quiz3sol - Spring 1999 Problem 1 VS = AT Operating Margin *...

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Unformatted text preview: Spring 1999 Problem 1 VS = AT Operating Margin * (1­ Reinvestment Rate) * (1 + g)/(WACC ­ g) Reinvestment Rate = g / ROC = g / (AT Operating Margin * Sales/Capital) Let the margin for Generic Office be x, VS for Generic Office = 1.5 = x (1­.05/2x)(1.05)/(.10­.05) Solve for x, x = (1.5*.05+(.05/2)*1.05)/1.05 x = 9.64% HK's after­tax operating margin = 9.64% (1.05) = HK's VS ratio =.1013 (1­.05/2*.1013)(1.05)/(.10­.05) = 10.13% ! I also gave full credit if you added 5% to get 14.64% 1.6023 ! Note that if you do not adjust the reinvestment rate, you get 1.575. Problem 2 a. Value of Developed Reserves = 100,000 * (300­200) * (PV of Annuity, 5 years, 9%) = $38,896,513 b. Value of Undeveloped Reserves (on DCF basis) Value of oil in the ground = 40,000 * (300­200) * (PV of Annuity, 9%, 12.5 years) = ### ! 40000 barrels a year for 12.5 years Value of oil in the ground allowing for development lag = 29,309,311/1.08 = ### Fixed cost of development = ### DCF Value of Undeveloped reserves = ### I also gave full credit for a number of variations, including a. Assuming that costs and prices are in present value dollars, in which case the value of reserves is [500000*(300­200)]/1.08 = 46,296,296 c. Inputs for Option Pricing Model y = Annual Production Revenue/Reserves = 40,000/500,000 = 8.00% ! Many of you used 1/15. You actually lose more because your production potential is much higher. S = PV of reserves discounted back by development lag = $27,138,251 ! Full credit also for $ 46,296,296 K = Upfront Cost of Developing Reserves = $50,000,000 t = Period for which firm has rights = 15 Variance = Expected variance in ln(gold prices) = 0.09 ! Use forward looking variance r = Riskfree rate = 6.00% d. The developed reserves will become less valuable, since oil prices are down. The undeveloped reserves may become more or less valuale depending upon whether the effect of S or the effect of variance is greater on the option value. Spring 2000 Problem 1 Adjusted EBIT = 1500­ 100 = Adjusted EBIT (1­t) = ­ Reinvestment = FCFF 1400 840 336 504 Total Beta = 0.80/0.5 = Levered beta = 1.6 (1 + (1­.4)(3/7)) = Cost of Equity = 6% + 2.01 (4%) = Cost of Capital = 14.04% (.7) + 7% (1­.4)(.3) = 1.6 Tax rate = 480/1200 = 40% (Do not divide by EBIT. That will result in a double counting of the interest tax benefit which is already being counted in the cost of capital) 2.0114285714 14.04% Use total beta rather than illiquidity discount, since you have 11.09% insufficient information for such a discount. Value of private firm = 504 (1.05)/(.1109­.05) = $8,692.51 Problem 2 Present Value of FCFF from developed reserves = 300 (PVA,10 years, 9.375%) = Cost of Capital = 12%(25/40) + 5% (15/40) = Value of undeveloped reserves = 4000 ­ 1894 = Problem 3 d1 = ­0.15 d2= ­0.90 N(d1) = N(d2) = $1,894 9.38% $2,106 ! Do not subtract from the value of equity. 0.4404 0.1841 Value of Equity = 400 (.4404) ­ 800 exp (­.06*6) (.1841) = Value of Debt = 400 ­ 73.41 Interest rate on debt = (800/326.59)^(1/6) ­ 1 = Default spread on debt = 16.08% ­ 6% = $73.41 $326.59 16.08% 10.08% Spring 2002 Problem 1 After­tax Margin Sales/ Capital ROC Reinvestment rate Value/Sales Value BigName 12% 2 24.00% 16.67% 2.08 10.4 Problem 2 Net Income ROE Total Beta PBV = MV of Equity = NoName 6% 2 12.00% 33.33% 0.832 4.16 Brand Name ! ROC = After­tax operating margin * Sales/BV of capital ! Reinvestment rate = g/ ROC 6.24 2 ! Remember to subtract after­tax expense = 2.6 ­ 1(1­.4) 20.00% 2.75 1.94 19.4 Problem 3 S = K = t = Variance = Riskless rate = cost of delay= 106.698524 131.698524 12 0.0225 5% 0.083333333 ! I think you can also make a reasonable case for 1/8 if you argued that competition would kick in after the 8th year. ! In fact, you can even make a reasonable case for it being 0. If you entered 0 and want to justify it, give me your reason… Fall 2002 Problem 1 First, clean up the market value of equity for the cross holdings Total market value of equity = 3000 ! 