Homework 6 (Key) Chapter 7 in the text book, Problems: 10, 15, 12, 17, 24, 25 7-10. The purchase price of a natural gas-fired commercial boiler (capacity X) was $181,000 eight years ago. Another boiler of the same basic design, except with capacity 1.42X, is being considered to purchase. If it is purchased, some optional features presently costing $28,000 would be added for your application. If the cost index was 162 for this type of equipment when the capacity X boiler was purchased, and is 221 now, and the applicable cost capacity factor is 0.8, what is your estimate of the purchase price for the new boiler? Let C A = cost of new boiler S A = 1.42 X C B = cost of new boiler S B = X C A = $181,000 *(221/162) = $246,920 C B = $246,920 *(1.42 X/X) 0.8 = $326,879 Total cost with options = $326,879 + $28,000 =$354,879 7-15. A 250-ft 2 shell and tube heat exchanger was purchased for $13,500 in 1989 when the index value was 830. Estimate the cost of a 150-ft 2 shell and tube heat exchanger in 2001 when the index value is 964 and the appropriate cost capacity factor is 0.6. C 2001 (250 ft 2 ) = $13,500*(964/830) = $15,680 C 2001 (150 ft 2 ) = $15,680*(150/250) 0.6 = $11,541 7-12. If an ammonia plant that produces 500,000 pounds per year cost $2,500,000 to construct eight years ago, what would a 1,500,000-pound-per year plant cost now? Suppose that the construction cost index has increased an average rate of 12% per year of the past eight years and that the cost-capacity factor (X) to reflect the economy of scale is 0.65. C B (8 years ago) = $2,500,000 C B (now) = 2,500,000*(1.12) 8 = $6,189,908 S A = 1,500,000 lbs/yr S B = 500,000 lbs/yr X = 0.65 C A = C B (S A /S B ) X = $6,189,908*(1,500,000/500,000) 0.65 = $12,641,919 1
7-17. The standard labor hours per output unit for Product A were based on a time study of the thirty-second unit. If the learning curve, based on previous experience with similar products, is 85%, (a) what was the number of hours required for the first unit and (b) what is the estimated number of hours needed for the 1,000 th output unit? Z 32 = 8.74 hours; s = 0.85 (85% learning curve); n = (log 0.85)/(log 2) = - 0.2345 (a) Z 32 = K*(32) 0.2345 = 8.74 K = (8.74)/(32) -0.2345 = 19.7 hours (b) Z 1000 = 19.7*(1000) 0.2345 = 3.9 hours 7-24. You have been asked to estimate the per unit selling price of a new line of widgets. Pertinent data are as follows: Direct labor rate $15.00 per hour Production material $375 per 100 widgets Factory overhead 125% of direct labor Packing costs 75% of direct labor Desired profit 20% of total manufacturing cost Past experience has shown that an 80% learning curve applies to the labor required for producing widgets. The time to complete the first widget has been estimated to be 1.76 hours. Use the estimated time to complete the 50 th widget as your as your standard time for the purpose of estimating the unit selling price. The estimate of direct labor hours is based on the time to produce the 50 th unit. K = 1.76 hours s = 0.8 (80% learning curve) n = (log 0.8)/(log 2) = -0.322 Z 50 = 1.76*(50) -0.322 = 0.5 hours Factory Labor = ($15/hr)*(0.5 hr/widget) = $7.50 / widget Production Material = $375 / 100 widgets = $3.75 / widget Factory Overhead = (1.25)*($7.50 / widget) = $9.375 / widget Packing Cost = (0.75)*($7.50 / widget) = $5.625 / widget Total Manufacturing Cost = $26.25 / widget Desired Profit = (0.20)*($26.25 / widget) = $5.25 / widget Unit Selling Price = 31.50 / widget 2
