FIN3010 - WA 8

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Thomas Edison State College *

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301

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Finance

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Feb 20, 2024

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Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro Written Assignment 08 2. The management of a firm wants to introduce a new product. The product will sell for $4 a unit and can be produced by either of two scales of operation. In the first, total costs are TC = $3,000 + $2.8Q. In the second scale of operation, total costs are TC = $5,000 + $2.4Q. a) What is the break-even level of output for each scale of operation? TC = 3000 + 2.8 Q TR = 4 Q 4 = 3000 + 2.8 4q-2.8q = 3000q 1.2q = 3000q q = 3000/1.2 q = 2500 TC=TR TC=$5000+2.4Q TR=4Q 4Q=5000+2.4Q 4Q-2.4Q=5000 1.6Q=5000 Q=5000/1.6 Q=3,125 TC=TR b) What will be the firm’s profits for each scale of operation if sales reach 5,000 units? TC=3000+2.8Q TR=4Q 3000+2.8x5,000 $4x5000 $17,000 20,000 TC=$17,000 TR=$20,000 Profit = TR-TC $3,000 TC=5000+2.4Q TR=4Q 5000+2.4x5000 4x5000 17,000 20,000 TC=17,000 TR=20,000 Profit = TR - TC 3,000
Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro c) One-half of the fixed costs are noncash (depreciation). All other expenses are for cash. If sales are 2,000 units, will cash receipts cover cash expenses for each scale of operation? TC 3000+2.8Q TR=4Q FC 3,000 4x2000 VC 2.8 TR=8000 TC 3000/2+2.8Q 1,500+2.8Q 1,500+2.8x2000 TC= 7,100 Cash Receipts 8000 > 7100 Expense First operation: Cash covers expenses TC=5000+2.4Q TR=4Q FC=5000 4x2000 VC=2.4Q TR=8000 TC=5000/2 + 2.4Q TC=2,500+2.4Q TC=2,500+2.4x2000 TC=7,300 Cash Receipts > 8000, 7300 expense Second operation also covers expenses d) The anticipated levels of sales are the following: Years Unit Sales 1 4000 2 5000 3 6000 4 7000
Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro If management selects the scale of production with higher fixed cost, what can it expect in years 1 and 2? On what grounds can management justify selecting this scale of operation? If sales reach only 5,000 a year, was the correct scale of operation chosen? TC =5000+2.4Q Q= 4000 $14,600.00 TR=$4Q Profit = TR-TC $16,000.00 $1,400.00 Year 1 TC =5000+2.4Q Q= 5000 $17,000.00 TR=$4Q Profit = TR-TC $20,000.00 $3,000.00 Year 2 Yes, management should choose this operation. Although the higher fixed cost and higher break- even point may seem like a drawback. It is important to note that this is a new product, high fixed costs are expected. Secondly, once the break in point is met, the volume of profit will be much greater. Secondly, yes, even if 5000 is achieved, the profit is still higher than the cheaper operation.
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Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro 3. A firm has the following total revenue and total cost schedules: TR = $2Q. TC = $4,000 + $1.5Q. a. What is the break-even level of output? What is the level of profits at sales of 9,000 units? TR=2Q TR=TC TC=4000+1.5Q 2Q=4000+1.5Q 2Q-1.5Q=4000 0.5Q=4000 Q=4000/0.5 Q=8000 units Break even = 8000 units Profit = TR-TC 2Q-(4000+1.5Q) (2x9000)-(4000+(1.5x9000)) 18,000-(4000+13,5000) 18,000 - 17,500 Profit = $500 Profit = $500 at 9000 units. b. As the result of a major technological breakthrough, the total cost schedule is changed to: TC = $6,000 + $0.5Q.
Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro What is the break-even level of output? What is the level of profits at sales of 9,000 units? TC = 6000+0.5Q Q = 6000/1.5 TR=TC 2q=6000+0.5q Q = 4000 units. 2Q-0.5Q=6,000 1.5Q=6000 Break even = 4000 units Profit = TR - TC 2Q-(6000+0.5Q) (2x9000)-(6000+(0.5x9000)) 18,000-(6000+4500) 18000-10500 7,500 Profit = $7,500 Profit = $7,500 4. The manufacturer of a product that has a variable cost of $2.50 per unit and a total fixed cost of $125,000 wants to determine the level of output necessary to avoid losses. a. What level of sales is necessary to break even if the product is sold for $4.25? What will be the manufacturer’s profit or loss on the sales of 100,000 units? FC 125,000 P 4.25 V 2.5 Q = 71428.57 Rounded = 71429 TC = 375000 Profit = TR - TC TR = 425000 $50,000.00
Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro b. If fixed costs rise to $175,000, what is the new level of sales necessary to break even? FC 175,000 P 4.25 V 2.5 Q = 100000.00 Rounded = 100,000 c. If variable costs decline to $2.25 per unit, what is the new level of sales necessary to break even? FC 125,000 P 4.25 V 2.25 Q = 62500.00 Rounded = 62,500 d. If fixed costs were to increase to $175,000, while variable costs declined to $2.25 per unit, what is the new break-even level of sales? FC 175,000 P 4.25 V 2.25 Q = 87500.00 Rounded = 87,500 e. If a major proportion of fixed costs were noncash (depreciation), would failure to achieve the break- even level of sales imply that the firm cannot pay its current obligations as they come due?
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Christopher Cauble TESU-FIN3010 Dr. Frank DeCaro On the surface no. However, with depreciation in mind, the total fixed costs should lower as time continues. With that in mind the total fixed costs may slowly fall below that required amount due to the total cost component. Suppose $100,000 of the above fixed costs of $125,000 were depreciation expense. What level of sales would be the cash break-even level of sales? FC 25,000 P 4.25 V 2.5 Q = 14285.71 Rounded = 14,286 new FC = 125,000 - 100,000 14,286 units.