#$7.$ Oracle Corporation acquires another business software applications vendor, PeopleSoft, Inc., for approximately $$10\mathrm{.}3$ billion. Oracle expects to achieve various synergies, and its strategy is to continue to support existing versions of PeopleSoft software solutions, create Oracle software to replace all of PeopleSoft's software, and then migrate PeopleSoft customers to Oracle software. Assume that, as a result of the merger, the company expects annual selling and administrative costs to decrease by $$750$ million, annual research and development costs to decrease by $$300$ million, and annual general and administrative costs to decrease by $$200$ million. Also, assume that Oracle will be able to migrate about $80\%$ of PeopleSoft's customers and keep the $$3$ billion in revenue associated with these customers in the first year after the merger, but that it will lose $20\%$ of PeopleSoft's customers and lose the $$600$mil. in revenue associated with these customers in the first year after the merger $($this revenue loss is a negative synergy$).$ Assume that the company will incur $$400$ million in fees, expenses, and integration$-$ and synergy$-$related costs in the first year after the merger and none thereafter. Assume that the appropriate discount rate for discounting synergies is $12\%$; that the post$-$merger income tax rate is $40\%$ on all income; that all revenue

streams were expected to grow at a $3\%$ rate $($with or without the merger$),$ and that variable costs are, on average, $55\%$ of revenues.

Measure the value of the synergies, assuming that the cost synergies begin in the first year after the merger, remain constant through the end of year $3,$ and then decline at a rate of $10\%$ in perpetuity beginning in the fourth year after the merger. Also assume that the migration of the customers will take place immediately after the merger and impact the Year $1$ cash flows.