Jam llc unexpectedly executed a share buy-back. Before the buy-back the number o
ID: 2727696 • Letter: J
Question
Jam llc unexpectedly executed a share buy-back. Before the buy-back the number of outstanding shares was 11,123,000, the market price of one share was $2.04 and the return on levered equity was 12.00%. The return on levered equity after the buy-back is 14.12%. The debt amount was $18,500,000. Also, the company has kept a constant debt level before and after the buy-back. The corporate tax rate is 35% the cost of debt is 2.45% and the return on unlevered equity is not aected by the buy-back.
How many shares were bought back? The answer is 4,344,316 (I posted this answer 2 timee and the answer given was incorrect. Please do not reply until the answer 4,344,316 is reached)
Explanation / Answer
Before Buy Back After Buyback Outstanding Shares 11123000 Outstanding Shares ? Market Price 2.04 Market Price 2.04 Return on levered equity 12% Return on levered equity 14.12% Debt 18500000 Debt 18500000 Cost of debt 2.45% Cost of debt 2.45% Tax Rate 35% Tax Rate 35% RL=RU+D/E*(1-tax)*(RU-Rd) where RL=cost of levered equity RU=Cost of unlevered equity D=debt E=equity Rd=cost of debt 12=RU+(18500000/(11123000*2.04)*(1-0.35)*(RU-2.45) 12=RU+0.53*(RU-2.45) 12+0.53*2.45=1.53RU RU=(12+0.53*2.45)/1.53= 8.69 Now calculate after buyback and let's say the number of shares be "s" 14.12=8.69+(18500000/(2.04*s))*(1-0.35)*(8.69-2.45) 5.43=36782353/s s=36782353/5.43= 6773914 HENCE SHARES BOUGHT BACK=11123000-6773914=4349086
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