6.7. Belo Horizonte Company plans to buy back 1.5 million shares of its own stoc
ID: 2716674 • Letter: 6
Question
6.7. Belo Horizonte Company plans to buy back 1.5 million shares of its own stock from its cash reserves at $65 a share. There will be no change in the debt of the company. This will increase the bankruptcy costs by $13 million, due to lower cash reserves of the company. Due to share buyback, the debt/assets ratio will go from 33% to 37%. The income tax rate of the company is 30%.
(A) Write two equations representing B/V of the company, before and after the share buyback.
(B) Solve them to find the initial and final value of the company.
(C) Calculate the number of shares of stock, before and after the buyback.
Answer: 10,535,750 and 9,035,750. Show solutions.
(D) Find the value of the stock per share after this buyback. Is the company making the right move? Answer: $63.56. Show solutions.
Explanation / Answer
A) Before buyback, Debt+Equity=Assets
Total equity repurchased =$65*1.5 million= $97.5 million shall reduce equity by this much
cost of bankruptcy =$ 13 million
Total reduction in equity = $97.5 million +$ 13 million=$110.5 million
The total Assets shall also reduce by $110.5 million
Debt shall remain the same before and after the purchase.
After buyback, Debt+(Equity-$110.5 million)=Assets-$110.5 million
.33=Debt/Assets ...1)
.37=(Debt)/(Assets-$110.5 million) ...2)
B) substitute 1 in 2) =>.37*(Assets-$110.5 million)=Debt=.33 Assets
=>.04Assets=.37*($110.5 million)=$ 40.885 million=>assets=40.885/.04=$ 1022.125 million
Debt=$ 1022.125 million*.33=$ 337.30125 million
Thus initial value of the company is $ 1022.125 million and final value of the company is $ 1022.125 million-$110.5 million=$ 911.625 million
C)Value of Equity before the buyback.=initial value of the company-Debt
Value of Equity before the buyback.=$ 1022.125 million-$ 337.30125 million=$ 684.82375 million
number of shares of stock, before the buyback = Value of Equity before the buyback/65 = $ 684.82375 million/$65=10.53575 million=10,535,750
number of shares of stock, after the buyback =number of shares of stock, before the buyback-shares repurchased
number of shares of stock, after the buyback =10,535,750-1,500,000=9,035,750
D)Value of Equity after the buyback.=final value of the company-Debt
Value of Equity after the buyback =$ 911.625 million-$ 337.30125 million=$574.32375 million=$574,323,750
value of the stock per share after this buyback= Value of Equity after the buyback/ number of shares of stock, after the buyback= $574,323,750/9,035,750=$63.56
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