Question

Spacely Sprockets (SS) makes sprockets – surprise! SS can currently produce 1,000 sprockets at a cost of $6/sprocket. SS could produce an additional 2,000 sprockets at a cost of $5/sprocket, but it would need to invest in a new machine at a cost of $8,000. The machine has a life of 2,000 sprockets and no salvage value. Sprocket demand and price are highly variable: there is a 10% probability sprockets will sell for $2/sprocket, a 30% probability of $25/sprocket and a 60% probability of $8/sprocket. The sprockets will be sold in one year and for simplicity assume the discount rate is zero. What is the expected selling price of a sprocket? How many sprockets would SS choose to produce at this price and what is the expected profit at this level of sales? What is the expected profit of the project if you can wait to decide the production level until price and demand are know?

Answer 1

Ans 01 :

Calculation of Expected Price :

Cumulative Price = Probability * Price in each scenario

Expected Price = Sum of Cumulative Price = 0.20 + 7.50 + 4.80 = 12.50

Probability	Price	Cumulative Price = (Probability * Price)
10%	2	0.20
30%	25	7.50
60%	8	4.80

Ans 02 :

Existing Units = 1,000

Cost of Existing Units = $ 6/ Sprocket

Additional Unit = 2,000

Cost of Additional Unit  = $5/sprocket

Machine Cost = $ 8,000

The machine has a life of 2,000 sprockets

Cost of Machine for Each Sprocket = Machine Cost / Units = 8000 / 2000 = $4/sprocket

So Total Cost for Additional Units = $5 + $4 = $9/sprocket

Since the Expected Price ($12.50) is Higher than Cost in Both Scenario ( $ 6/ Sprocket &$9/sprocket)

Total Units can be produced =Existing Units + Additional Units = 1000 + 2000 = 3000

Expected Profit =

Existing Units * ( Expected Price - Cost of Existing Units ) + Additional Unit * ( Expected Price -  Total Cost for Additional Units )

= 1000 * ( 12.5 - 6) + 2000 * ( 12.5 - 9)

= 6500 + 7000

=13,500

Ans : Total Units = 3000 Expected Profit =  13,500

Ans 03 :

expected profit of the project if you can wait to decide the production level until price and demand are know

Scenario 1 : When Orice is $2/sprocet.

Cost in in Both Scenario ( $ 6/ Sprocket &$9/sprocket) is much higher.

Company will not produce any sprocket.

Scenario 2 : When Orice is $25 /sprocet.

Cost in Both Scenario ( $ 6/ Sprocket &$9/sprocket) is much lower.

So company will produce both.

Total Units can be produced =Existing Units + Additional Units = 1000 + 2000 = 3000

Profit =

Existing Units * ( Price - Cost of Existing Units ) + Additional Unit * ( Price -  Total Cost for Additional Units )

= 1000 * ( 25 - 6) + 2000 * ( 25- 9)

= 19000 + 32000

=51,000

Ans : Total Units = 3000 Profit =  51,000

Scenario 3 : When Orice is $8 /sprocket.

Cost in Additional Unit ($9/sprocket) is higher than the price. But cost in existing unit ($ 6/ Sprocket)is less than the price.

So company will produce only existing units.

Total Units can be produced =Existing Units = 1000

Profit =

Existing Units * ( Price  - Cost of Existing Units )  

= 1000 * ( 8 - 6)

= 2000