Question

A company is considering submitting a tender for a job.
Producing the tender will cost the company $1500, which must be paid even if the company does not win the tender
The company's current expectation of the cost of the project is that there is a 0.58 probability that the cost is $7700, and otherwise the cost is $10900. These costs do not include the cost
of producing the tender.
The company also believes that their is a 0.28 probability that the lowest competing bid will be $9200, a 0.37 probability that the lowest competing bid will be $14400, and otherwise the
lowest competing bid will be $12000
In regard to the tender price the company is considering whether it should bid $10600, bid $13200, or not bid.
You may assume that the probabilities given for the costs of the project are independent to the probabilities of the values of the lowest competing bid. Thus if they submit a price of $13200
then the probability that they will make the maximum profit ($13200 - $7700 - $1500 = $4000) is P(winning) * P(low cost) = 0.37 * 0.58.
Draw a decision tree that represents this situation and show all EMVs and probabilities. Indicate selection of decision options with probability = 1 for preferred
options and probability = 0 for rejected options.
Monetary values should be answered to the nearest dollar. Probabilities should be answered to three decimal places.

Answer 1

The company is coonsidering 3 choices

1. Bid $10,600

   1. The company will lose the tender if the lowest competing bid is less than $10,600. The probability that competing bid is less than $10,600 is the (probability that the lowest competing bid is 9200) = 0.28. This is the probability of losing the tender. The probability of winning = 1- 0.28=0.72

2. Bid $13200
   1. The company will win the tender if the lowest competing bid is more than $13200. The probability that competing bid is more than $13200 is the (probability that the lowest competing bid is $14440) = 0.37. This is the probability of winning the tender. The probability of losing = 1- 0.37=0.63
3. No bid

If it bids, then the cost of tender is $1500. If it wins then the cost of the project may be low($7700) with a probability of 0.58 or it could be high ($10900) with a probability of 0.42

The following is the decision tree

We move from right to left of the decison tree

Chance node 4:

• Revenue from the project $10600
• The cost of tender $1500
• the cost of the project is $10,900 with a probaility p(high cost)=0.42.
  • The payoff = 10600 - 1500 - 10900 = -$1800
• the cost of the project is $7700 with a probaility p(low cost)=0.58
  • The payoff = 10600 - 1500 - 7700 = $1400

EMV(node 4)= (payoff when high cost)*(probability of high cost) +(payoff when low cost)*(probability of low cost) = -1800*0.42+1400*0.58 = $56

Chance node 5:

• Revenue from the project $13200
• The cost of tender $1500
• the cost of the project is $10,900 with a probaility p(high cost)=0.42.
  • The payoff = 13200 - 1500 - 10900 = $800
• the cost of the project is $7700 with a probaility p(low cost)=0.58
  • The payoff = 13200 - 1500 - 7700 = $4000

EMV(node 5)= (payoff when high cost)*(probability of high cost) +(payoff when low cost)*(probability of low cost) = 800*0.42+4000*0.58 = $2656

Chance node 2:

• The probability of winning the tender when the bid is $10,600 = p(win) = 0.72. The EMV of when win is $56 (from node 4)
• The probability of losing the tender is p(lose) = 0.28. The company would lose the tender cost of $1500.

EMV(node 2) = (payoff if win)*(probability of winning) +(payoff when lose)*(probability of losing) = 56*0.72-1500*0.28 = -$380

Chance node 3:

• The probability of winning the tender when the bid is $13,200 = p(win) = 0.37. The EMV of when win is $2656 (from node 5)
• The probability of losing the tender is p(lose) = 0.63. The company would lose the tender cost of $1500.

EMV(node 3) = (payoff if win)*(probability of winning) +(payoff when lose)*(probability of losing) = 2656*0.37-1500*0.63 = $38

At node 1 the copany has 3 choices.

1. Bid $10,600. EMV = -$380
2. Bid $13200. EMV = $38
3. Do not bid . EMV = $0

Since bidding $13200 gives the highest expected monitory value of $38, the company should bid at $13,200