Problem #1
As we know, the total profit can be calculated as revenue minus total cost. In turn, revenue is price multiplied by the quantity, total cost is variable cost plus fixed cost. The fixed cost is to run a manufacturing batch, which is equal to $250,000. The variable cost is marginal cost multiplied by the number of boards produced:
VC=MC*Q=2*200000=$400,000
Hence, the total cost is equal to:
TC=250000+400000=$650,000
The revenue can be calculated as follows:
TR=P*Q=5*200000=$1,000,000
Then, the profit of manufacturing 200,000 boards initially is:
π=1000000-650000=$350,000
Note that this is a potential profit, in case if SAEL orders another delivery of 100,000 boards. In case if they do not order it, there will be a $150,000 loss instead of profit.
Problem #2
The company has the following options to select:
Produce 100,000 boards initially
Produce 200,000 boards initially
In both options, there are the following cases:
SAEL will order an additional delivery in 3 months
SAEL will not order the second delivery
The decision tree has the following form:
Problem #3
We have to calculate the expected profit for all the four cases mentioned in the problem #2.
In case #1, BUYU produces only 100,000 boards initially, and then SAEL orders another 100,000. In this case, the manufacturing batch will be running two times:
FC=2*250000=$500,000VC=2*200000=$400,000TC=400000+500000=$900,000TR=1000000-900000=$100,000
The expected profit in case #1 is $100,000.
In case #2, produces only 100,000 boards initially, and then SAEL does not order another 100,000. In this case, the manufacturing batch will be run only one time.
FC=$250,000VC=2*100000=$200,000TC=250000+200000=$450,000
TR=PQ=5*100000=$500,000π=500000-450000=$50,000
The expected profit in case #2 is $50,000.
Since, in the first option the company acts in the conditions of uncertainty, we have to calculate the expected profit of the second option. We know that the chances that SAEL will order the second delivery is 50%. Hence, the expected profit on the 2nd option is:
100000*0.5+50000*0.5=$75,000
In case #3, BUYU produces 200,000 boards initially, and then SAEL orders another 100,000. In this case, the manufacturing batch will be run one time:
FC=$250,000VC=2*200000=$400,000
TC=250000+400000=$650,000
TR=P*Q=5*200000=$1,000,000
π=1000000-650000=$350,000
The expected profit in case #3 is $350,000.
In case #4, BUYU produces 200,000 boards initially, and then SAEL does not order another 100,000. In this case, the manufacturing batch will be run one time.
FC=$250,000VC=2*200000=$400,000
TC=250000+400000=$650,000
TR=P*Q=5*100000=$500,000
π=500000-650000=-$150,000
The expected profit in case #4 is -$150,000. The company loses $150,000.
Since, in the second option the company acts in the conditions of uncertainty, we have to calculate the expected profit of the second option. We know that the chances that SAEL will order the second delivery is 50%. Hence, the expected profit on the 2nd option is:
350000*0.5+-150000*0.5=$100,000
Since the expected profit in option #2 is better, we suggest to take a risk and produce 200,000 boards initially.
Problem #4
The company may receive a profit from $100,000 to $350,000 if SAEL orders a new delivery.
The expected value of a perfect information is:
EVPI=EV|PI-EMV=0.5*100000+0.5*350000-100000=$125,000
Problem #5
If the company is risk averse with a risk tolerance of $100,000, it will choose option #1, because it provides no risks of being in the loss. In this case, the expected monetary value is $75,000.
The expected value of a perfect information is:
EVPI=EV|PI-EMV=0.5*100000+0.5*350000-75000=$150,000
