Chapter 25, Problem 5BP

a.

To determine

Ascertain the contribution margin per machine hour that each product generates.

Explanation of Solution

Contribution margin:

Contribution margin is a measurement of performance where only revenue and variable costs are taken into consideration. Hence, this measurement is useful in the evaluation of the probable outcomes of decisions including pricing decisions and other marketing strategies that affect primarily revenue and variable costs.

Ascertain the contribution margin of Product R:

$\begin{array}{c}\begin{array}{l}\text{Contribution margin per}\\ \text{machine hour of Product R}\end{array}\}=\frac{\text{Contribution margin per unit}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{\$40}}{0.4\text{ hours per unit}}\\ =\$100\end{array}$

Ascertain the contribution margin of Product T:

$\begin{array}{c}\begin{array}{l}\text{Contribution margin per}\\ \text{machine hour of Product T}\end{array}\}=\frac{\text{Contribution margin per unit}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{\$35}}{1.0\text{ hours per unit}}\\ =\$35\end{array}$

b.

To determine

Indicate the number of units of Product R and Product T that the company should produce if it continues to operate with only one shift, and compute the total contribution margin that this mix would produce each month.

Explanation of Solution

Indicate the number of units of Product R and Product T that the company should produce if it continues to operate with only one shift as follows:

Ascertain the output of Product R:

$\begin{array}{c}\text{Maximum output of Product R}=\frac{\text{Total number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{8 hours }\times \text{22 Working days}}{0.4\text{ hours per unit}}\\ =\frac{\text{\$176 hours per month}}{\text{0}\text{.4 hours per unit}}\\ =\$44\text{0 units}\end{array}$

Ascertain the output of Product T:

$\begin{array}{c}\text{Maximum output of Product T}=\frac{\text{Total number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{8 hours }\times \text{22 Working days}}{\text{1}\text{.0 hours per unit}}\\ =\frac{\text{\$176 hours per month}}{\text{1}\text{.0 hours per unit}}\\ =\$176\text{ units}\end{array}$

From the above calculation it is clear that if the company continues to operate with only one shift, then it would produce a maximum output of 440 units per month of Product R, whereas it would produce only 176 units per month of Product T. Hence the company should produce as much of Product R as possible.

Compute the total contribution margin at recommended sales mix as follows:

$\begin{array}{c}\begin{array}{l}\text{Contribution margin }\\ \text{of Product R}\end{array}\}=\left[\begin{array}{l}\text{Maximum output of Product R}\times \\ \text{Contribution margin per unit of Product R}\end{array}\right]\\ =\text{440 units}\times \$40\text{ per unit}\\ =\$17,600\text{ per month}\end{array}$

c.

To determine

Compute the number of units of Product R and Product T that the company should produce, if it adds another shift, and ascertain the total contribution margin that this mix produce would each month, also explain whether the company should add the new shift.

Explanation of Solution

Compute the number of units of Product R and Product T that the company should produce, if it adds another shift as follows:

Ascertain the output of Product R under extra shift:

$\begin{array}{c}\text{Maximum output of Product R}=\frac{\text{Total number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\left[\text{8 hours}+\text{8 hours}\right]\times \text{22 Working days}}{0.4\text{ hours per unit}}\\ =\frac{\text{\$352 hours per month}}{\text{0}\text{.4 hours per unit}}\\ =\$88\text{0 units}\end{array}$

Ascertain the output of Product T under extra shift:

$\begin{array}{c}\text{Maximum output of Product T}=\frac{\text{Remaining number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{132 hours per month (W}\text{.N}\text{.1)}}{\text{1}\text{.0 hours per unit}}\\ =\frac{\text{\$176 hours per month}}{\text{1}\text{.0 hours per unit}}\\ =\$132\text{ units}\end{array}$

In this case, the maximum unit sales per month are restricted to 550 units. However, the computed level of output under extra shift exceeds the company’s market constraint of 550 units of Product R per month.  Thus the company should produce only 550 units of Product R, and commit the remainder of the productive capacity to Product T.

Working note 1:

Particulars	Hours	Hours
Total hours $\left[\begin{array}{l}\left[\text{8 hours}+\text{8 hours}\right]\\ \times \text{22 Working days}\end{array}\right]$		352 hours
Units of Product R (a)	550 units per month
Hours per unit (b)	0.4 hours
Hours used for Product R $\left(\text{a}\times \text{b}\right)$		220 hours
Hours available for Product T		132 hours

Table (1)

Ascertain the total contribution margin that this mix produce would each month as follows:

Particulars	Units (a)	Contribution per unit (b)	Total$\left(\text{a}\times \text{b}\right)$
Product R	550	$40	$22,000
Product T	132	35	4,620
Less: Extra shift costs			3,250
Total contribution margin			$23,370

Table (2)

Explain whether the company should add the new shift as follows:

The company should add the new shift, because the contribution margin of extra shift ($23,370) exceeds the contribution margin generated by one shift alone ($17,600).

d.

To determine

Describe whether the company should pursue the given strategy and explain whether it is recommendable.

Explanation of Solution

Ascertain the output of Product R under the new strategy:

$\begin{array}{c}\text{Maximum output of Product R}=\frac{\text{Total number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\left[\text{8 hours}+\text{8 hours}\right]\times \text{22 Working days}}{0.4\text{ hours per unit}}\\ =\frac{\text{\$352 hours per month}}{\text{0}\text{.4 hours per unit}}\\ =\$88\text{0 units}\end{array}$

Ascertain the output of Product T under the new strategy:

$\begin{array}{c}\text{Maximum output of Product T}=\frac{\text{Remaining number of hours per month}}{\text{Machiner hours to produce 1 unit}}\\ =\frac{\text{82 hours per month (W}\text{.N}\text{.2)}}{\text{1}\text{.0 hours per unit}}\\ =\frac{\text{\$82 hours per month}}{\text{1}\text{.0 hours per unit}}\\ =\$82\text{ units}\end{array}$

In this case, the maximum unit sales per month are extended to 675 units. However, the computed level of output under extra shift exceeds the company’s market constraint of 675 units of Product R per month.  Thus the company should produce only 675 units of Product R, and commit the remainder of the productive capacity to Product T.

Working note 2:

Particulars	Hours	Hours
Total hours $\left[\begin{array}{l}\left[\text{8 hours}+\text{8 hours}\right]\\ \times \text{22 Working days}\end{array}\right]$		352 hours
Units of Product R (a)	675 units per month
Hours per unit (b)	0.4 hours
Hours used for Product R $\left(\text{a}\times \text{b}\right)$		270 hours
Hours available for Product T		82 hours

Table (3)

Ascertain the total contribution margin that this mix produce would each month as follows:

Particulars	Units (a)	Contribution per unit (b)	Total$\left(\text{a}\times \text{b}\right)$
Product R	675	$40	$27,000
Product T	82	35	2,870
Less: Extra shift costs			3,250
Less: Extra marketing costs			4,500
Total contribution margin			$22,120

Table (4)

Explain whether the company should pursue the new strategy as follows:

The company should not pursue the new strategy, because the contribution margin of new strategy ($22,120) is less than the contribution margin of extra shift ($23,370).