91Ó°ÊÓ

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

Present Value of year 1-5:

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

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

Present Value of year 6-15:

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

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

Present Value of year 16-20:

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

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

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.