35 points total Dab Ynapmoc 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 e ective 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 rA tc EBIT 0 6 20 60 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 rm We can nd the value of the levered rm 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 quity 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 devided between 10M shares Thus the new equity price is P00 64 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 1 v 2 points What is the equity return of the recapitalized levered company 0 We nd rE from E0 1 tc EBIT 0 rE rD D 0 rE 1 tc EBIT E0 rD D 0 6 200M 0 05 100M 21 67 540M vi 1 point What is D Y s WACC We can nd WACC from VL 1 1 tc EBIT W ACC W ACC tc EBIT 0 6 200M 18 75 VL 640M 3 D Y has decided not to go with the recapitalization i e it is still allequity rm Instead D Y has a new investment opportunity It can reinvest 10 per share for 5 years out of its earnings into developing a new drug After 5 years the drug will be developed The return on the project is 40 r 40 and each 1 of investment pays forever The rst investment will be made 1 year from now and the last one will be made in year 5 a 7 points What is the D Y s price per share with the project First lets nd current earnings E0 1 tc EBIT 0 6 20 12 Next we need to nd the dividends and then discount them using Et Et 1 r It 1 T ime E I D E I 0 12 0 12 1 12 10 2 2 12 4 16 10 6 3 16 4 20 10 10 4 20 4 24 10 14 We can now calculate the price P00 2 6 10 14 18 1 32 89 91 1 2 1 22 1 23 1 24 1 25 1 25 0 2 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 29 91 rA z 60 c 8 points D Y now decides to nance its project with debt instead of earnings Speci cally it is going to issue 100M one period debt 10 per share 2 5 24 4 28 10 18 6 28 4 0 32 cost in year 1 use it to make the investment and then repay the principal plus interest in year 2 Then D Y will repeat the same procedure in years 2 to 5 i e it will issue 100M in debt in year 2 invest and repay it in year 3 then do it again etc Overall D Y will have to make 5 interest payments Use APV to calculate the new price per share with this nancing D Y s cost of debt remains at 5 Each interest payment is equal to 0 05 100M 5M or 0 5 per share The interest tax shield per share is 0 4 0 5 0 2 The rst interest payment is made in year 2 and the last one is made in year 6 The APV per share is equal to 0 2 AP V 29 91 z P V T ax Shields 29 91 0 05 1 P V GO and the new price per share is P00 1 1 1 30 60 5 1 052 1 05 z 0 79 tc EBIT AP V 90 60 rA z 60 d 7 points After some deliberation D Y decides on a di erent debt contract It will borrow the PV All Investment at 5 use it to nance all ve investments and will repay it as a perpetual bond Use APV to calculate the new price per share with this nancing We need to calculate the total debt per share D 10 1 0 05 1 43 30 1 055 Then since the debt is perpetual we need to calculate the interest tax shield per share tc D 0 4 43 30 17 32 and we obtain the new price per share P00 89 91 17 32 107 23 3