Chapter 11, Problem 6PA

Product pricing using the cost-plus approach methods; differential analysis for accepting additional business

Crystal Displays Inc. recently began production of a new product, flat panel displays, which required the investment of $1,500,000 in assets. The costs of producing and selling 5,000 units of flat panel displays are estimated as follows:

Crystal Displays Inc. is currently considering establishing a selling price for flat panel displays. The president of Crystal Displays has decided to use the cost-plus approach to product pricing and has indicated that the displays must earn a 15% return on invested assets.

Instructions

1. 1. Determine the amount of desired profit from the production and sale of flat panel displays.
2. 2. Assuming that the product cost method is used, determine (A) the cost amount per unit, (B) the markup percentage, and (C) the selling price of flat panel displays.
3. 3. (Appendix) Assuming that the total cost method is used, determine (A) the cost amount per unit, (B) the markup percentage (rounded to two decimal places), and (C) the selling price of flat panel displays. (Round markup to nearest whole dollar.)
4. 4. (Appendix) Assuming that the variable cost method is used, determine (A) the cost amount per unit, (B) the markup percentage (rounded to two decimal places), and (C) the selling price of flat panel displays. (Round markup to nearest whole dollar.)
5. 5. Comment on any additional considerations that could influence establishing the selling price for flat panel displays.
6. 6. Assume that as of August 1, 3,000 units of flat panel displays have been produced and sold during the current year. Analysis of the domestic market indicates that 2,000 additional units are expected to be sold during the remainder of the year at the normal product price determined under the product cost method. On August 3, Crystal Displays Inc. received an offer from Maple Leaf Visual Inc. for 800 units of flat panel displays at $225 each. Maple Leaf Visual Inc. will market the units in Canada under its own brand name, and no variable selling and administrative expenses associated with the sale will be incurred by Crystal Displays Inc. The additional business is not expected to affect the domestic sales of flat panel displays, and the additional units could be produced using existing factory, selling, and administrative capacity.
   1. A. Prepare a differential analysis of the proposed sale to Maple Leaf Visual Inc.
   2. B. Based on the differential analysis in part (A), should the proposal be accepted?

To determine

Ascertain the desired profit of Company CD.

Explanation of Solution

Product pricing: Product pricing is the method used for fixing the price for the products sold or the services offered to the consumers.

Product cost pricing: Product cost pricing is a pricing technique which sums up the costs involved in the production of the product alone and the markup is added to the sum.

$\text{Product Cost per unit = }\frac{\text{Total Product Cost}}{\text{Estimated Units Produced and sold}}$

Total cost pricing: Total cost pricing is a pricing technique which sums up all the costs involved in the production of the product and the markup is added to the sum.

Total Variable Cost: Total variable cost refers to the costs involved in the production of the product.

Markup Percentage: The markup percentage is the percentage of additional costs added to the product cost to get the selling price of the product.

$\text{Markup Percentage = }\frac{\left(\begin{array}{l}\text{Desired}\\ \text{Profit}\end{array}\right)\text{ + }\left(\begin{array}{l}\text{Total Selling and}\\ \text{Admininstrative Expenses}\end{array}\right)}{\text{Total Product Cost}}$

Selling Price: Selling price is calculated by summing up the product cost per unit and the per unit markup cost

Desired Profit: Company CD aims at earning a profit of 15% of the total investment made of $1,500,000.

Calculate the desired profit of Company CD.

  $\begin{array}{c}\text{Desired profit = 15\% of Invested assets}\\ \text{= \$1,500,000 × 15\%}\\ \text{= \$1,500,000 × }\frac{\text{15}}{\text{100}}\\ \text{= \$255,000}\end{array}$

Hence, the desired profit of Company CD is $225,000

To determine

Calculate on the basis of product cost concept, for Company CD

1.                i.        Cost per unit
2.              ii.       Markup percentage
3.           iii.        Selling price of flat panel displays

Explanation of Solution

Product cost pricing: Product cost pricing is a pricing technique which sums up the costs involved in the production of the product alone and the markup is added to the sum.

i)

Calculate the cost per unit of flat panel display.

Variable Cost   (1)	$1,000,000
Fixed Cost	$250,000
Total	$1,250,000
Divide by: Number of units	5,000
Cost per unit	$250
(Table 1)

Hence, the cost per unit of flat panel display is $250.

Working Note:

(1) Calculate the variable cost.

  $\begin{array}{c}\text{Varaible Cost=}\left(\begin{array}{c}\text{Direct Materials+Direct Labor}\\ \text{+Factory Overhead}\end{array}\right)\text{ ×5000 units}\\ \text{=}\left(\text{\$120+\$30+\$50}\right)\text{ ×5,000 units}\\ \text{= \$200 ×5,000 units}\\ \text{= \$1,000,000}\end{array}$

ii)

Calculate the markup percentage of flat panel display.

