General Systems, a computer manufacturer, announces that it will be acquiring Fa
ID: 1171616 • Letter: G
Question
General Systems, a computer manufacturer, announces that it will be acquiring FastWorks Software. You know the following General Systems had a levered beta of 1.09 prior to the merger. The firm has a market value of equity of $12 billion and $16 billion in debt outstanding FastWorks Software had a levered beta of 1.30 prior to the merger. The firm has a market value of equity of $6.00 billion and $6.00 billion in debt outstanding a) Estimate the unlevered beta of the combined firm b) If you were told that the combined firm's levered beta will be 1.270 after the acquisition, how much debt did General Systems use to acquire FastWorks?You can assume that General Systems will assume Fastworks' existing debt]. Both firms have a 40.00%Tax rateExplanation / Answer
Beta levered of General Systems = 1.09
The Debt/Equity Ratio (D/E) of General Systems = Debt/Equity = 16/12 = 4/3
Beta Unlevered = Beta Levered /(1 + (1 -tax rate )*D/E) = 1.09/(1+(1-40%)*4/3) = 0.6055
Market Value of firm = 12 + 16 = 28
Beta levered of Fastworks Software = 1.30
The Debt/Equity Ratio (D/E) of Fastwork Software = Debt/Equity = 6/6 =1
Market Value of firm = 6+ 6 = 12
Beta Unlevered = Beta Levered /(1 + (1 -tax rate )*D/E) = 1.3/(1+(1-40%)*1) = 0.8125
Total market value of combined firm = 28+ 12 = 40
a) Beta Unlevered of Combined Firm = Market value of General Systems /Total market value of combined firm) * Beta unlevered + (Market value of Fastworks Software /Total market value of combined firm)* Beta unlevered = (28/40)* 0.6055 + (12/40)* 0.8125= 0.6676
b) Beta levered of the combined firm = 1.270
Beta Levered of the combined firm = Beta unlevered* ( 1+ (1 -tax rate)*D/E) =
1.270= 0.6676 * ( 1 + (1-40%)* Debt new/Equity new)
Debt new/Equity new
= ((1.270/0.6676) -1 )/ 0.6 = 1.5038
Total Equity = 12 + 6 = 18
So new debt = (D/E)* Total Equity = 1.5038 * 18 = 27.0701
Total old debt = 16+6 =22
So new debt = 27.0701 - 22 = 5.07
Best of Luck. God Bless
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