Chapter 8, Problem 19P

a)

Summary Introduction

To determine: The output at which two locations will have same profit.

Introduction: Location is one of the important element for a business that controls the cost and expenses. Location strategies support in framing other strategies for a firm where optimal location point will provide competitive advantage to a firm.

Answer to Problem 19P

At 120 machine tools, the profits at both the locations are identical.

Explanation of Solution

Given information:

Site	Fixed cost per year	Variable cost per year
B	$800,000	$14,000
Mc	$920,000	$13,000

Calculation to find the output at which two locations will have same profit:

Denote the volume of production of machine tools as “x”.

Given the selling price of each machine tool at $29,000, the total revenues, denoted by TR are

$\text{TR}=\$29,000x$ (1)

Given the B location has a fixed cost of $800,000 per year and a variable cost of $14,000, express the total cost TC_B for a production volume of “x” machine tools as follows.

${\text{TC}}_{\text{B}}=\$14,000x+\$800,000$ (2)

Given the Mc location has a fixed cost of $920,000 per year and a variable cost of $13,000, express the total cost TC_Mc for a production volume of “x” machine tools as follows.

${\text{TC}}_{\text{Mc}}=\$13,000x+\$920,000$ (3)

Calculate the volume of output “x” where both locations have the same profit

$\begin{array}{c}\$29,000\times x-\$14,000\times x-\$800,000=\$29,000-\$13,000\times x-\$920,000\\ \left(\$29,000-\$14,000\right)\times x-\$800,000=\left(\$29,000-\$13,000\right)\times x-\$920,000\\ \$1,000\times x=\$120,000\\ x=120\text{units}\end{array}$

Equating the equations and solving for x, the volume of production of 120 machine tools, the profits at both the locations are identical.

Hence, at 120 machine tools, the profits at both the locations are identical

b)

Summary Introduction

To determine: The output at which location B will have high profit than location Mc.

Introduction: Location is one of the important element for a business that controls the cost and expenses. Location strategies support in framing other strategies for a firm where optimal location point will provide competitive advantage to a firm.

Answer to Problem 19P

Upto production level of 120 units Location B will have high profit.

Explanation of Solution

Given information:

Site	Fixed cost per year	Variable cost per year
B	$800,000	$14,000
Mc	$920,000	$13,000

Calculation to find the output at which location B will have high profit than location Mc:

To find out at what range of output the location B will have higher profits compared to the location Mc draw graphs of the two cost functions TC_B and TC_Mc besides the revenues TR as shown below.

The graph lines for TC_B and TC_Mc intersect at a production volume of 120 machine tools.

The location B is cost effective up to a production volume of 120 units. Therefore, profitability also will be higher at location B upto a production level of 120 units.

Hence, upto production level of 120 units Location B will have high profit.

c)

Summary Introduction

To determine: The output at which location Mc will have high profit than location B.

Answer to Problem 19P

For production level above 120 units Location Mc will have high profit.

Explanation of Solution

Given information:

Site	Fixed cost per year	Variable cost per year
B	$800,000	$14,000
Mc	$920,000	$13,000

Calculation to find the output at which location Mc will have high profit than location B:

For production volumes above 120 machine tools, the Mc location is preferable as costs are lower and the profitability improves.

Hence, above production level of 120 units Location Mc will have high profit.

d)

Summary Introduction

To determine: The break-even point of each location.

Answer to Problem 19P

The break-even point for location B is 54 machine tools and for location Mc is 58 machine tools.

Explanation of Solution

Given information:

Site	Fixed cost per year	Variable cost per year
B	$800,000	$14,000
Mc	$920,000	$13,000

Calculation of break-even point:

Calculate the break even point for Bhnm location by linking equations (1) and (2), since at the break even point the total revenues are same as total costs.

$\begin{array}{c}14,000\times x+800,000=29,000\times x\\ 15,000x=800,000\\ x=\frac{800,000}{\begin{array}{c}15,000\\ =53.3\end{array}}\end{array}$

Ignoring the fractional part, the location B breaks even at a production volume of 54 machine tools.

Similarly calculate the break even point for Mckny location by linking equations (1) and (3), since at the break even point the total revenues are same as total costs.

$\begin{array}{c}13,000\times x+920,000=29,000\times x\\ 16,000x=920,000\\ x=\frac{920,000}{16,000}\\ x=57.5\end{array}$

Ignoring the fractional part, the Mc location breaks even at a production volume of 58 machine tools. Breakeven production volumes for both the locations are much below the crossover production volume of 120 machine tools.

Hence, the break-even point for location B is 54 machine tools and for location Mc is 58 machine tools.