Question

A machine shop owner is thinking of expanding his operations. He has 3 options: a drill press, a lathe, and a grinder. The return on investment for each tool is largely determined by whether the company wins a government military contract. The profit and loss for each purchase and the probabilities associated with each contract outcome are shown in the payoff table below: Contract No Contract Purchase 0.40 0.60 Drill Press Lathe $40,000 $20,000 $12,000 ($8,000) $4,000 $10,000 Grinder Part 1) Compute for the expected value of each alternative and select the best option. The owner of the machine shop was approached by a consultant who offered to help ascertain whether the owner will win the government contract. The consultant previously worked for the military and maintained strong connections with various personnel within the military. The owner found out that there is a 0.70 probability that the consultant would present a favorable report, given that the contract is awarded to the shop and a 0.80 probability that the consultant would present an unfavorable report, given that the contract is not awarded. Part 2) Using a decision tree analysis, determine the best strategy for the owner of the machine shop. Include the expected value (EMV) of the strategy and the maximum fee that the owner should pay the consultant.

Answer 1

Expected value can be used to assess the options or alternatives available and make the decisions that are best suited to the organisation. There can be multiple outcomes of a single decision and hence the values of all the alternatives needs to be analysed and the highest value should be chosen in case of revenues and lowest in case of costs.

Formula for EV :

EV = Summation of the (probability of outcome x value of outcomes)

Purchase	Probability of getting contract	Probability of not getting contract	Expected value	Calculation
Probability	0.4	0.6
Drill Press	40000	(8000)	$ 11,200	40,000x0.4+(8000)x 0.6
Lathe	20000	4000	$ 10,400	20000 x 0.4+4000x 0.6
Grinder	12000	10000	$ 10,800	12000x 0.4+10000x0.6

The above matrix shows the expected value of the profit and loss for each of the purchases and since it is related profits we choose the highest value as the best option.

Drill Press is the best option as it has the highest expected monteary value -: $ 11,200

B	It is assumed the contractor has been hired and the report is favourable or unfavourable and the
	EMV has been calculated . Hence probability of awarding the contract is not considered.
	Price paid to the contractor = Highest price in table below - Highest price in (a) above
	=27200-11200=16000
Tabular representation using Decision tree analysis
	If	Nature of Report	Alternative	Amounts	Probability	EMV of alternatives
	Contract is awarded					( Jt prob x Amount )
	0.4	Favourable report	Drill Press	$       40,000	0.7	$                   28,000.00
		0.7	Lathe	$       20,000	$                   14,000.00
			Grinder	$       12,000	$                     8,400.00
		Unfavourable report	Drill Press	$       40,000	0.2	$                     8,000.00
		0.2	Lathe	$       20,000	$                     4,000.00
			Grinder	$       12,000	$                     2,400.00
	Contract is not awarded	Favourable report	Drill Press	$       (8,000)	0.3	$                   (2,400.00)
		0.3	Lathe	$         4,000	$                     1,200.00
	0.6		Grinder	$       10,000	$                     3,000.00
		Unfavourable report
		0.8	Drill Press	$       (8,000)	0.8	$                   (6,400.00)
			Lathe	$         4,000	$                     3,200.00
			Grinder	$       10,000	$                     8,000.00
	EMV for Drill =	28000+8000-2400-6400	$             27,200
	EMV for Lathe =	14000+4000+1200+3200	$             22,400
	EMV for Grinder =	8400+2400+3000+8000	$             21,800