule is devised with the idea that cash flows go from negative to positive, not the other way around. Problem 28.b Yes, when the CF is reversed....(you should explain carefully). See also exercise 28.a. Problem 29 D/E at 0.8 means these values for Enterprise value = 18; Debt = 8; Equity = 10. The Beta asset can be found as: 10/(10 + 8) * 1.1 = 0.61 The company under the new financial structure will be: Enterprise value = 22; Debt = 12; Equity = 10. If the financial structure changes there is no effect on beta asset. Whereas Beta equity = Beta asset * (B + S)/S = 0.61 * 22/10 = 1.34 Problem 30 Enterprise value = 15; Debt = 5 Equity = 10. WACC = 15%*10/(10+5) + 12*(1-0,32)*5(10 + 5) = 12.72% To calculate the present value of cost savings we use the Annuity of 7 years at 12.72% Annuity = 4.46 NPV = - 30 + 7*4.46 = + 1.23 The project should be undertaken. Problem 31 With the information given, we can find the cost of equity using the CAPM. The cost of equity is: 14 Re = .045 + 1.30 (.12 - .045) = .1425 or 14.25% Problem 32 Total Asset Value is (15.77 + 1.21) = 16.98 billion. This means that the weight of Debt is 0.07126 and the weight of equity is 0.92874. WACC = 0.07126(0.05)(1-.24) + 0.92874(.1996) = .1880 or 18.8% Problem 33 a. Using the equation to calculate WACC, we find: WACC = .105 = (1/1.8)(.15) + (.8/1.8)(1 - .35)Rd Rd = .0750 or 7.50% b. Using the equation to calculate WACC, we find: WACC = .105 = (1/1.8)Re + (.8/1.8)(.064) Re = .1378 or 13.78% 15