150 *20 ­ Value of equity in Coleman Holdings = 500 ! 20% of 2500 ­ Value of equity in Silicon Tech = 1200 ! 60% of 2000 Value of Equity in Steel business = 1300 Next clean up the debt for the consolidated debt from Silicon Value of debt = 2000 ­ Value of Debt in Silicon Tech = 500 ! Silicon Tech's debt is consolidated in balance sheet Value of debt in Steel business = 1500 Finally, clean up the EBITDA Consolidated EBITDA = ­ EBITDA of Silicon Tech = EBITDA of Steel Business = 700 300 400 EV of Steel Business = EV/ EBITDA of Steel Business = 2800 7.00 Problem 2 a. Estimated PS in year 5 = 3.5 ! Net margin = 10%; 1.5 + .2 (10) = 3.5 Estimated Equity value in year 5 = 1750 ! 3.5 * 500 b. Total beta = 2.25 Cost of equity = 14.00% c. Value of equity today (going concern) = $908.90 ! 1750/1.14^5 Survival adjusted equity value = $363.56 ! 908.90 * .40 Spring 2003 Problem 1 a. Unlevered beta = Total beta = Cost of equity = 1 2.5 15.00% ! Use total beta because buyer is not diversified Return on capital = Reinvestment rate = 0.175 ! 280/1600 0.228571429 !4%/17.5% EBIT (1­t) ­ Reinvestment FCFF $280.00 $64.00 ! 22.86% of EBIT (1­t) $216.00 Value of firm = $2,042.18 ! 224 (1.04)/(.15­.04) b. Unlevered beta = Cost of equity = Return on capital= Reinvestment rate = EBIT (1­t) ­ Reinvestment FCFF 1 ! IPO valuation: use market beta 9.00% 0.15 ! Using reestimated return on capital 0.266666667 ! 3.5%/15% $240.00 ! Reestimate operating income with 40% tax rate $64.00 ! 23.33% of 240 $176.00 Value of firm = $3,660.80 ! 176 (1.04)/(.09­.04) c. There should be an illiquidity discount in the private transaction but not on the IPO. Problem 2 Part a Value of commercial product = Value of R&D = Total = $88.63 $45.00 $133.63 Market value of firm = Value of patent = $240.00 $106.37 Part b If the firm develops the patent today, you will replace the option value above with the NPV NPV = $49.39 Change in value = ­$56.98 ! 49.39 ­ 106.37 New firm value = $183.02 ! 240 ­ 56.98 Fall 2003 Problem 1 a. Intrinsic price to book ratio = 0.833333333 ! (ROE ­ g)/ (COE ­g); ROE =8%, Cost of equity = 5+4% = 9%) Stock is undervalued slightly. b. if the market is correct Price to book ratio = .8 = (.08­.03)/(r­.03) Solving for r, Cost of equity = 9.25% Problem 2 Levered beta = EV/Sales based upon regression= Actual EV/Sales ratio = Stock is overvalued by Problem 3 Total beta = Cost of equity = Reinvestment rate = Status quo value of firm = Value of 25% stake in firm = 1.56 2.028 ! 0.30 + .08 (15/100) ­ 1.2 (1.56) + .12 (20) 2.5 ! (200 + 100 ­50)/100 23.27% ! Divided the actual by the expected value ! You cannot compare the predicted value to the average for the sector. That tells you very little. 3 ! Sale in a private transaction. Divided beta by correlation. 17.00% ! 5% + 3*4% 0.4 ! G/ROC = 4%/10% 6.923076923 ! 1.5 (1­.4)/(.17­.04); I don't need a (1+g) because 1.5 is next year's income 1.730769231 With a doubled return on capital Reinvestment rate = 0.2 ! Doubled return on capital only on new investments. So existing operating income unaffected Optimal firm value = 9.230769231 ! 1.5 (1­.2)/(.17­.04) Value of 51% stake in firm = 4.707692308 For IPO valuation Market beta = Cost of equity = Status quo value = Optimal firm value = Value per voting share = Value per voting share = 0.9 8.600% $19.57 ! 1.5 (1­.4)/(.086­.04) $26.09 ! 1.5 (1­.2)/(.086­.04) $4.89 $5.54 !4.89+.2(26.09­19.57)/2 Since this is an IPO valuation, you have to revalue the company with a market beta. Spring 2004 Problem 1 After­tax Operating Margin Return on Capital Reinvestment Rate EV/Sales Enterprise Value Gloria Inc. Generic Brand Name Value 0.15 0.075 0.25 0.125 0.2 0.4 2.4 0.9 2400 900 1500 Problem 2 Cost of equity = Part a. Under existing management EBIT (1­t) Return on capital = Reinvestment Rate = Value of firm = 10.0% ! Use market beta since this is for initial public offering 5 0.1 0.4 ! 