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quiz3sol - Spring1999 Problem1...

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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 after-tax operating margin = 9.64% (1.05) = 10.13% ! I also gave full credit if you added 5% to ge HK's VS ratio =.1013 (1-.05/2*.1013)(1.05)/(.10-.05) = 1.6023 ! Note that if you do not adjus get 1.575. Problem 2 a. Value of Developed Reserves = 100,000 * (300-200) * (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 * (300-200) * (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*(300-200)]/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 your production potential is m S = PV of reserves discounted back by development lag =  $27,138,251  ! Full credit also for $ 46,296, 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 t Spring 2000 Problem 1 Adjusted EBIT = 1500- 100 = 1400 Adjusted EBIT (1-t) = 840  - Reinvestment = 336 FCFF 504 Tax rate = 480/1200 = 40% (D will result in a double counting Total Beta = 0.80/0.5 = 1.6 which is already being counte Levered beta = 1.6 (1 + (1-.4)(3/7)) = 2.0114285714 Cost of Equity = 6% + 2.01 (4%) = 14.04% Use total beta rather than illiqu Cost of Capital = 14.04% (.7) + 7% (1-.4)(.3) = 11.09% insufficient information for suc 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%) =  $1,894  Cost of Capital = 12%(25/40) + 5% (15/40) = 9.38% Value of undeveloped reserves = 4000 - 1894 =  $2,106  ! Do not subtract from the value of equity. Problem 3 d1 = -0.15 N(d1) = 0.4404 d2= -0.90 N(d2) = 0.1841 Value of Equity = 400 (.4404) - 800 exp (-.06*6) (.1841) =  $73.41  Value of Debt = 400 - 73.41  $326.59  Interest rate on debt = (800/326.59)^(1/6) - 1 = 16.08% Default spread on debt = 16.08% - 6% = 10.08% Spring 2002 Problem 1 BigName NoName Brand Name After-tax Margin 12% 6% ! ROC = After-tax operating margin * Sales/BV of capital
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