For the $900,000 machine, the probabilities of different outcomes are as follows:

(a) The single most likely outcome (with 65.6% probability) is that the machine will operate for all 5 years (because there is only a 10% breakage probability each year). At this most likely outcome, the present value would be PV = ($300,000/0.12) . (1 − 1/1.125) ≈ $1,081,433. The NPV would be $181,433.

(b) The expected lifetime of the machine is about 4.1 years. If the machine lasted for 4 years, the present value would be $911,205.

(c) The true expected value is $906,737.

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Scenario D WD WWD Probability 10% 90% 10% 90% 10% WWWD 90% 3. 10% WWWWD Exp Val 1 - rest = 0.10 = 0.09 = 0.081 = 0.0729 = 0.6561 Lifetime (years) 1 2 3 4 5 4.095 PV $267,857 $507,015 $720,549 $911,205 $1,081,433 $906,737