Question

A construction firm is deciding on whether to bid on a government project. The preparation of the bid costs $100,000 and has a 25% chance of success. If the bid is successful, then the firm has an 80% chance of making $500,000 and a 20% chance of losing $200,000, minus the cost of the bid preparation. If the bid fails, the cost of bid preparation is lost. If the firm decides not to bid, the money it would have spent on bid preparation accrues 10% interest.
(a) Construct a decision tree to account for all decision alternatives, states of nature, and associated payoffs.
(b) Calculate the expected payoff if the firm decides to bid.

(c) According to your analysis, recommend whether the firm should bid or not bid based on the expected value approach.

Answer 1

(a)

(b) If the firm decides to bid, then there will be 2 outcomes: Sucess and Fail with a probability of 0.25 and 0.75 respectively.

Expected pay-off if the firm bids and it fails = p(loss)* total cost = 0.75* 100000 = -75000 [negative sign denotes loss]

there are 2 outcomes if the firm's bid is successful: Make Profit OR Loss with a probability of 0.80 and 0.20 respectively.

Expected pay-off if the firm's bid is successful and makes profit = [p(success)* p(making profit) * 500,000] - [cost of bid]

= (0.25*0.80*500,000) - 100,000

=100000 - 100000 = 0

Expected pay-off if the firm's bid is successful and inccur a loss = [p(success)*p(loss)*200,000] - [cost of bid]

=(0.25*0.20*200000)- 100000

=10000 - 100000 = - 90000    [negative sign denotes loss]

(c) From the above analysis we can say that the firm should not bid as he is worse off even when the bidding is successful and he makes a profit.

Expected pay-off if the firm does not bid = (10/100)*100000 = 10000

The Firm should not bid.