University of California Walter A Haas School of Business UGBA 103 Introduction to Finance Prof Dmitry Livdan 15 May 2013 Solutions to the FINAL 1 a 12 points First the appropriate discount rate r is given by the CAPM r rf rm rf rf rm rf 1 rm 14 Given that the returns on the new investments are perpetual we know that the earnings at the end of year t will be equal to the earnings the previous year plus the returns on the new investments made last year i e Et Et 1 rt It 1 1 where rt denotes the rate of return in year t on the new investments made at the end of the previous year We also know that earnings are either reinvested or distributed to shareholders as dividends Et It Dt 2 We are told that r1 r2 r3 20 and that r4 r5 16 The information given also allows us to calculate the earnings at the end of every year from the growth rates gt in earnings Et Et 1 1 gt We can therefore use 1 to back out the reinvested earnings for every year and then use 2 to calculate the dividends This is all done in the following table Year t 0 1 2 3 4 Growth in earnings gt 20 15 10 8 Return on reinvestments rt Earnings Et Reinvestments It Dividends Dt 20 20 20 16 4 000 4 800 5 520 6 072 6 558 4 000 3 600 2 760 3 036 3 279 0 000 1 200 2 760 3 036 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 1 200 2 760 3 036 1 42 111 2 1 14 1 14 0 14 0 08 1 14 2 UGBA 103 FINAL Solutions 2 28 57 c 3 points AIP generate AIP Er0 4 00 0 14 28 57 or a fraction 42 11 0 679 of the stock price PVGO thus represents a fraction of 0 321 of the stock price 2 a 10 points First we can calculate rD rf rm rf D 0 03 0 09 0 25 5 25 rE rf rm rf E 0 03 0 09 2 0 21 The weighted average cost of capital is then D E WACC 1 tc rD rE V V 25 52 1 0 34 0 0525 0 21 25 52 25 52 15 3 Tu Stout s chief nancial o cer estimates that EBL s expected after tax cash ows its unlevered free cash flows will be as follows you need to ll empty cells 1 Operating income 2 Tax on operating income 1 2 620 891 End of Year 2 3 4 3 406 3 712 4 045 1 158 1 262 1 375 3 4 5 6 7 After tax operating income Depreciation Capital expenditures Change in working capital Proceeds from asset sales 1 729 425 524 200 3 500 2 248 450 518 250 1 800 2 450 450 525 205 2 670 450 535 225 2 858 450 554 254 8 After tax cash ows UFCF 5 330 4 230 2 170 2 360 2 500 5 4 330 1 472 The CFO also estimates that these after tax cash ows will grow at an annual rate of 2 3 after year 5 Under this set of assumptions the maximum bid that Tu Stout should consider is 5 330 4 230 1 2 170 2 360 2 500 2 3 4 1 153 1 153 1 153 1 153 0 153 0 023 1 153 4 21 437 PV b 25 points In order to get a clearer picture of EBL s value Tu Stout s CFO decides to calculate the adjusted present value in two parts the value of EBL s unlevered assets plus the value of the expected tax shields that the new debt will bring to Tu Stout She also decides to be more precise about the exact nature of the extra debt capacity resulting from the acquisition To nance the acquisition Tu Stout will be able to borrow 9 million at 8 competitive market rate for such loans and the proper discount rate for the interest tax shields for the acquisition of EBL The rest will be nanced in cash using last year s earning The UGBA 103 FINAL Solutions 3 debt contract is a ve year contract during which Tu Stout is expected to repay the bank in ve equal end of year installments The U S Government is looking to promote light beer consumption and is willing to subsidize the loan by lowering its interest by 0 5 to 7 5 9 000 2 225 x 1 1 1 5 0 075 1 075 Under this scenario the CFO conservatively assumes that Tu Stout will not be able to take on more debt as a result of acquiring EBL Since EBL is not publicly traded the risk has to be assessed using a comparable rm Luckily Tu Stout is such a comparable rm and so the CFO decides to use Tu Stout s asset beta to estimate the risk of EBL s assets EBL TSI rA rA WACCUTSI WACCLTSI 0 153 17 2 D TSI 25 1 0 34 25 52 1 tc V The unlevered net present value is equal to 5 330 4 230 2 170 2 360 2 500 1 2 3 4 1 172 1 172 1 172 1 172 0 172 0 023 1 172 4 19 119 NPVU This is the value of EBL if it did not have any debt capacity i e if it were all equity nanced We need to gure out the interest payment on the debt each year This is done in the following table where the initial debt outstanding is 9 000 and so the rst interest payment is 7 5 9 000 675 Debt outstanding Payments on the debt Interest paid Principal paid Interest tax shield 1 7 450 2 225 675 1 550 230 End of Year 2 3 4 5 784 3 993 2 067 2 225 2 225 2 225 559 434 299 1 666 1 791 1 926 190 148 102 5 0 2 225 155 2 067 53 The present value of the tax shield is therefore PV tax shields 230 190 148 102 53 604 2 3 4 1 08 1 08 1 08 1 08 1 08 5 However the loan itself now has a positive NPV 2 225 1 NPV loan 9 000 1 116 0 08 1 08 5 Finally APV 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 RRB A RRB E D RRB 1 1 tc D ED RRB 1 tc E RRB 5 2 2 15 1 …