4./10 50 ! No surprise here. If you earn your cost of capital, MV = BV Part b. Under new management EBIT (1­t) Return on capital = Reinvestment Rate = Value of firm = $6.50 13.00% 30.77% ! 4/13 $75.00 Value of control = $5.00 ! (100 ­ 75) *.20 Value per non­voting share = Value per voting share = $10.00 ! Divide status quo value by total number of shares $12.50 ! Add Value of control/ Number of voting shares Fall 2004 Problem 1 EV/Sales = After­tax operating margin ( 1­ g/ ROC)/ (Cost of capital ­ g) 1.20 = .10 (1 ­.04/ ROC)/ (.09 ­ .04) ! There are other ways to get to the same solution. You could set up firm value Solving for return on capital, we get 3000 = 250 (1­.04/ROC)/ (.09­.04) Return on capital = 10.00% ! While technically you do not need a (1+g) in the numerator since I have given you next year's operating income I did give full credit to those who used it. Problem 2 Bank PBV ROE Hibernia Bank 1.25 Bancomer 1.1 North Fork Bank 0.9 North Fork Bank is the most undervalued bank….. If we use the regression, Hibernia Bank Bancomer North Fork Bank 16% 14% 12% PBV 1.25 1.1 0.9 Predicted PBV 1.2 Overvalued 1.1 Correctly valued 1 Under valued b. Low Price to book, high ROE, low risk, high growth Problem 3 Corrected income = After­tax income= $300,000.00 $180,000.00 Total beta = Cost of equity = ! Subtracted out rent (75,000), accounting expense (25,000) and dental salary of 150,000. Why subtract out the dentist salary? If you don't, you will be paying a premium to the owner of the practice for something that does not belong to him. Another way to think of this is as a pure business. You could be a non­dentist, buy this business and hire a dentist to work for you for 150,000….. 2.4 ! 0.80*3 13.85% Value of practice = ! On the total beta calculation, I did give full credit if you assumed that the R squared was 33% and took the square root of it. ### Spring 2005 Problem 1 a. Tax Rate: The higher the tax rate, the lower the EV/EBITDA multiple should be (not higher) b. EV/EBITDA = 2.26 + .1513 (Tax Rate) + .2156 (Return on Capital) – .1335 EV/EBITDA = 7.9059 Problem 2 Market value fo equity = Net Income next year = Problem 3 Total Beta = Cost of equity = 5% + 3*4% = Reinvestment rate = Value of firm = ! You cannot change the sign on a regression coefficient if you don't agree with it. 1800 1500 MV of Equity/ Forward Earnings = PE =1.2 = Payout Ratio / (.10 ­ .04) Payout ratio = Return on equity = g/ (1­ Payout ratio) = 1.2 ! 1800/1500 ! Cost of equity = 10%; Growth rate = 4% 7.20% 1.2/.4 = 4.31% ! Loser company but dem's the breaks… 3 ! Market beta/ Square root of R squared 17.00% 0.25 ! G/ ROC $66.21 Cost of equity to publicly traded firm = new return on capital = New reinvestment rate = Value of firm = Value of 51% = 151.470588 77.25 0.098 0.18 0.16666667 ! Investors in publicly traded firm are diversified. ! I also gave full credit if you adjusted the growth rate upwards to 4.5% ! Only the growth rate or reinvestment rate will be affected…. Existing operating income remains unchanged. Fall 2007 Problem 1 Enterprise value = Equity + Debt ­ Cash EV/Sales = 2500 1.25 ! 2500/2000 b. Estimated ROC = 0.075 ! Assumed book equity = 1000 b. If the market value is right, ! The book value of capital was missing on this problem. So, I gave full credit to any book EV/Sales = Expected operating margin next year/(1­RIR) (Cost of capital ­g) value of capital that was rasonable. The solution assumes that the book value of equity 1.25 = 0.075(1­ .03/.075)/ (Cost of capital ­ .03) ! After­tax Margin = 150/2000 is $ 1 billion and the book value of capital is $ 2 billion. Solving for the cost of capital, Cost of capital = 6.60% ! If you assume a 5% return on capital, this number will be lower (5.4%) Problem 2 Market value of equity of parent company = Debt of parent company = Cash of parent company = Enterprise value of parent company = EBITDA of parent company = EV/EBITDA for parent company = 650 ! 