University of California Walter A Haas School of Business UGBA 103 Introduction to Finance Prof Dmitry Livdan 2 December 2013 Solutions to the Final 1 a 4 points The new investment of 8 00 will generate an extra 8 00 125 10 00 in earnings this year so that E1 8 00 10 00 18 00 Since 40 of these earnings will be reinvested we have I1 0 4 18 00 7 20 and D1 E1 I1 10 80 b 4 points In year 2 the initial investment will generate 8 00 25 2 00 and the investment made at the end of the first year will generate 7 20 25 1 80 These are in addition to the original no growth earnings of 8 00 so that E2 8 00 2 00 1 80 11 80 Again 40 of these earnings will be reinvested and the rest will be distributed to shareholders I2 0 4 11 80 4 72 and D2 E2 I2 7 08 c 7 points The long term growth rate in earnings and dividends is g 25 0 4 0 1 In fact using the same reasoning as in the first two years you can verify that the dividends in year 3 will be D3 D2 1 g 7 788 So the expected dividends that will be paid to the shareholders are as follows 0 1 2 3 4 P0 10 80 7 08 7 08 1 1 7 08 1 1 2 The appropriate discount rate r is obtained from the CAPM r rf rm rf 0 06 0 14 0 06 1 5 18 Therefore the value of EY s stock is 10 80 7 08 1 10 80 7 08 1 84 1525 P0 1 r r g 1 r 1 18 0 18 0 1 1 18 44 44 d 5 points AIP generate AIP Er0 8 00 0 18 44 44 or a fraction 84 15 0 528 of the stock price PVGO thus represents a fraction of 0 472 of the stock price 2 a 4 points The current value of D R s debt is D 150 and the current value of its equity is E 10 15 150 The total current value of the firm is therefore VL D E 300 b 4 points The weighted average cost of capital is WACC 1 tc rD D E 150 150 rE 1 0 40 0 08 0 16 10 4 VL VL 300 300 UGBA 103 Final Solutions 2 c 4 points We have VL X 1 tc WACC 300 X 1 0 40 0 104 X 52 d 4 points We know that VL VU tc D so that VU VL tc D 300 0 4 150 240 e 4 points We have VU X 1 tc r 240 52 1 0 40 r r 13 f 3 points The net present value of the project is NPV 75 19 5 1 0 40 15 0 13 g 5 points The adjusted net present value APV of the project consists of the net present value under an all equity financing policy and the present value of the future tax shields resulting from the additional debt issued as a result of this new project APV tc rD L 75 APV rD NPV tc L 75 APV NPV 15 0 40 0 25 75 APV We can solve for APV in this last equation to obtain APV 25 h 5 points The adjusted rate of return is given by the Modigliani Miller formula h i r r 1 tC L 0 13 1 0 40 0 25 11 7 The adjusted net present value of the project is simply APV 75 19 5 1 0 40 25 0 117 i 4 points The additional debt that will be issued is D L 75 APV 0 25 75 25 25 The equity of the firm will be increased by E 1 L 75 APV 1 0 25 75 25 75 j 5 points The total value of the firm s debt is now D0 D D 150 25 175 and that of the equity is E 0 E E 150 75 225 UGBA 103 Final Solutions 3 The total value of the firm is therefore VL0 D0 E 0 175 225 400 Also the firm will now generate annual pre tax earnings of X 0 X 19 5 52 19 5 71 5 The new weighted average cost of capital WACC 0 must therefore satisfy VL0 X 0 1 tc WACC 0 400 71 5 1 0 40 WACC 0 WACC 0 10 725 k 8 points We need to figure out the interest payment on the debt each year This is done in the following table Debt outstanding Principal paid Interest paid Interest tax shield 1 4 000 1 000 412 5 165 End of Year 2 3 4 3 000 2 000 1 000 1 000 1 000 1 000 330 247 5 165 132 99 66 5 0 1 000 82 5 33 The present value of the tax shield is therefore PV tax shields 165 132 99 66 33 409 721 2 3 4 1 0825 1 0825 1 0825 1 0825 1 0825 5