Company A is preparing a deal to acquire company B$.$ One analyst estimated that the merger would produce $160$ 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 $3\%$ a year. In addition the analyst is assuming an after$-$tax integration cost of $280$ million dollars, and taxes of $21\%.$ Assume that the integration cost of $280$ million dollars happens one year after the merger is completed $($year $1).$ The analyst is using a cost of capital of $8\%$ to value the synergies.Company B$$s equity is trading at $5\mathrm{.}1$ B dollars $($market value of equity$).$ Company A is planning to pay a $30\%$ premium for company B$.$ 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$?$ Why?