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.

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 rate

a. debt to equity ratio after the merger(in decimal form)
b. debt to capital after transaction
c. dollar value of debt in the merged firm
d. dollar value of debt in existing companies
e. new debt issued to finance the transaction

Answer 1

a) Market Value of Equity of general systems = $12billion

Market Value of Debt of general systems = $16billion

Levered Beta of General Systems = 1.09

Unlevered Beta = Levered Beta/ [1 + Debt/ Equity* (1-tax)]

Or, Unlevered Beta = 1.09/ [1+16/12*0.6] = 0.6055

If Post Merger the Levered Beta becomes 1.27, then

0.6055* [1 + Debt/ Equity*0.6] = 1.27

Or, 1 + Debt/ Equity*0.6 = 2.0975

Or, Debt/ Equity = 1.0975/ 0.6 = 1.83

1. Debt to Capital = Debt/ (equity + Debt)

Or, Debt / Capital = 1.83/ 1.83+1 = 0.65

Previously Debt to Capital = 16/28 = 0.57

b) Debt/ Capital = 0.65

Or, Debt/ Debt + equity = 0.65

Or, debt/ debt + 12 = 0.65

Or, debt = 0.65 debt + 7.8

Or, 0.35debt = 7.8

Or, Debt = $22.23billion

The dollar value of debt in the merged firm would be $22.23billion

c) As existing companies dollar value of debt would be $22

General Systems $16 billion & Fast Works $6 billion

d) Exiting Debt was $16billion and dollar value in the merged firm would be $22.23 billion so external finance after assuming the Fast Works debt funds would be; $22.23 - $16 = $6.23billion.