Chapter 6, Problem 62IC

Product Costing, Cost Estimation, and Decision Making

I don’t understand this. Last year [year 1], we decided to drop our highest-end Red model and only produce the Yellow and Green models, because the cost system indicated we were losing money on Red. Now, looking at the preliminary numbers, our profit is actually lower than last year and it looks like Yellow has become a money loser, even though our prices, volumes, and direct costs are the same. Can someone please explain this to me and maybe help me decide what to do next year?

Robert Dolan

President & CEO

Dolan Products

Dolan Products is a small, family-owned audio component manufacturer. Several years ago, the company decided to concentrate on only three models, which were sold under many brand names to electronic retailers and mass-market discount stores. For internal purposes, the company uses the product names Red, Yellow, and Green to refer to the three components.

Data on the three models and selected costs follow:

This year (year 2), the company only produced the Yellow and Green models. Total overhead was $650,000. All other volumes, unit prices, costs, and direct labor usage were the same as in year 1. The product cost system at Dolan Products allocates manufacturing overhead based on direct labor-hours.

Required

1. a.      Compute the product costs and gross margins (revenue less cost of goods sold) for the three products and total gross profit for year 1.
2. b.      Compute the product costs and gross margins (revenue less cost of goods sold) for the two remaining products and total gross profit for year 2.
3. c.       Should Dolan Products drop Yellow for year 3? Explain.

To determine

Compute the product costs and gross margins for the three products and total gross profit for year 1.

Answer to Problem 62IC

The values of product costs and gross margins for the three products and total gross profit for Year 1 are as follows:

Particulars	Red	Yellow	Green
Product Cost	$ 978,571	$ 914,286	$ 907,143
Gross Profit	($ 228,571)	$ 85,714	$ 592,857
Gross margin	$200,000	$300,000	$700,000

Table: (1)

Explanation of Solution

Gross margin: Gross margin is calculated by subtracting the cost of goods sold (COGS) from the revenue of the business. It defines the profit earned only because of the production of the goods. It does not account for indirect expenses. It is also known as gross profit.

Total product cost: It includes direct materials cost, direct labor cost, and manufacturing overhead (MOH).

Compute the total product cost:

For Product Red:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$550,000}\left(1\right)\text{+}\text{\$428,571}\left(4\right)\\ \text{=}\text{\$978,571}\end{array}$

For Product Yellow:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$700,000}\left(2\right)\text{+}\text{\$214,286}\left(5\right)\\ \text{=}\text{\$914,286}\end{array}$

For Product Green:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$800,000}\left(3\right)\text{+}\text{\$107,143}\left(6\right)\\ \text{=}\text{\$907,143}\end{array}$

Thus, the values of the total cost for Product Red, Yellow and Green are $978,571, $914,286 and $907,143 respectively.

Compute the gross margins and gross profit for the three products and total gross profit for year 1:

Year 1
Particulars	Red	Yellow	Green	Total
Sales Revenue: $\left(\begin{array}{l}\text{Number}\text{of}\text{units}\text{sold}\\ \text{×}\text{Sales}\text{price}\text{per}\text{unit}\end{array}\right)$	$ 750,000	$ 1,000,000	$ 1,500,000	$ 3,250,000
Less: Variable cost	$ 550,000	$ 700,000	$ 800,000	$ 2,050,000
Gross Margin	$ 200,000	$ 300,000	$700,000	$ 1,200,000
Less: Fixed manufacturing overhead	$ 428,571	$ 214,286	$ 107,143	$ 750,000
Gross profit	($ 228,571)	$ 85,714	$ 592,857	$ 450,000

Table: (2)

Compute the gross margin:

For Product Red:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$750,000}-\text{\$550,000}\left(1\right)\\ \text{=}\text{\$200,000}\end{array}$

For Product Yellow:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$1,000,000}-\text{\$700,000}\left(2\right)\\ \text{=}\text{\$300,000}\end{array}$

For Product Green:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$1,500,000}-\text{\$800,000}\left(3\right)\\ \text{=}\text{\$700,000}\end{array}$

Thus, the value of gross margin for the Product Red, Yellow and Green are $200,000, $300,000 and $700,000 respectively.

Compute the gross profit:

For Product Red:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$750,000}-\text{\$978,571}\\ \text{=}\text{(\$228,571)}\end{array}$

For Product Yellow:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$1,000,000}-\text{\$914,286}\\ \text{=}\$85,714\end{array}$

For Product Green:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$1,500,000}-\text{\$907,143}\\ \text{=}\$592,857\end{array}$

Thus, the values of gross profit for the Product Red, Yellow and Green are ($228,571), $85,714 and $592,857 respectively.

