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# Berkeley UGBA 103 - Introduction to Finance

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University of CaliforniaWalter A. Haas School of BusinessUGBA 103Introduction to FinanceProf. Dmitry Livdan 15 May 2013Solutions to the FINAL1. (a) (12 points) First, the appropriate discount rate r is given by the CAPM:r = rf+ (rm− rf)β = rf+ (rm− rf)(1) = rm= 14%.Given that the returns on the new investments are perpetual, we know that the earningsat the end of year t will be equal to the earnings the previous year plus the returns onthe new investments made last year, i.e.Et= Et−1+ r∗tIt−1, (1)where r∗tdenotes the rate of return in year t on the new investments made at the endof the previous year. We also know that earnings are either reinvested or distributed toshareholders as dividends:Et= It+ Dt. (2)We are told that r∗1= r∗2= r∗3= 20% and that r∗4= r∗5= · · · = 16%. The informationgiven also allows us to calculate the earnings at the end of every year (from the growthrates gtin earnings):Et= Et−1(1 + gt).We can therefore use (1) to “back out” the reinvested earnings for every year, and thenuse (2) to calculate the dividends. This is all done in the following table:Growth in Return onYear earnings reinvestments Earnings Reinvestments Dividends(t) (gt) (r∗t) (Et) (It) (Dt)0∗4.000 4.000 0.0001 20% 20% 4.800 3.600 1.2002 15% 20% 5.520 2.760 2.7603 10% 20% 6.072 3.036 3.0364 8% 16% 6.558 3.279 3.279..................∗Year 0 represents last year.(b) (5 points) Since the dividends are going to keep growing at the same rate as the earnings(i.e. 8%), we can discount them back to time zero (using the discount rate of 14%calculated above) to get today’s stock price:P0=1.2001.14+2.760(1.14)2+3.0360.14 − 0.081(1.14)2= 42.111.UGBA 103 FINAL – Solutions 2(c) (3 points) AIP generate AIP =E0r=\$4.000.14= \$28.57 or a fraction\$28.57\$42.11= 0.679 of thestock price. PVGO thus represents a fraction of 0.321 of the stock price.2. (a) (10 points) First, we can calculaterD= rf+ (rm− rf)βD= 0.03 + 0.09(0.25) = 5.25%;rE= rf+ (rm− rf)βE= 0.03 + 0.09(2.0) = 21%.The weighted average cost of capital is thenWACC =(DV)(1 − tc)rD+(EV)rE=2525 + 52(1 − 0.34)(0.0525) +5225 + 52(0.21)= 15.3%.Tuﬀ Stout’s chief ﬁnancial oﬃcer estimates that EBL’s expected after-tax cash ﬂows (itsunlevered free cash flows) will be as follows (you need to ﬁll empty cells).End of Year1 2 3 4 5(1) Operating income 2,620 3,406 3,712 4,045 4,330(2) Tax on operating income 891 1,158 1,262 1,375 1,472(3) After-tax operating income 1,729 2,248 2,450 2,670 2,858(4) + Depreciation 425 450 450 450 450(5) − Capital expenditures 524 518 525 535 554(6) − Change in working capital -200 -250 205 225 254(7) + Proceeds from asset sales 3,500 1,800(8) After-tax cash ﬂows (UFCF) 5,330 4,230 2,170 2,360 2,500The CFO also estimates that these after-tax cash ﬂows will grow at an annual rate of2.3% after year 5.Under this set of assumptions, the maximum bid that Tuﬀ Stout should consider isPV =5,3301.153+4,230(1.153)2+2,170(1.153)3+2,360(1.153)4+2,5000.153 − 0.0231(1.153)4= 21,437.(b) (25 points) In order to get a clearer picture of EBL’s value, Tuﬀ Stout’s CFO decides tocalculate the adjusted present value in two parts: the value of EBL’s unlevered assetsplus the value of the expected tax shields that the new debt will bring to Tuﬀ Stout.She also decides to be more precise about the exact nature of the extra debt capacityresulting from the acquisition.To ﬁnance the acquisition, Tuﬀ Stout will be able to borrow \$9 million at 8% (competitivemarket rate for such loans and the proper discount rate for the interest tax shields) forthe acquisition of EBL. The rest will be ﬁnanced in cash using last year’s earning. TheUGBA 103 FINAL – Solutions 3debt contract is a ﬁve-year contract, during which Tuﬀ Stout is expected to repay thebank in ﬁve equal end-of-year installments. The U.S. Government is looking to promotelight beer consumption and is willing to subsidize the loan by lowering its interest by0.5% to 7.5%.x =9,00010.075[1 −1(1.075)5]= 2,225.Under this scenario, the CFO conservatively assumes that Tuﬀ Stout will not be able totake on more debt as a result of acquiring EBL. Since EBL is not publicly traded, therisk has to be assessed using a comparable ﬁrm. Luckily, Tuﬀ Stout is such a comparableﬁrm, and so the CFO decides to use Tuﬀ Stout’s asset beta to estimate the risk of EBL’sassets.rEBLA= rTSIA= WACCTSIU=WACCTSIL1 − tc(DV)TSI=0.1531 − 0.342525+52= 17.2%.The unlevered net present value is equal toNPVU=5,3301.172+4,230(1.172)2+2,170(1.172)3+2,360(1.172)4+2,5000.172 − 0.0231(1.172)4= 19,119.This is the value of EBL if it did not have any debt capacity, i.e., if it were all-equityﬁnanced.We need to ﬁgure out the interest payment on the debt each year. This is done inthe following table, where the initial debt outstanding is 9,000 (and so the ﬁrst interestpayment is 7.5% × 9,000 = 675).End of Year1 2 3 4 5Debt outstanding 7,450 5,784 3,993 2,067 0Payments on the debt 2,225 2,225 2,225 2,225 2,225Interest paid 675 559 434 299 155Principal paid 1,550 1,666 1,791 1,926 2,067Interest tax shield 230 190 148 102 53The present value of the tax shield is thereforePV (tax shields) =2301.08+190(1.08)2+148(1.08)3+102(1.08)4+53(1.08)5= 604,However, the loan itself now has a positive NPV:NPV (loan) = 9,000 −2,2250.08[1 −1(1.08)5]= 116.FinallyAPV = NPVU+ PV (tax shields) + NPV (loan) = 19,119 + 604 + 116 = 19,839.UGBA 103 FINAL – Solutions 4(c) (20 points) First we need to unlever RRB’s equity beta to get its asset beta:βRRBA=βRRBE+(DE)RRB(1 − tc)βRRBD1 +(DE)RRB(1 − tc)=2.2 +(515)(1 − 0.34)0.41 +(515)(1 − 0.34)= 1.88.This becomes the CFO’s best estimate of the asset beta of the project (the acquisitionof EBL): βpA= βRRBA= 1.88. To ﬁnd the risk and cost of equity capital, the CFO mustassess the debt capacity of the project, i.e., the extra debt that Tuﬀ Stout will be ableto aﬀord as a result of the acquisition).Using comparables and other industry numbers, the CFO estimates that Tuﬀ Stout’sdebt capacity will increase by a fraction of about 30% of EBL’s value (i.e., 30% of theproject’s value). Also, this extra debt would come with a premium of 3% over the riskfreerate.That is, rpD= 3.0% + 3.0% = 6.0% which corresponds to debt beta of βpD= 0.33.Using this debt capacity information, she relevers the asset beta estimated from RRBto getβpE= βpA+(DE)p(1 − tc)(βpA− βpD)= 1.88 +0.300.70(1 −

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