4. Firm A (the acquiring firm) is in the similar business as Firm T (the acquired or target firm) and is considering acquiring Firm T. Firm A expects to generate annual before-tax cost savings from the acquisition of $100 million by the end of year 5. The cost savings benefit would be $40 million in year 2, increase by $20 million per year until it reaches $100 million in year 5, and remain at $100 million thereafter. Firm A also expects that, following the merger, it would incur before-tax costs associated with integrating the two companies for a total of $150 million over the first three years (i.e., $50 million for each year). Below is the information for Firm T. Year 0 is the year of valuation.

Firm T ($ millions)
	Year 0	Year 1E	Year 2E	Year 3E	Year 4E	Year 5E	Year 6E
Pre-tax sales	$1,000	$1,080.0	$1,166.4	$1,259.7	$1,360.5	$1,469.3	$1,542.8
Pre-tax operating income		129.6	140.0	151.2	163.3	176.3	185.1
Pre-tax cost savings		0.0	40.0	60.0	80.0	100.0	100.0
Pre-tax cost of integrating businesses		50.0	50.0	50.0	0.0	0.0	0.0
Depreciation expense		100.0	105.0	110.0	120.0	90.0	0.0
Capital expenditures		120.0	125.0	130.0	135.0	140.0	100.0

Firm Ts annual total net working capital is 10 percent of sales for the year. Tax rate is 25%. The firms pre-tax cost of debt is 8 percent per year. The annual risk free rate of return is 5 percent and the annual market rate of return is 12 percent. The company has a debt to equity ratio of 0.60 and a levered equity beta of 1.6. Assume that free cash flows grow at a constant annual growth rate of 5% forever after year 6. Find the value of the firm with synergies based on the free cash flow valuation model.

Notes:

o Sales estimated using 8% growth through year 5 and 5% growth beyond year 5. o Pre-tax operating income estimated as 12% of sales. The pre-tax operating income is the earnings before interest and taxes (EBIT) defined as Sales Fixed costs Variable costs Depreciation expense.