A machine that costs $2,000 is likely to break irreparably with 20% probability at the end of each year (assuming it worked the previous year). You can neither replace it nor use it for more than 5 years. (Many electric devices without moving parts have such breakdown characteristics.) The machine can produce

$1,000 in profit every year. The discount rate is 12% per annum.

(a) What is the most likely operating time? If this comes true, what is the value?

(b) What is the expected operating time? If this comes true, what is the value?

(c) What is the true net present value of this machine? (Hint: First work this out case by case for a 2-year machine, then for a 3-

year machine. Think “D,” “WD,” “WWD,”

“WWWD,” and “WWWWD,” where W means working and D means dead.)