Summer CH4 Solutions

Summer CH4 Solutions - MIME 310 ENGINEERING ECONOMY...

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1 M I M E 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM EXERCISES – PRODUCTION AND COST ANALYSES 1. According to the information given, both the revenue and cost functions associated with snow removal activities are linear. i) The number of hours required to break even (Q * ) is determined from the following relation- ship: Q * = FC / (f - vc) in which FC represents the daily fixed cost, f the hourly fee, and vc the constant average variable cost. Q * = 70 / (30.00 - 12.50) = 4 hours ii) The additional number of hours required to produce a before-tax profit of $60 is deter- mined by dividing the profit requirement by the contribution margin, i.e. (f - vc): 60 / (30.00 - 12.50) = 3.4 Thus, the total number of hours required is 7.4. 2. At the annual sales volume of 80 000 units, and in the absence of depreciation allowances, the taxable income (TI) is: TI = 80 000 p - (FC + 80 000 vc) = 80 000 p - [100 000 + 80 000 (5)] = 80 000 p - 500 000 in which p is the selling price, FC the fixed costs, and vc the average variable cost at a produc- tion rate of 80 000 units per year . Therefore, the after-tax profit (TP) is: TP = 80 000 p - 500 000 - t (80 000 p - 500 000) = (80 000 p - 500 000) (1 - t) in which t is the tax rate. For an after-tax profit of $20 000, (80 000 p - 500 000) (1 - 0.45) = 20 000 and p = 6.705 A selling price of $6.70 per unit is required.
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2 3. The plant's annual budget of $8.5 million consists of $8 million of operating expenses and the $0.5 million contribution to the city's general fund. If the water-softening circuit is added to the facility, the operation should again just break even, with the same $0.5 million contribution to the city's general fund. Therefore, the increase in costs should be balanced by the increase in revenues: 300 000 + VC = 8 500 000 (0.1) in which VC represents the maximum allowable amount to be spent on additional chemical products. VC = 850 000 - 300 000 = 550 000 A maximum of $550 000 (or $0.025 per 1000 litres) can be spent on the additional chemicals required by the water-softening circuit without jeopardizing the contribution to the city's general fund. 4. According to the information given, the revenue function associated with the packaging process is linear. As the unit bulk product and packaging material costs are constant, the average variable cost is constant and equal to: vc = (113 500 + 11 500) / 25 000 = 5 i) Under current conditions, the break-even quantity is: Q * = FC / (p - vc) = 120 000 / (10 - 5) = 24 000 packages per year ii) Under the proposed conditions, the following would apply. Sales volume: 25 000 (1 + 0.6) = 40 000 Selling price: 10 (1 - 0.15) = 8.50 Fixed costs: 120 000 Average constant bulk product cost: 113 500 / 25 000 = 4.54 Average constant packaging cost: (1 + 0.4) (11 500 / 25 000) = 0.644 Thus, the average variable cost would increase to: vc = 4.54 + 0.644= 5.184 Therefore, the break-even quantity would be: Q * = 120 000 / (8.50 - 5.184) = 36 188 packages per year
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.

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Summer CH4 Solutions - MIME 310 ENGINEERING ECONOMY...

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