Question

A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time. The estimated probability of low demand is .30, and the estimated probability of high demand is .70. The net present value associated with the purchase of two machines initially is $79,200 if demand is low and $130,600 if demand is high. The net present value for one machine and low demand is $99,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of $124,680. A second option is to subcontract; that would have a net present value of $115,650. The third option is to purchase a second machine. This option would have a net present value of $123,540.

a. What is the EMV (expected monetary value) for alternative buy one machine? The EMV is $.___________

b. What is the EMV (expected monetary value) for alternative buy two machines? The EMV is $.__________

c. How many machines should the manager purchase initially? The manager should purchase__________ machine(s) initially.

Answer 1

a) EMV for one machine = Probability of Low Demand X Net Prsent Value + Probability of High Demand X Net present value

= 0.3 X 99000 + 0.7 X 124680 [out of 3 options with high demand and one machine, the option with highes NPC has been chosen]  

=$116076

b) EMV with two machines = Probability of Low Demand X Net Prsent Value + Probability of High Demand X Net present value

= 0.3 X 79200 + 0.7 X 130600 = $115180

c) Since expected value is more with one machine, the manager should purchase one machine initially