7-25. A personal computer company is trying to bring a new model of PC ( Pentium Plus ) to the market. According to the marketing department, the best selling price for a similar model from a world-class competitor is $2,500 per computer. The company wants to sell at the same price as its best competitor. The cost breakdown of the new model is shown below: Assembling time for the 1 st unit: 1.00 hr Handling time: 10% of Assembling Time Direct labor rate: $15/hr Planning labor: 10% of Direct Labor Quality Control: 50% of Direct Labor Factory Overhead: 200% of Total Labor General & Administrative expense: 300% of Total Labor Direct material cost: $200/per computer Outside manufacture: $2000/per computer Packing cost: 10% of Total Labor Facility rental: 10% of Total Labor Profit: 20% of Total Manufacturing Cost Number of Units: 20,000 Since the company mainly produces sub-assemblies purchased from other manufacturers and repackages the product, the direct material cost is estimated at only $200 per computer. Direct labor time consists of handling time and assembling time. The company estimates the learning curve for assembling the new model is 95%. How can the company reduce its cost to meet the best competitors price? Before examining potential cost reductions, the current manufacturing cost must be estimated. Total Direct Labor Time = Assembly Time + Handling Time A 95% learning curve applies to the assembly time K = 1 hr, s = 0.95, n = log 0.95 / log2 = -0.074 20000 Time to assemble all 20,000 units = (1)S 1 (u) -0.074 T 20,000 = 10,378.26 hours Adding in handling time as 10% of assembly time Total Factory (direct) Labor = (10,378.26)*(1.1) = 11,416.09 hours 3
Using the table (from the book), the total manufacturing cost and selling price are $2,284.94 and $2,741.92 respectively. MANUFACTURING COST ELEMENTS Unit Estimate Units Cost/ Units Factor of Row Row Total A. Factory Labor 11416.09 $15.00 $171,241.35 B. Planning Labor 10% A 17,124.14 C. Quality Control 50% A 85,620.68 D. TOTAL LABOR $273,986.17 E. Factory Overhead 200% D 547,972.32 F. General & Admin. Expense 300% D 821,958.48 G. Production Material 20000 $200.00 4,000,000 H. Outside Manufacture 20000 $2,000.00 40,000,000 I. SUBTOTAL 45,643,916.97 J. Packaging Costs 10% D 27,398.62 K. TOTAL DIRECT CHARGE 45,671,315.59 L. Other Direct Charge M. Facility Rental 10% D 27,398.62 N. TOYAL MANUFACTURING COST 45,698,714.21 O. Quantity (lot size) 20000 P. MANUFACTURING COST/ UNIT 2,284.94 Q. Profit/ Fee 20% P 456.99 R. UNIT SELLING PRICE 2,741.93 Given the competitor s selling price of $2,500 and assuming a desired return on sales of 20%, the target cost is given by: Target Cost = (1 0.2)*($2,500) = $2,000 It will be difficult for the company to assemble the computer for less than $2,000. The estimated outside manufacturing cost alone is $2,000 per computer. This cost should be reduced if the target cost of $2000 is to be achieved. 4
As shown in the following table, the cost of $2,00 can be reached if the outside manufacturing cost can be reduced to 1,715 (a 14.25 reduction). MANUFACTURING COST ELEMENTS Unit Estimate Units Cost/ Units Factor of Row Row Total A. Factory Labor 11416.09 $15.00 $171,241.35 B. Planning Labor 10% A 17,124.14 C. Quality Control 50% A 85,620.68 D. TOTAL LABOR $273,986.17 E. Factory Overhead 200% D 547,972.32 F. General & Admin. Expense 300% D 821,958.48 G. Production Material 20000 $200.00 4,000,000 H. Outside Manufacture 20000 $1,715.06 34,301,286 I. SUBTOTAL 39,945,202.78 J. Packaging Costs 10% D 27,398.62 K. TOTAL DIRECT CHARGE 39,972,601.40 L. Other Direct Charge M. Facility Rental 10% D 27,398.62 N. TOYAL MANUFACTURING COST 40,000,000.02 O. Quantity (lot size) 20000 P. MANUFACTURING COST/ UNIT 2,000.00 Q. Profit/ Fee 20% P 400 R. UNIT SELLING PRICE 2,400.00 5