Brau Auto, a national autoparts chain, is considering purchasing a smaller chain

ID: 2699183 • Letter: B

Question

Brau Auto, a national autoparts chain, is considering purchasing a smaller chain, South Georgia Parts.

Auto's analysts project that the merger will result in the following

incremental free cash flows and horizon values (in millions):

Year 1 2 3 4

Free cash flow $2 $4 $5 $10

Unlevered horizon value 107

Assume that all cash flows occur at the end of the year. SGP is currently financed with

30% debt at a rate of 10%. The acquisition would be made immediately, and if it is undertaken,

SGP would retain its current $15 million of debt and issue enough new debt to continue at the

30% target level. The interest rate would remain the same. SGP's pre-merger beta is 2.0, and its

post-merger tax rate would be 34%. The risk-free rate is 8% and the market risk premium is 4%.

What is the value of SGP to Sid?

Please show work.

return on equity = 8% + 2 * 4% = 16%

WACC = 0.3 * 10% + 0.7 * 16% = 14.2%

value of operations = NPV = 2/(1+0.142) + 4/(1+0.142)^2 + 5/(1+0.142)^3 + (10 + 107)/(1+0.142)^3 = 76.96

value of equity = value of operations - value of debt = 76.96 - 15 = 61.96 million

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