University of California Walter A Haas School of Business UGBA 103 Introduction to Finance Prof Dmitry Livdan 17 December 2015 Solutions to the FINAL 35 points total Deiter Yolen D Y is an all equity perpetual company with 10 million shares outstanding trading at the current P E ratio of 5 Its assets have just produced EBIT per share of 20 and it pays all of its earnings as dividends Its effective tax rate is equal to 40 D Y has only assets in place and thus does not grow 1 2 points What is D Y s cost of capital i e rA and what is its price per share P0 We can calculate rA from the P E ratio P0 1 1 E0 rA 20 rA P E 5 The price per share can be calculated as P0 E0 1 tc EBIT 0 6 20 60 rA rA 0 2 2 D Y is considering issuing 100 million in perpetual debt at a cost of rD 5 to buy back some equity If D Y decides to do the buy back i 1 point What is the value of the levered firm We can find the value of the levered firm from VL VU tc D 60 10M 0 4 100M 640M ii 1 point What is the value of equity after the recapitalization 100M in equity get bought back and the remaining 500M gets the interest tax shield E 0 500M 0 4 100M 540M iii 2 points What is the price at which equity is repurchased The value added by the tax shield per share is 4 total tax shield of 40M is divided between 10M shares Thus the new equity price is P00 64 UGBA 103 FINAL Solutions 2 iv 2 points How many shares have to be repurchased D Y buys back 100M worth of equity at 64 per share Therefore n 100M 1 56M 64 v 2 points What is the equity return of the recapitalized levered company 0 from We find rE E0 1 tc EBIT rD D 1 tc EBIT rD D 0 6 200M 0 05 100M 0 rE 21 67 0 0 rE E 540M vi 1 point What is D Y s WACC We can find WACC from VL 1 tc EBIT 0 6 200M 1 tc EBIT W ACC 18 75 W ACC VL 640M 3 D Y has decided not to go with the recapitalization i e it is still all equity firm Instead D Y has a new investment opportunity reinvest 12 per share during first 2 years and then 10 per share during last 3 years out of its earnings into developing a new drug After 5 years the drug will be developed The return before taxes on the project is 60 r 60 for the first 2 years i e in years when you invest 12 and 40 also before taxes for the last 3 years i e in years when you invest 10 and each 1 of investment pays forever starting one year after the investment has been made The first investment will be made 1 year from now and the last one will be made in year 5 a 8 points What is the D Y s price per share with the project First lets find current earnings E0 1 tc EBIT 0 6 20 12 Next we calculate after tax returns as 0 6 60 36 and 0 6 40 24 Finally we find the dividends and then discount them Year 0 1 2 3 4 5 6 7 Et 12 12 12 0 36 12 16 32 12 0 36 24 20 64 12 0 24 34 20 16 12 0 24 44 22 56 12 0 24 54 24 96 24 96 It 0 12 12 10 10 10 0 0 Dt 12 0 4 32 10 64 10 16 12 56 24 96 24 96 We can now calculate the price P00 0 4 32 10 64 10 16 12 56 1 24 96 69 26 2 3 4 5 1 2 1 2 1 2 1 2 1 2 1 25 0 2 UGBA 103 FINAL Solutions 3 b 2 points What is D Y s PVGO per share with this project We can use P00 1 tc EBIT P V GO P V GO 9 26 rA z 60 c After some deliberation D Y decides to finance its new project with debt rather than earnings Specifically it will borrow today the PV All Investment at 3 use it to finance all five investments and will repay it as a perpetual bond i 7 points Calculate the new price per share with project and debt financing HINT Now company is levered We need to calculate the total debt per share D 12 1 10 1 1 49 62 1 1 2 2 0 03 1 03 1 03 0 03 1 033 Then since the debt is perpetual we need to calculate the interest tax shield per share tc D 0 4 49 624 19 8496 and we obtain the new price per share P00 69 26 19 8496 89 11 ii 3 points What is D Y s WACC with this financing We calculate the value of the levered firm as 0 VL D E 49 624 10M 89 11 10M 138 734 10M We can now use it to calculate WACC W ACC rA 1 tc D 49 62 20 1 0 4 17 14 VL 138 734 iii 2 points Show that you can get the answer in part a by discounting D Y s dividends with WACC P00 4 32 10 64 10 16 12 56 1 24 96 89 11 2 3 4 5 5 1 1714 1 1714 1 1714 1 1714 1 1714 0 1714