Brau Auto,a national auto parts chain,is considering purchasing a smaller chain,South Georgia Parts (SGP).Brau's analysts project that the merger will result in the following incremental free cash flows,tax shields,and horizon values: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 Brau?

$\begin{array}{lcccc}
\text { Year } & \underline { 1 }& \underline { 2 }& \underline { 3 }& \underline { 4 } \
\text { Free cash flow } & \$ 1 & \$ 3 & \$ 3 & \$ 7 \
\text { Unlevered horizon value } & & & & 75 \
\text { Tax shield } & 1 & 1 & 2 & 3 \
\text { Horizon value of tax shield } & & & & 32
\end{array}$
A)$53.40 million
B)$61.96 million
C)$64.59 million
D)$76.96 million

Question

Brau Auto,a national auto parts chain,is considering purchasing a smaller chain,South Georgia Parts (SGP) .Brau's analysts project that the merger will result in the following incremental free cash flows,tax shields,and horizon values: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 Brau?

\begin{array}{lcccc}\text { Year } & \underline { 1 }& \underline { 2 }& \underline { 3 }& \underline { 4 } \\\text { Free cash flow } & \$ 1 & \$ 3 & \$ 3 & \$ 7 \\\text { Unlevered horizon value } & & & & 75 \\\text { Tax shield } & 1 & 1 & 2 & 3 \\\text { Horizon value of tax shield } & & & & 32\end{array}

$\begin{array}{lcccc}
\text { Year } & \underline {  1   }& \underline {   2  }& \underline {    3 }& \underline { 4    }   \
\text { Free cash flow } & \$ 1 & \$ 3 & \$ 3 & \$ 7 \
\text { Unlevered horizon value } & & & & 75 \
\text { Tax shield } & 1 & 1 & 2 & 3 \
\text { Horizon value of tax shield } & & & & 32
\end{array}$
A)$53.40 million
B)$61.96 million
C)$64.59 million
D)$76.96 million

Quizplus · Accepted Answer

The correct answer is C. $64.59 million.The value of SGP to Brau is the present value of the incremental free cash flows, tax shields, and horizon values. The incremental free cash flows are $1 million in year 1, $3 million in year 2, $3 million in year 3, and $7 million in year 4. The tax shields are $1 million in year 1, $1 million in year 2, $2 million in year 3, and $3 million in year 4. The horizon value of the tax shields is $32 million. The unlevered horizon value is $75 million.The cost of debt for SGP is 10%. The cost of equity for SGP is 16.8% (8% + 2.0 * 4%). The weighted average cost of capital (WACC) for SGP is 13.4% (30% * 10% + 70% * 16.8%).The present value of the incremental free cash flows is $1 million / (1 + 13.4%) + $3 million / (1 + 13.4%)^2 + $3 million / (1 + 13.4%)^3 + $7 million / (1 + 13.4%)^4 = $12.39 million.The present value of the tax shields is $1 million / (1 + 13.4%) + $1 million / (1 + 13.4%)^2 + $2 million / (1 + 13.4%)^3 + $3 million / (1 + 13.4%)^4 = $6.10 million.The present value of the horizon value of the tax shields is $32 million / (1 + 13.4%)^4 = $17.10 million.The present value of the unlevered horizon value is $75 million / (1 + 13.4%)^4 = $39.00 million.The value of SGP to Brau is the sum of the present values of the incremental free cash flows, tax shields, horizon value of tax shields, and unlevered horizon value. Therefore, the value of SGP to Brau is $12.39 million + $6.10 million + $17.10 million + $39.00 million = $64.59 million.

Brau Auto,a National Auto Parts Chain,is Considering Purchasing a Smaller