Question

Company A is preparing a deal to acquire company B. One analyst estimated that the merger would produce 175 million dollars of annual cost savings, from operations, general and administrative expenses and marketing. These annual cost savings are expected to begin two years from now, and grow at 2% a year. In addition the analyst is assuming an after-tax integration cost of 0.3 billion, and taxes of 20%. Assume that the integration cost of 0.3 billion happens right when the merger is completed (year 0). The analyst is using a cost of capital of 8% to value the synergies. Company B’s equity is trading at 2.3 B dollars (market value of equity). Given this, Company A is planning to pay a 30% premium for company B.

a)   Compute the value of the synergy as estimated by the analyst. Please show your calculations.

b)   Does the estimate of synergies in a) justify the premium that company A offered to company B? (1 paragraph at most)

Answer 1

A) Calculating the value of synergy:

Expected Synergy	175 Mn after 2 years, Expected to grow by 2% p.a. after that
Cost of Capital	8.00%
Initial Expenses at T0	0.3 Bn
Taxes	20%
Since we have a constant growth rate for synergy from Y3 onwards, we will calculate the value at the end of Y2
Formula:	V(t=2) = (Synergy amount at year 2 + growth)(1-Tax Rate)/(Cost of capital-growth)
	(175*1.02)(1-0.2)/(0.08-0.02)
Value at Y2 End in Mn	2380.00
Since we have the value at the end of Y2 of the synergies, we now need to discount it back to T=0
Formula:	PV = FV/(1+CoC)^n
	PV = 2380/(1.08)^2
Value of Synergy at T=0 in Mn	2040.47
Calculating the Net Synergy as at T=0
Value of Synergy at T=0	2040.47 Mn
Cost of Synergy at T=0	300 Mn (0.3 Bn)
Net Value of Synergy at T=0	2040.47-300 = 1740.47 Mn (Final Answer)

3B) Justification of Premium Paid:

Net Value of Synergy at T=0 (Answer 3a)	1740.47 Mn
Current Market Cap of Co B	2.3 Bn Dollars
Premium Paid by Co A	30%
Premium Paid by Co A ($)	Market Cap of Company B + Premium to be paid
	2300 Mn*1.3
Premium Paid by A in $Mn	2990.00
To justify the premium paid by an Acquirer for a Target Company, the Value of Synergies to be received from the transaction should be greater than premium paid
Value to Acquirer after Premium Paid	PV of Synergies - Premium Paid
	1740.47-2990
	-1249.53
Since the net value to Company A after paying a 30% premium is negative $1249.53 Mn , they should consider paying a much lower premium

Please feel free to ask in comments if you have any further doubts!