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.
Explanation / Answer
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