Normal depreciation

Q12.24 A machine that costs $2,000 is likely to break irreparably with 20% probability at the end of each year (assuming it worked the previ- ous 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 (a) What is the most likely operating time? If (b) What is the expected operating time? If this 12% per annum. this comes true, what is the value? 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.) Q12.24 A machine that costs $2,000 is likely to break irreparably with 20% probability at the end of each year (assuming it worked the previ- ous 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 (a) What is the most likely operating time? If (b) What is the expected operating time? If this 12% per annum. this comes true, what is the value? 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.)