     $\begin{array}{c}\text{Markup Percentage = }\frac{\left(\begin{array}{l}\text{Desired}\\ \text{Profit}\end{array}\right)\text{ + }\left(\begin{array}{l}\text{Total Selling and}\\ \text{Admininstrative Expenses}\end{array}\right)}{\text{Total Product Cost}}\\ \text{= }\frac{\text{\$225,000 + \$150,000+ }\left(\text{\$35×5,000 units}\right)}{\text{\$1,250,000}}\\ \text{= }\frac{\text{\$375,000+\$175,000}}{\text{\$1,250,000}}\\ \text{= }\frac{\text{\$550,000}}{\text{\$1,250,000}}\\ \text{= 44\%}\end{array}$

Hence, the markup percentage of flat panel display is 44%,

iii)

Calculate the selling price per unit of flat panel display

Cost per unit	$250
Markup per unit $\left(\text{\$}250\times 44\text{\%}\right)$	$110
Selling price per unit	$360

(Table 2)

Hence, the selling price per unit of flat panel display is $360.

To determine

Calculate on the basis of total cost concept, for Company CD

1.                i.        Cost per unit
2.              ii.       Markup percentage
3.           iii.        Selling price of flat panel displays

Explanation of Solution

Total cost pricing: Total cost pricing is a pricing technique which sums up all the costs involved in the production of the product and the markup is added to the sum.

i)

Calculate the cost per unit of flat panel display.

Variable Cost $\left(\text{\$235×5,000 units}\right)$	$1,175,000
Fixed Cost $\left(\text{\$250,000 + \$150,000}\right)$	$400,000
Total	$1,575,000
Divide by: Number of units	5,000
Cost per unit	$315

(Table 3)

Hence, the cost per unit of flat panel display is $315.

ii)

Calculate the markup percentage of flat panel display (rounded).

  $\begin{array}{c}\text{Markup Percentage = }\frac{\text{Desired Profit}}{\text{Total Costs}}\\ \text{= }\frac{\text{\$225,000}}{\text{\$1,575,000}}\\ \text{= 14}\text{.29\% }\left(\text{rounded}\right)\end{array}$

Hence, the markup percentage of flat panel display, rounded o 2 places is 14.29%,

iii)

Calculate the selling price per unit of flat panel display

Cost per unit	$315
Markup per unit $\left(\text{\$}315\times 14.29\text{\%}\right)$	$45
Selling price per unit	$360

(Table 4)

Hence, the selling price per unit of flat panel display is $360.

To determine

Calculate on the basis of variable cost concept, for Company CD

1.           i.        Cost per unit
2.         ii.        Markup percentage
3.       iii.        Selling price of flat panel displays

Explanation of Solution

Total Variable Cost: Total variable cost refers to the costs involved in the production of the product.

i)

Variable cost per unit of flat panel display is $235.

Total variable cost of flat panel display is $1,175,000$\left(\text{\$}235\times 5,000\text{ units}\right)$.

ii)

Calculate the markup percentage of flat panel display.

  $\begin{array}{c}\text{Markup Percentage = }\frac{\left(\begin{array}{l}\text{Desired}\\ \text{Profit}\end{array}\right)\text{ + }\left(\text{Total Fixed Costs}\right)}{\text{Total Variable Cost}}\\ \text{= }\frac{\text{\$225,000 + \$250,000+ \$150,000}}{\text{\$1,175,000}}\\ \text{= }\frac{\text{\$625,000}}{\text{\$1,175,000}}\\ \text{= 53}\text{.19\%}\end{array}$

Hence, the markup percentage of flat panel display is 53.19%,

iii)

Calculate the selling price per unit of flat panel display

Cost per unit	$235
Markup per unit $\left(\text{\$}235\times 53.19\text{\%}\right)$	$125
Selling price per unit	$360

(Table 5)

Hence, the selling price per unit of flat panel display is $360.

To determine

Comment on any other considerations that would influence the price of flat panel display.

Explanation of Solution

Company CD should consider the following things before determining the price of flat panel display.

• • The general price of flat panel displays in the market, the competitive price must be considered.
• • The price should be revised in short run instead of fixing a price for long run.

To determine

Prepare the differential analysis of Company CD, for the proposed offer to either accept or reject it.

Explanation of Solution

Prepare the differential analysis for Company CD for the given alternatives.

Differential Analysis of Company CD
Reject Order (Alt 1) or Accept Order (Alt 2)
August 03
	Reject Order (Alternative 1)	Accept Order (Alternative 1)	Differential Effect on income
Revenues	$0	$180,000	$180,000
Costs
Variable Manufacturing Costs	$0	(2)   (-)  $152,000	(-)   $152,000
Income (loss), per unit	$0	$28,000	$28,000

(Table 6)

The differential analysis of Company CD shows a profit of $28,000 on accepting the offer, hence the offer should be accepted.

Working Note:

(2) Calculate the variable manufacturing cost.

    $\begin{array}{c}\text{Varaible Manufacturing Cost=}\left(\begin{array}{l}\text{Offer price }-\text{ Selling and}\\ \text{Administrative Expenses}\end{array}\right)\text{ ×800 units}\\ \text{=}\left(\text{\$225 }-\text{\$35}\right)\text{ ×800 units}\\ \text{= \$190 ×800 units}\\ \text{= \$152,000}\end{array}$

To determine

Calculate on the basis of differential analysis of Company CD, should the proposed offer be accepted or not.

Explanation of Solution

 The differential analysis of Company CD shows a profit of $28,000 on accepting the offer. If the offer is not accepted the Company CD may not be able to generate the revenue of $28,000; hence the offer should be accepted