Question

Williams Inc. produces a single product, a part used in the manufacture of automobile transmissions. Known for its quality and performance, the part is sold to luxury auto manufacturers around the world. Because this is a quality product, Williams has some flexibility in pricing the part. The firm calculates the price using a variety of pricing methods and then chooses the final price based on that information and other strategic information. A summary of the key cost information follows. Williams expects to manufacture and sell 55,500 parts in the coming year. While the demand for Williams’s part has been growing in the past 2 years, management is not only aware of the cyclical nature of the automobile industry, but also concerned about market share and profits during the industry’s current downturn.

	Total Costs
Variable manufacturing	$	4,669,000
Variable selling and administrative		844,650
Facility-level fixed overhead		2,334,875
Fixed selling and administrative		664,495
Batch-level fixed overhead		349,000
Total investment in product line		22,339,000
Expected sales (units)		55,500

Required:

1. Determine the price for the part using a markup of 39% of full manufacturing cost.

2. Determine the price for the part using a markup of 20% of full life-cycle cost.

3. Determine the price for the part using a desired gross margin percentage to sales of 40%.

4. Determine the price for the part using a desired life-cycle cost margin percentage to sales of 27%.

5. Determine the price for the part using a desired before-tax return on investment of 14%.

6. Determine the total contribution margin and total operating profit for each of the methods in requirements 1 through 5.

Answer 1

1. Price using markup of 39% of full manufacturing Cost

   PARTICULARS	AMOUNT (in $)
   Variable Manufacturing Costs	$4,669,000
   Facility level Fixed Overhead	$2,334,875
   Batch level Fixed Overhead	$349,000
   Total Manufacturing Costs (A)	$7,352,875
   Variable Selling and Administrative overheads	$844,650
   Fixed Selling and Administrative overheads	$664,495
   Total Selling and Administrative overheads (B)	$1,509,145
   Total Costs ( A+ B )	$8,862,020
   Add : Margin @ 39% of $7,352,875	$2,867,621.25
   Total Sale	$11,729,641.25
   No. of Units	55,500
   Price per Unit ( Sales / No. of units)	$211.34

2. Price using markup of 20% of full life cycle Cost

   PARTICULARS	AMOUNT (in $)
   Variable Manufacturing Costs	$4,669,000
   Facility level Fixed Overhead	$2,334,875
   Batch level Fixed Overhead	$349,000
   Total Manufacturing Costs (A)	$7,352,875
   Variable Selling and Administrative overheads	$844,650
   Fixed Selling and Administrative overheads	$664,495
   Total Selling and Administrative overheads (B)	$1,509,145
   Total Costs ( A+ B )	$8,862,020
   Add : Margin @ 20% of $8,862,020	$1,772,404
   Total Sale	$10,634,424
   No. of Units	55,500
   Price per Unit ( Sales / No. of units)	$191.61

3. Price Using desired gross margin prcentage to sales of 40%

   PARTICULARS	AMOUNT (in $)
   Variable Manufacturing Costs	$4,669,000
   Facility level Fixed Overhead	$2,334,875
   Batch level Fixed Overhead	$349,000
   Total Manufacturing Costs (A)	$7,352,875
   Variable Selling and Administrative overheads	$844,650
   Fixed Selling and Administrative overheads	$664,495
   Total Selling and Administrative overheads (B)	$1,509,145
   Total Costs ( A+ B )	$8,862,020
   Add : Margin ( See note below the table)	$3,393,016.76
   Total Sale	$12,255,036.76
   No. of Units	55,500
   Price per Unit ( Sales / No. of units)	$220.81

   
   Let sales be $100 then profit is $40 and cost is $60 ( $100 - $40)
   Now if Gross margin on sales is 40% then
   Gross margin on cost is 40/60 *100 = 66.67%
   Gross Profit = 66.67% of $7,352,875 = $4,902,161.76
   Less : Selling & Administrative Cost = $1,509,145
   Margin = $3,393,016.76
   
4. Price using desired life-cycle cost margin percentage to sales of 27%
   

   PARTICULARS	AMOUNT (in $)
   Variable Manufacturing Costs	$4,669,000
   Facility level Fixed Overhead	$2,334,875
   Batch level Fixed Overhead	$349,000
   Total Manufacturing Costs (A)	$7,352,875
   Variable Selling and Administrative overheads	$844,650
   Fixed Selling and Administrative overheads	$664,495
   Total Selling and Administrative overheads (B)	$1,509,145
   Total Costs ( A+ B )	$8,862,020
   Add : Margin @ 36.98% of $8,862,020 (see note below the table)	$3,277,174.99
   Total Sale	$12,139,194.99
   No. of Units	55,500
   Price per Unit ( Sales / No. of units)	$218.72

   
   Let sales be $100 then profit is $ 27 and cost is $73( $100 - $27)
   Now if margin percentage to sales is 27% then
   margin percentage to cost is 27/73 *100 = 36.98%
   
5. Price using desired before tax return on investment of 14%
   

   PARTICULARS	AMOUNT (in $)
   Variable Manufacturing Costs	$4,669,000
   Facility level Fixed Overhead	$2,334,875
   Batch level Fixed Overhead	$349,000
   Total Manufacturing Costs (A)	$7,352,875
   Variable Selling and Administrative overheads	$844,650
   Fixed Selling and Administrative overheads	$664,495
   Total Selling and Administrative overheads (B)	$1,509,145
   Total Costs ( A+ B )	$8,862,020
   Add : Margin @14% of $22,339,000	$3,127,460
   Total Sale	$11,989,480
   No. of Units	55,500
   Price per Unit ( Sales / No. of units)	$216.03

   
   
6. Calculation of total Contribution and total operating profit

   Particulars	Method 1	Method 2	Method 3	Method 4	Method 5
   Sales	$11,729,641.25	$10,634,424	$12,255,036.76	$12,139,194.99	$11,989,480
   Variable costs:
   Variable Manufacturing Costs	$4,669,000	$4,669,000	$4,669,000	$4,669,000	$4,669,000
   Variable Selling & Administrative costs	$844,650	$844,650	$844,650	$844,650	$844,650
   Total Variable Costs	$5,513,650	$5,513,650	$5,513,650	$5,513,650	$5,513,650
   Contribution ( Sales - Total Variable costs)	$6,215,991.25	$5,120,774	$6,741,386.76	$6,625,544.99	$6,475,830
   Fixed Costs :
   Facility level fixed overhead	$2,334,875	$2,334,875	$2,334,875	$2,334,875	$2,334,875
   Fixed selling & administrative overhead	$664,495	$664,495	$664,495	$664,495	$664,495
   Batch level fixed overhead	$349,000	$349,000	$349,000	$349,000	$349,000
   Total Fixed Costs	$3,348,370	$3,348,370	$3,348,370	$3,348,370	$3,348,370
   Profit ( Contribution - Total Fixed Costs)	$2,867,621.25	$1,772,404	$3,393,016.76	$3,277,174.99	$3,127,460