Working note 1:

Compute the variable cost For Product Red:

$\begin{array}{c}\text{Variable}\text{cost}\text{=}\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ \text{=}\text{(\$70}\text{×}\text{5,000)}\text{+}\text{(\$20}\text{×}\text{2}\text{×}\text{5,000)}\\ \text{=}\text{\$550,000}\end{array}$

Working note 2:

Compute the variable cost For Product Yellow:

$\begin{array}{c}\text{Variable}\text{cost}=\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ \text{=}\text{(\$50}\text{×}10\text{,000)}\text{+}\text{(\$20}\text{×}1\text{×}10\text{,000)}\\ \text{=}\text{\$700,000}\end{array}$

Working note 3:

Compute the variable cost For Product Green:

$\begin{array}{c}\text{Variable}\text{cost}\text{=}\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ =\text{(Direct}\text{materials}\text{cost}\text{per}\text{unit}\text{×}\text{Units}\text{produced}\text{and}\text{sold)}\\ \text{+}\text{(Direct}\text{labor-hours}\text{per}\text{unit}\text{×}\text{Wage}\text{rate}\text{per}\text{hour}\\ \text{×}\text{}\text{Units}\text{produced}\text{and}\text{sold)}\\ \text{=}\text{(\$30}\text{×}20\text{,000)}\text{+}\text{(\$20}\text{×}0.5\text{×}20\text{,000)}\\ \text{=}\text{\$800,000}\end{array}$

Working note 4:

Compute the fixed manufacturing overhead For Product Red:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}\text{=}\left(\frac{\text{Total}\text{manufacturing}\text{overhead}}{\text{Total}\text{of}\text{direct}\text{labor-hours}\text{per}\text{unit}}\right)\\ \text{×}\text{Direct}\text{labor-hours}\text{per}\text{unit}\\ \text{=}\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}\text{2}\\ \text{=}\text{\$428,571}\end{array}$

Working note 5:

Compute the fixed manufacturing overhead For Product Yellow:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}\text{=}\left(\frac{\text{Total}\text{manufacturing}\text{overhead}}{\text{Total}\text{of}\text{direct}\text{labor-hours}\text{per}\text{unit}}\right)\\ \text{×}\text{Direct}\text{labor-hours}\text{per}\text{unit}\\ =\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}1\\ \text{=}\$214,286\end{array}$

Working note 6:

Compute the fixed manufacturing overhead For Product Green:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}=\left(\frac{\text{Total}\text{manufacturing}\text{overhead}}{\text{Total}\text{of}\text{direct}\text{labor-hours}\text{per}\text{unit}}\right)\\ \text{×}\text{Direct}\text{labor-hours}\text{per}\text{unit}\\ \text{=}\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}0.5\\ \text{=}\text{\$107,143}\end{array}$

To determine

Compute the product costs and gross margins for the two products and total gross profit for year 2.

Answer to Problem 62IC

The product costs and gross margins for the two products and total gross profit for year 2 are as follows:

Particulars	Yellow	Green
Total Cost	$  1,133,333	$  1,016,667
Gross Profit	$   (133,333)	$     483,333
Gross margin	$     300,000	$     700,000

Table: (3)

Explanation of Solution

Gross margin: Gross margin is calculated by subtracting the cost of goods sold (COGS) from the revenue of the business. It defines the profit earned only because of the production of the goods. It does not account for indirect expenses. It is also known as gross profit.

Total product cost: It includes direct materials cost, direct labor cost, and manufacturing overhead (MOH).

Compute the total product costs For Product Red:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$550,000}\text{+}\text{\$428,571}\\ \text{=}\text{\$978,571}\end{array}$

Thus, the value of total production costs for Product Green is $978,571.

Compute the total product costs For Product Yellow:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$700,000}\text{+}\text{\$214,286}\\ \text{=}\text{\$914,286}\end{array}$

Thus, the value of total production costs for Product Yellow is $914,286.

Compute the total product costs For Product Green:

$\begin{array}{c}\text{Total}\text{product}\text{cost}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{manufacturing}\text{overhead}\\ \text{=}\text{\$800,000}\text{+}\text{\$107,143}\\ \text{=}\text{\$907,143}\end{array}$

Thus, the value of total production costs for Product Green is $907,143.

Compute the gross margins for the three products and total gross profit for year 2:

Year 2
Particulars	Yellow	Green	Total
Sales Revenue	$  1,000,000	$  1,500,000	$  2,500,000
Less: Variable cost	$     700,000	$     800,000	$  1,500,000
Gross Margin	$     300,000	$     700,000	$  1,000,000
Less: Fixed manufacturing overhead	$     433,333	$     216,667	$     650,000
Gross profit	$   (133,333)	$     483,333	$     350,000

Table: (4)

Compute the gross margin for Product Red:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$750,000}-\text{\$550,000}\\ \text{=}\text{\$200,000}\end{array}$

Thus, the value of the gross margin for Product Red is $200,000.

Compute the gross margin for Product Yellow:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$1,000,000}-\text{\$700,000}\\ \text{=}\text{\$300,000}\end{array}$

Thus, the value of the gross margin for Product Yellow is $300,000.

