Chapter 11, Problem 45P

1.

To determine

Develop a schematic diagram of the two-stage production process.

Explanation of Solution

Develop a schematic diagram of the two-stage production process:

Figure (1)

Note: In this case, the manufacturing overhead is entirely fixed, as such; hence it is considered a sunk cost with respect to the sell-or-process-further decision.

2.

To determine

Indicate whether the output price $5.10 will affect the all the sales:

Explanation of Solution

In this case, the number of processing hours (Scarce resource) is limited, so the short-term objective would be to maximize the contribution margin per hour of processing time. Contribution margin per hour for output from Process 1 and Process 2 are as follows:

Particulars	Process 1	Process 2
Net selling price per unit (a)	$ 2	$ 5.10
Less: Cost of goods sold
Direct material cost per unit	$ 1.00	$ 1.50
Direct labor cost per unit	$ 0.20	$ 0.40
Transferred in costs from process 1	$ 0.00	$ 1.20
Total variable cost per unit  (b)	$ 1.20	$ 3.10
Contribution margin per unit $\left(\text{c}=\text{a}-\text{b}\right)$	$ 0.80	$ 2.00
Number of hours per unit  (d)
$\left(\frac{1}{60}\right)$	0.0167
$\left(\frac{1+2}{60}\right)$		0.0500
Contribution margin per unit $\left(\frac{\text{c}}{\text{d}}\right)$	$ 47.90	$ 40.00

Table (1)

From the above calculation, it is clear that Contribution margin per unit of Process 1 output is more profitable than output from Process 2. Therefore, the short-run operating income would be maximized if all available hours were used to produce Process #1 output.

3.

To determine

Compute the lowest acceptable selling price per unit for the output from Process 2 to make this output as profitable as the output from Process 1.

Explanation of Solution

Compute the lowest acceptable selling price per unit for the output from Process 2 to make this output as profitable as the output from Process 1:

Particulars	Process 1	Process 2
Current selling price per unit		$5.10 per unit
The required increase in profitability per processing hour $\left(\$48-\$40\right)$	$ 8
Multiply by: One unit of output from Process 2 requires	0.05 hours
Increase in selling price		$0.40
Minimum selling price the output from Process 2		$5.50 per unit

Table (2)

4.

To determine

Compute the following, by Assuming that 50% of the total overhead costs are variable:

Explanation of Solution

Compute the given by Assuming that 50% of the total overhead costs are variable:

Particulars	Process 1	Process 2
Net selling price per unit (a)	$ 2	$ 5.10
Less: Cost of goods sold
Direct material cost per unit	$ 1.00	$ 1.50
Direct labor cost per unit	$ 0.20	$ 0.40
Variable overhead @50%	$0.30	$0.60
Transferred in costs from process 1 $\left(\$1.00+\$0.20+\$0.30\right)$	$ 0.00	$ 1.50
Total variable cost per unit  (b)	$ 1.50	$4.00
Contribution margin per unit $\left(\text{c}=\text{a}-\text{b}\right)$	$ 0.50	$1.10
Number of hours per unit (d)
$\left(\frac{1}{60}\right)$	0.0167
$\left(\frac{1+2}{60}\right)$		0.0500
Contribution margin per unit $\left(\frac{\text{c}}{\text{d}}\right)$	$29.94	$22.00

Table (3)

From the above calculation, it is clear that the conclusion reached above in Requirement 2 still holds.

5.

To determine

Calculate the contribution margin per processing hour using the sensitivity analysis for both Process 1 output and Process 2 output under the given assumptions regarding the percentage of variable overhead costs: 0%, 25%, 50%, and 100%. Perform these calculations for Process 2 output both for a selling price of $5.10 per unit and a selling price of $5.50 per unit.

State the general conclusion that could be drawn on the basis of this sensitivity analysis.

Explanation of Solution

Contribution margin or processing hour
% VOH	$Process\#2sellingprice=\$5.10/unit$			$Process\#2sellingprice=\$5.50/unit$
	P1	P2	Δ	P1	P2	Δ
0%	$48.00	$40.00	$4.00	$48.00	$58.00	$10.00
25%	$39.00	$31.00	$8.00	$39.00	$49.00	$10.00
50%	$30.00	$22.00	$8.00	$30.00	$40.00	$10.00
100%	$12.00	$4.00	$8.00	$12.00	$22.00	$10.00

Table (4)

In this case, the sensitivity analysis aids to explain the result obtained in Requirement 4, and when Process #2 output uses three times as much processing time per unit, when compared to Process #1. This is independent of selling prices and the composition of variable overhead. Moreover, the amount of variable overhead charged per unit of Process #2 output is always three times as much variable overhead charged per unit of output from Process #1.

Since these ratios are “constant across selling prices per unit for output from Process #2 and also constant across levels of variable overhead, the difference in contribution margin per hour between Process #1 and Process #2 output, at each assumed selling price per unit for Process #2 output, will be constant and independent of the proportion of total overhead that is variable”.