1000*10 ­ 0.1*500 ­0.75*400 300 ! 500 ­200 50 ! 150 ­ 100 900 150 ! 250 ­100 6 ! 900/150 Problem 3 C. Best combination: Low P/BV, Low risk, High growth, High ROE ! One point for D and F. They were close but failed one one dimension (D on growth and F on risk) b. Expected price to book for company A = Actual price to book ratio = Company is overvalued by apprroximately 0.8 1.25 36.00% ! Mechanical errors: ­0.5 point c. PBV of C = 1.2 = 0.80 + 0.75 X ­ 0.5 (1) Solving for X ROE for company C would have to be 12% The ROE would have to be approximately 12%… it is actually 20% ! Used intrinsic equation: ­1 point ! Set up equation in way to make solution impossible: ­1 point ! Mechanical erorrs: ­0.5 point Fall 2008 Problem 1 Current price to book ratio = 1.5 Current cost of equity = 9% Expected growth rate= 3% PBV = 1.5 = (ROE ­g)/ (Cost of equity ­g) 1.5 = (ROE ­.03)/ (.09­.03) ROE = 12% b. Book equity increases by = New return on equity = New cost of equity= New price to book ratio = Problem 2 Company Used wrong cost of equity: ­0.5 point Math error: ­0.5 point each New ROE incorrect: ­1 point New cost of equity incorrect: ­1 point 20% 10.00% ! Old ROE/ (1 + Capital increase) 11% ! Riskfree rate + New ERP 0.875 ! (10%­3%)/(11%­3%) Primary shares Price/Share Net Income # Options Zap Tech InfoRock Lo Software 100 500 80 $20 $6 $5 $100 $150 $20 Value/option 10 80 20 $10 Using regular PE completely misses the options oustanding: ­2 points $1.50 Using diluted PE treats all options as equal: ­1 point $0.50 Market Cap Net Income PE Ratio Diluted EPS Diluted PE Total Equity Value Modified PE Zap Tech $2,000 $100.00 20.00 $0.91 22.00 $2,100 21.00 InfoRock $3,000 $150.00 20.00 $0.26 23.20 $3,120 20.80 Lo Software $400 $20.00 20.00 $0.20 25.00 $410 20.50 Lo Software is the cheapest stock. It's modified PE ratio is the lowest. Problem 3 Value of private firm = EBIT (1­t) next year = Reinvestment rate = FCFF next year = 2000 300 20% ! g/ ROC = 3/15 = 20% 240 Used EBIT (1­t) as FCFF: ­1 point Reinvestment rate wrong: ­0.5 point Math errors: ­0.5 point each To solve for the cost of equtiyt used: ! Market beta computation wrong: ­1 point Value of firm = 2000 = 240/ (r ­ .03) Cost of capital = Cost ofequity = 15% Cost of equity = 15% = 4% + Beta (5%) Total beta used = 2.2 Market beta = 1.1 ! Total beta * Correlation with the market Cost of equity = 4% +1.1*5% = 9.50% Correct value of the firm = 3692.307692 ! 240/ (.095­.03) Fall 2009 Problem 1 Part a Return on capital = 0.15 ! Aftertax operating margin* Sales/Bv oF Capital Reinvestment Rate = 0.2 ! g/ ROC EV/Sales Ratio = 1.333333333 ! AT Oprating Margin (1­RIR)/ (Cost of capital ­g) Part b New Return on Capital = 0.16 ! 0.08 *(1.5*1.3333) Reivestment Rate = 0.1875 EV/Sales Ratio = 1.083333333 New EV = 1.444440833 ! Remember that revenues are higher by 33.33% Value of the firm increaases by about 8.33% Problem 2 SunTrust SouthEast Market value of equity $150.00 $100.00 Book Value of equity $90.00 $80.00 Expected Net income next year $18.00 $12.00 P/BV 1.666666667 1.25 ROE 20.00% 0.15 If SunTrust Bank is fairly valued, P/BV = 1.6667 = (.20­.03)/(Cost of equity ­.03) Cost of equity = !Did not compute return on capital: ­1 point ! Math errors: ­1/2 point ! Did not recompute sales/cap ratio: ­1/2 poitn ! Did not recompute value: ­1/2 point ! Wrong cost of equity: ­1 point 1 Did not compare to actual P/BV: ­0.5 point 0.132 Valuing SouthEast Bank with this cost of equity Intrinsic P/BV = 1.17647059 Actual P/BV = 1.25 Overvalued by 6.25% Problem 3 Expected EBIT(1­t) 170 ! 