Compute the gross margin for Product Green:

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\text{Revenue}-\text{Variable}\text{cost}\\ \text{=}\text{\$1,500,000}-\text{\$800,000}\\ \text{=}\text{\$700,000}\end{array}$

Thus, the value of the gross margin for Product Green is $700,000.

Compute the gross profit for Product Red:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$750,000}-\text{\$978,571}\\ \text{=}\text{(\$228,571)}\end{array}$

Thus, the value of gross profit for Product Red is ($228,571).

Compute the gross profit for Product Yellow:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$1,000,000}-\text{\$914,286}\\ \text{=}\$85,714\end{array}$

Thus, the value of gross profit for Product Yellow is $85,714.

Compute the gross profit for Product Green:

$\begin{array}{c}\text{Gross}\text{profit}\text{=}\left(\text{Sales}\text{revenue}-\text{Total}\text{cost}\right)\\ \text{=}\text{\$1,500,000}-\text{\$907,143}\\ \text{=}\$592,857\end{array}$

Working note 1:

Compute the variable cost for Product Red:

$\begin{array}{c}\text{Variable}\text{cost}\text{=}\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ \text{=}\text{(\$70}\text{×}\text{5,000)}\text{+}\text{(\$20}\text{×}\text{2}\text{×}\text{5,000)}\\ \text{=}\text{\$350,000}\text{+}\text{\$200,000}\\ \text{=}\text{\$550,000}\end{array}$

Working note 2:

Compute the variable cost for Product Yellow:

$\begin{array}{c}\text{Variable}\text{cost}\text{=}\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ \text{=}\text{(\$50}\text{×}10\text{,000)}\text{+}\text{(\$20}\text{×}1\text{×}10\text{,000)}\\ \text{=}\text{\$500,000}\text{+}\text{\$200,000}\\ \text{=}\text{\$700,000}\end{array}$

Working note 3:

Compute the variable cost for Green:

$\begin{array}{c}\text{Variable}\text{cost}=\text{Direct}\text{materials}\text{cost}\text{+}\text{Direct}\text{labor}\text{cost}\\ \text{=}\text{(\$30}\text{×}20\text{,000)}\text{+}\text{(\$20}\text{×}0.5\text{×}20\text{,000)}\\ \text{=}\text{\$600,000}\text{+}\text{\$200,000}\\ \text{=}\text{\$800,000}\end{array}$

Working note 4:

Compute the fixed manufacturing overhead for Product Red:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}\text{=}\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}\text{2}\\ \text{=}\text{\$214,285}\text{.71}\text{×}\text{2}\\ \text{=}\text{\$428,571}\end{array}$

Working note 5:

Compute the fixed manufacturing overhead for Product Yellow:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}\text{=}\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}1\\ \text{=}\text{\$214,285}\text{.71}\text{×}1\\ \text{=}\$214,286\end{array}$

Working note 6:

Compute the fixed manufacturing overhead for Product Green:

$\begin{array}{c}\text{Fixed}\text{manufacturing}\text{overhead}\text{=}\left(\frac{\text{\$750,000}}{\text{2+1+0}\text{.5}}\right)\text{×}0.5\\ \text{=}\text{\$214,285}\text{.71}\text{×}0.5\\ \text{=}\text{\$107,143}\end{array}$

To determine

Explain should the product Yellow be dropped or not for year 3.

Explanation of Solution

No, the product Yellow should not be dropped for Year 3. Product Red was dropped for the production for year 2. The total manufacturing overhead was reduced by $100,000. The implication of a reduction of $100,000 might seem favorable as well. Reduction in cost would directly result in more profit.

But, in the situation given, reduction in total manufacturing overhead by eliminating the product Red has reduced the gross profit and gross margin as well. Gross profit was declined to $483,333 from $592,857 resulting in an 18% decrease in gross profit. 

For Year 1 the total cost, gross profit and gross margin for Products Red, Yellow and Green are as follow:

Particulars	Red	Yellow	Green	Total
Total cost	$ 978,571	$ 914,286	$ 907,143	$ 2,800,000
Gross profit	($ 228,571)	$ 85,714	$ 592,857	$ 450,000
Gross margin	$ 200,000	$ 300,000	$ 700,000	$ 1,200,000

Table: (5)

For Year 2 the total cost, gross profit and gross margin for Products Red, Yellow and Green are as follow:

Particulars	Yellow	Green	Total
Total Cost	$  1,133,333	$  1,016,667	$  2,150,000
Gross Profit	$   (133,333)	$     483,333	$     350,000
Gross margin	$     300,000	$     700,000	$  1,000,000

Table: (6)

Due to the elimination of product Red total gross profit has been reduced to $350,000. The reduction of $100,000 implies the reduction in cost as a whole. The total gross profit has declined by 18%.

But, to evaluate both the years separately the total impact on the cost and profit is negligible and there is a difference of 4% in gross margin with respect to total cost.

Hence, it is not advisable to drop the Product Yellow.