Raymond Supply, a national hardware chain, is considering purchasing a smaller chain, Strauss & Glazer Parts (SGP). Raymond's analysts project that the merger will result in the following incremental free cash flows, tax shields, and horizon values: $\begin{array} { l c c c r }
\text { Year } & 1 & 2 & 3 & 4 \
\text { Free cash flow } & \$ 1 & \$ 3 & \$3 & \$ 7 \
\text { Unlevered harizan value } & & & & 75 \
\text { Tax sheld } & 1 & 1 & 2 & 3 \
\text { Harizon value of tar shield } & & & &32
\end{array}$
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%. Using the compressed adjusted present value approach, what is the value of SGP to Raymond?

Question

Raymond Supply, a national hardware chain, is considering purchasing a smaller chain, Strauss & Glazer Parts (SGP). Raymond's analysts project that the merger will result in the following incremental free cash flows, tax shields, and horizon values: $\begin{array} { l c c c r } 
\text { Year } & 1 & 2 & 3 & 4 \
 \text { Free cash flow } & \$ 1 & \$ 3 & \$3  & \$ 7  \
\text { Unlevered harizan value } & & & & 75 \
\text { Tax sheld } & 1 & 1 & 2 & 3 \
\text { Harizon value of tar shield } & & & &32
\end{array}$
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%. Using the compressed adjusted present value approach, what is the value of SGP to Raymond?

Quizplus · Accepted Answer

rsL = rRF + b(RPM) = 8% + 2.0(4%) = 16%. rsU = wdrd + wsrs = 0.30(10%) + 0.70(16%) = 14.2%. Since all of the cash flows are to be discounted at the same rate, we don't need to separately calculate the values of the tax shield and unlevered value of operations. We can simply add the tax shields and free cash flows together each year to input in the financial calculator: Time line: (In millions) 11ed2c42_612f_80ae_9c1d_732e0f25f91e_TB1228_00 Financial calculator solution: (In millions) Inputs: CF₀ = 0; CF₁ = 2; CF₂ = 4; CF₃= 5; CF₄ = 117; I/YR = 14.2. Output: NPV = $76.96 million = Value of operations. Value of equity = Value of operations - Value of debt = $76.96 - 15 = $61.96 million. Some students will calculate separately the value of the tax shield and the unlevered value of operations and add them together. In that case, the separate calculations are: Unlevered value of operations: Inputs: CF₀ = 0; CF₁ = 1; CF₂ = 3; CF₃ = 3; CF₄= 75 + 7 = 82; I/YR = 14.2. Output: NPV = $53.40 million = Unlevered value of operations. Value of tax shields: Inputs: CF₀ = 0; CF₁= 1; CF₂ = 1; CF₃= 2; CF₄ = 3 + 32 = 35; I/YR = 14.2. Output: NPV = $23.56 million = Value of tax shields. Value of operations = Value of tax shields + Unlevered value of operations = $53.40 + $23.56 = $76.96 million.

Raymond Supply, a National Hardware Chain, Is Considering Purchasing a Smaller