200 ­ 50 (1­.4) Reinvestment rate = 0% ! Because growth is zero Value to undiversifed investor = 850 Cost of equity to undiversified investor =0.00% 2 Impliws Total Beta = 2.666666667 Correlation with the market = 40% Market beta = 1.066666667 Cost of equity = 10.400% Value of business = 1634.615385 ! After­tax operating income wrong: ­1 point ! Did not compute correct cost of equity: ­1 point ! Did not adjust for market beta: ­1 point Fall 2010 Problem 1 Current EV/Sales Ratio = 1.7 Reinvestment Rate= 0.15 ! Growth rate/ ROC EV/Sales = After­tax margin (1­RIR)/ (Cost of capital ­g) 1.7 = After­tax margin (1­.15)/(.09­.03) After­tax margin = 12.00% ! Ignored reinvestment rate = ­1 point 1 Math errors: ­0.5 point each If you can reduce margins by 25% and increase sales turnover (sales/capital) by 50% After­tax margin (Generic) = 6.00% ! Did not recompute return on captial: ­1 point Current sales/capital = 1.67 ! ROC/After­tax margin of Slim Joe's ! Math errors: ­0.5 point each Return on capital (Generic) = 10.00% Reinvestment rate = 0.3 Sales to capital (Generic) = 0.70 Problem 2 Lugano Market value of equity Book value of equity + Market value of debt Book value of debt ­ Cash ­ Market value of minority holdings Book value of minority holdings + Market value of minority interests Book value of minority interests Tax rate Net Income Interest expenses EBIT DA Stulz 9000 4000 5000 4500 1500 1500 500 1000 400 40% 600 500 1500 500 13000 6000 5000 4500 2000 1000 500 3000 1000 20% 1200 500 2000 1000 ! EV computed incorrectly: ­0.5 to ­1.5 points ! EBITDA computed incorrectly: ­0.5 to ­1 point ! Did not consider ROC or tax rate in making judgment: ­0.5 point ! Net Income/ (1­t) + Interest expenses EV = 12000 18000 ! MV Equity + MV Debt ­ Cash ­ MV Minority Holdings + MV Minority Interests EBITDA 2000 3000 ! EBIT +DA EV/Ebitda 6.00 6.00 ROC= 12.86% 18.82% Since Stulz has a hgher ROC, lower tax rate and trades at the same multiple, it is cheaper. Problem 3 PBV = (ROE­g)/(Cost of equity ­g) For publicly traded firms 1.6 = (.12­.04)/ (Cost of equity ­.04) Cost of equity = 0.09 Given riskfree rate = 4% and ERP =5% Beta = 1 Total beta = 2.5 ! Beta/ 0.4 Cost of equity = 16.50% PBV ratio of Seacrest = ! Didnot solve correctly for beta: ­1 point ! No total beta computation: ­1 point ! Math errors: ­0.5 point each 1.28 Fall 2011 Problem 1 a. Intrinsic PE = 0.60/(.08­.02) = b. Estimated value for equity = ­ Value of options Value of equity in common stock Value per share Problem 2 Value of equity = Debt Cash EBITDA KMD 10 ! All or nothing (Ok if you use (1+g) and get 10.4…) 1000 50 ! 10*5 950 9.5 ! 950/100 9000 5000 2000 2100 Problem 3 Corrected after­tax EBIT After­tax Operating margin = Total Beta = Expected growth = Estimated EV/Sales = Estimated EV = !Used diluted number of shares = ­1.5 !Did not subtract out value of options = ­1 point ! Did not divide by actual number of shares: ­1 point RAD holdingsKMD just steel 3000 6000 ! Net out 60% of market value of RAD 3000 2000 1000 1000 700 1400 Enterprise Value EV/ EBITDA The steel business is fairly valued. ! EBITDA for steel business wrong: ­1 point ! Equity value of steel business wrong: ­1 point ! Added minority interest or subracted it : ­1 point ! Other errors: ­0.5 point each 7000 5 250 0.25 3 ! 1.2/0.4 0.1 2.5 2500 ! Did not use any reinvestment: ­0.5 point (No ROC would support this) ! Reinvestment rate wrong (given your ROC): ­0.5 point ! Failed to consider operating margin: ­0.5 point ! Other mechanical errors: ­0.5 point each ! Did not net out cash of consolidated sub: ­0.5 point ! Got parent EBITDA incorrect: ­0.5 to ­1 point ! Other computational errors: ­0.5 point each ! Did not adjust margin correctly = ­1 point ! Did not get total beta = ­1 point ! Other errors: ­0.5 to ­1 point ...
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