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Case4.1a A firm plans to begin production of a new small appliance. Management should decide whether to make the small engine of this product in-plant, or buy it from an outside source. If management decide to make the engine, then there are 2 alternatives (1) To built it with a simple manufacturing system, or (2) To built it with an advanced manufacturing system. The fixed cost of alternative (1) is 10,000$ / year and its variable cost is 8$ per unit. The fixed cost of alternative (2) is 30,000$ / year and its variable cost is 5$ per unit. Purchase price of the engine depends on the volume of purchase. Price is 10$ per unit if volume is less than per year. However, it is reduced to 7$ if sales exceed per year. (Price of all units are reduced to 7$) Prepare a table and tell the management what to do. Include all your calculation.
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Manufacturing; Alternatives (1) and (2)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Q= Q 3Q=20000 30,000+5Q 10,000+8Q Q=6667
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Purchasing; No discount
If the demand is between 0 and 6667, Alternative (1) is preferred to Alternative (2). But is alternative (1) preferred to buy? Is alternative (2) preferred to buy with discount? Is alternative (1) preferred to buy? Total cost of alternative (1) is 10,000+8Q Total cost of buy is 10Q We intersect them 10,000+8Q=10Q 2Q = 10,000 Q=5000
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Summary (I) Theretofore, if the demand is between 0 and 5000,
Buy is preferred to Alternative (1). Up to know we could summarize our conclusion as follows Demand Recommendation Q <= Buy 5000 < Q < = Built : Alternative (1) 6667 < Q < Alternative 2
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Purchasing (With discount)
But what about after 12000, Is Alternative (2) preferred to buy with discount? We write their total cost formula Total cost of (2) is 30,000+5Q Total cost of buy with discount is 7Q We intersect them 30,000+ 5Q = 7Q 2Q = 30,000 Q = 15000 From 12,000 up to 15,000, buy with discount is better than built
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Summary (II) If our demand forecast is 0< Q < 5000 Buy
If our demand forecast is 5000 =< Q < Built (1) If our demand forecast is 6667 =< Q < Built (2) If our demand forecast is =< Q < Buy ( discounted) If our demand forecast is =< Q Built (2) But we still need a correction? What is that. Does has any meaning to you?
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Purchase more that what is needed?
What is the total cost of at discounted price? 12000(7)= 84000 Are we ready to spend more, and get less than 12000? Therefore, we manufacture using alternative 2 only up to a point where the total cost is 84000 TC of Alternative 2 is Q Q<=84000 5Q<= 54000 Q<10800 If demand >1080 do not manufacture, purchase at cost of $7
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Summary (Final) If our demand forecast is 0< Q < 5000 Buy
If our demand forecast is 5000 =< Q < Built (1) If our demand forecast is 6667 =< Q < Built (2) If our demand forecast is =< Q < Buy ( or more) If our demand forecast is =< Q Built (2)
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Case4.1b (1) You can manufacture a product at your own plant or buy it from outside. If you manufacture it, F = 900, V= 1. If you buy it, P = 4 up to 400 units. P=2 for any additional unit . Conduct BEP analysis. Note, the analysis is the same as if you were supposed to sell the product at the above prices. (2) Now suppose F= 1800, Conduct a BEP analysis. (3) Now again suppose F=900, V=1. However, P = 4 if you want to buy up to 400 units or less, if you buy more than 400, the price is P=2 for all units, No P=4. Conduct a BEP analysis.
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Manufacturing Cost ( F= 900, V=1)
2000 1800 1600 1400 TC=900+Q 1200 1000 800 600 400 200 100 200 300 400 500 600 700 800 900 1000
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Purchasing Cost ( P= 4, after 400, P=2 for additions)
2000 TR=1600+2(Q-400) TR=800+2Q 1800 1600 1400 1200 1000 TR=4Q 800 600 400 200 100 200 300 400 500 600 700 800 900 1000 F = 900, V= 1, P = 4 up to 400 units, any unit after that P=2
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Break Even Analysis; F=900, V=1, P=4 then 2
2000 TR=800+2Q 1800 TC=900+Q 1600 1400 F+VQ = PQ 900+ Q = 4Q 900 = 3Q Q = 300 1200 1000 TR=4Q 800 600 400 200 100 200 300 400 500 600 700 800 900 1000 F = 900, V= 1, P = 4 up to 400 units, any unit after that P=2
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Now suppose F= 1800, Find the BEP.
TR=800+2Q 1800+Q = 4Q Q = 600 TC=1800+Q TR=4Q 2000 1800 1600 1400 1200 1000 800 600 400 200 100 200 300 400 500 600 700 800 900 1000
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Break Even Analysis F=1800, V= 1, P= 4 then 2
TR=800+2Q TC=1800+Q 1800+Q = 800+2Q Q= 1000 2000 1800 1600 1400 1200 1000 TR=4Q 800 600 400 200 100 200 300 400 500 600 700 800 900 1000
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Break Even Analysis; F=900, V=1, P=4 or 2
Now again suppose F=900, V=1 P = 4 if you want to sell up to 400 units, if you want to sell more you need to have P=2 from the beginning, No P=4. Find the BEP
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P=4 or P=2 TR=4Q TR=2Q 2000 1800 1600 1400 1200 1000 800 600 400 200 100 200 300 400 500 600 700 800 900 1000
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Purchasing Cost TR=2Q TR=4Q 2000 1800 1600 1400 1200 1000 800 600 400
300 400 500 600 700 800 900 1000
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How Many BEPs? 900+ Q = 4Q Q = 300 TC=900+Q 900+ Q = 2Q Q = 900 TR=2Q
2000 1800 900+ Q = 4Q Q = 300 1600 TC=900+Q 900+ Q = 2Q Q = 900 1400 TR=2Q 1200 1000 800 600 TR=4Q 400 200 100 200 300 400 500 600 700 800 900 1000
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How Many BEPs? 2000 1800 1600 1400 1200 1000 800 600 400 B M B M 200 100 200 300 400 500 600 700 800 900 1000
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Purchasing Cost TR=2Q TR=4Q 2000 1800 1600 1400 1200 1000 800 600 400
300 400 500 600 700 800 900 1000
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The Actual Purchase Cost curve
2000 1800 1600 TR=2Q 1400 1200 1000 TR=400 800 600 TR=4Q 4Q=2(400) Q=200 400 200 100 200 300 400 500 600 700 800 900 1000
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Only One BEP TC=900+Q 2Q=900+Q Q=900 TR=2Q TR=400 TR=4Q 2000 1800 1600
1400 TR=2Q 1200 1000 TR=400 800 600 TR=4Q 400 200 100 200 300 400 500 600 700 800 900 1000
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