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

Calculation of the valuation of Synergy

Expected Synergy=175 million dollars, Taxes of 20%, After-tax integration cost of 0.3 billion,Growth(g)= 2 %,

cost of capital of =8%

As we are having a constant growth rate for synergy from Year3(Y3), we will calculate the value at the end of Year 2 (Y2)

= (Synergy amount at Y2+ growth(g))(1-tax)/ (Cost of capital -g)

= {(175*1.02)(1-0.20)/ 0.08-0.02} = (142.8/0.06) = $2380

So value at the end of Y2 is $2,380

Since we have value at the end of Y2, we will have to discount it back to (t=o) that is now

Value at t=0 = FV/(1+ cost of capital)^t = $2380/(1.08)² = $2550

Calculation of Net Synergy

Value of the Synergy Now(t=0)	$2040.47
Cost of the Synergy at Now(t=0) (0.3 billion)	$300
Net value of the synergy	$1740.47

2)Justification of the premium paid by company A to Company B

Current market Capitalisation of company B= 2.3 billion(2300 million)

The net value of the synergy=$1740.47

Premium paid by Company A= 30%

Premium paid by Company A = (Market capitalisation + Premium) = ( 2300*1.30)= $2,990

So the Net value of the company A after paying a premium of 30%= PV of Synergy- Premium paid to company B

= ($1740.47- $2,990)=$(1250)

It is not justifiable since the Net value of company A after paying a premium to company B is negative