A manager is trying to decide whether to build a small, medium, or large facilit

Question

A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.40, 0.35, and 0.25, respectively A small facility is expected to earn an after-tax net present value of just $24,000 if demand is low. If demand is average, the small facility is expected to earn $25,000; it can be increased to medium size to earn a net present value of $30,000. If demand is high, the small facility is expected to earn $50,000 and can be expanded to medium size to earn $60,000 or to large size to earn $155,000 A medium-sized facility is expected to lose an estimated $75,000 if demand is low and earn $90,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $100,000; it can be expanded to a large size for a net payoff of $115,000 If a large facility is built and demand is high, earnings are expected to be $160,000. If demand is average for the large facility, the present value is expected to be $80,000; if demand is low, the facility is expected to lose $80,000 Choose the correct decision tree below. Note that each payoff is given in thousands ($000)

Explanation / Answer

Large facility

At point 1, Payoff = 0.25*160+0.35*80-0.4*80 = 44000 $

Medium facility

At point 2, Payoff = 115 $ when expanded to large facility

At point 1, Payoff = 0.25*115+0.35*90-0.4*75 = 30250 $

Small facility

At point 3, Payoff = 155 $ when expanded to large facility

At point 4, Payoff = 30 $ when expanded to medium facility

At point 1, Payoff = 0.25*155+0.35*30+0.4*24 = 58850 $

Hence, the management should build a small facility in order to achieve the highest expected payoff of 58850 $

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