J & J Enterprises is considering a cash acquisition of Patterson Steel Company for \(4,500,000. Patterson will provide the following pattern of cash inflows and synergistic benefits for the next 20 years. There is no tax loss carryforward.

Years 1–5 6–15 16–20 Cash inflow (aftertax) ...................... \)490,000 \(650,000 \)850,000 Synergistic benefits (aftertax) ......... 45,000 65,000 75,000

The cost of capital for the acquiring firm is 12 percent. Compute the net present value. Should the merger be undertaken? (If you have difficulty with deferred time value of money problems, consult Chapter 9.)

To calculate the total cash inflow first of all PV factor table is created:

Present Value of year 1-5:

$\begin{array}{rcl}\mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflow}& \mathbf{=}& \mathbf{Cash}\mathbf{}\mathbf{Inflow}\mathbf{+}\mathbf{Synergistic}\mathbf{}\mathbf{Benefits}\\ & \mathbf{=}& \mathbf{\$}\mathbf{490}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{535}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{Present}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflows}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{Factor}\\ & \mathbf{=}& \mathbf{\$}\mathbf{535}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{.}\mathbf{605}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{928}\mathbf{,}\mathbf{675}\end{array}$

Present Value of year 6-15:

$\begin{array}{rcl}\mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflow}& \mathbf{=}& \mathbf{Cash}\mathbf{}\mathbf{Inflow}\mathbf{+}\mathbf{Synergistic}\mathbf{}\mathbf{Benefits}\\ & \mathbf{=}& \mathbf{\$}\mathbf{650}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{715}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{Present}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflows}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{Factor}\\ & \mathbf{=}& \mathbf{\$}\mathbf{715}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{.}\mathbf{206}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{292}\mathbf{,}\mathbf{290}\end{array}$

Present Value of year 16-20:

$\begin{array}{rcl}\mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflow}& \mathbf{=}& \mathbf{Cash}\mathbf{}\mathbf{Inflow}\mathbf{+}\mathbf{Synergistic}\mathbf{}\mathbf{Benefits}\\ & \mathbf{=}& \mathbf{\$}\mathbf{850}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{75}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{925}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{Present}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflows}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{Factor}\\ & \mathbf{=}& \mathbf{\$}\mathbf{925}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{658}\\ & \mathbf{=}& \mathbf{\$}\mathbf{608}\mathbf{,}\mathbf{650}\end{array}$

Net Present Value:

$\begin{array}{rcl}\mathbf{Net}\mathbf{}\mathbf{Present}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{Inflow}\mathbf{-}\mathbf{Cash}\mathbf{}\mathbf{Outflow}\\ & \mathbf{=}& \mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{829}\mathbf{,}\mathbf{615}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{329}\mathbf{,}\mathbf{615}\end{array}$

Hence the net present value is $329,615. Hence, the merger should be taken.