Oscar Co. is contemplating the replacement of an old machine with a new one. The following information has been gathered: Old Machine New Machine Cost $ 250 , 000 $ 500 , 000 Accumulated Depreciation 75 , 000 − 0 - Remaining useful life 10 years − 0 - Useful life − 0 - 10 years Annual operating costs $ 200 , 000 $ 150 , 500 \begin{array}{lll} & ext { Old Machine} & ext { New Machine }\ ext { Cost } & \$ 250,000 & \$ 500,000 \ ext { Accumulated Depreciation } & 75,000 & -0 ext { - } \ ext { Remaining useful life } & 10 ext { years } & -0 ext { - } \ ext { Useful life } & -0 ext { - } & 10 ext { years } \ ext { Annual operating costs } & \$ 200,000 & \$ 150,500\end{array} Cost Accumulated Depreciation Remaining useful life Useful life Annual operating costs Old Machine $250 , 000 75 , 000 10 years − 0 - $200 , 000 New Machine $500 , 000 − 0 - − 0 - 10 years $150 , 500 If the old machine is replaced it can be sold for $20000. The net advantage (disadvantage) of replacing the old machine isA) $15000B) $20000C) $(5000)D) $(50000)

Question

Oscar Co. is contemplating the replacement of an old machine with a new one. The following information has been gathered:    Old Machine  New Machine   Cost  $ 250 , 000 $ 500 , 000  Accumulated Depreciation  75 , 000 − 0  -   Remaining useful life  10  years  − 0  -   Useful life  − 0  -  10  years   Annual operating costs  $ 200 , 000 $ 150 , 500 \begin{array}{lll} & 	ext { Old Machine} & 	ext { New Machine }\	ext { Cost }  &  \$ 250,000  &  \$ 500,000 \	ext { Accumulated Depreciation }  &  75,000  &  -0 	ext { - } \	ext { Remaining useful life }  &  10 	ext { years }  &  -0 	ext { - } \	ext { Useful life }  &  -0 	ext { - }  &  10 	ext { years } \	ext { Annual operating costs }  &  \$ 200,000  &  \$ 150,500\end{array}  Cost   Accumulated Depreciation   Remaining useful life   Useful life   Annual operating costs  ​  Old Machine $250 , 000 75 , 000 10  years  − 0  -  $200 , 000 ​  New Machine  $500 , 000 − 0  -  − 0  -  10  years  $150 , 500 ​   If the old machine is replaced it can be sold for $20000. The net advantage (disadvantage)  of replacing the old machine isA)  $15000B)  $20000C)  $(5000)D)  $(50000)

Megan Causey · Accepted Answer

Final Answer : A, Explanation :   The net advantage of replacing the old machine is the present value of the savings in operating costs over the remaining life of the old machine, less the cost of the new machine plus the salvage value of the old machine.The present value of the savings in operating costs is:  P V = A r ∗ ( 1 − ( 1 + r ) − n ) PV = \frac{A}{r} * (1 - (1 + r)^{-n}) P V = r A ​ ∗ ( 1 − ( 1 + r ) − n )  where:* A is the annual savings in operating costs ($50,000)* r is the discount rate (10%)* n is the number of years (10)  P V = 50 , 000 0.10 ∗ ( 1 − ( 1 + 0.10 ) − 10 ) PV = \frac{50,000}{0.10} * (1 - (1 + 0.10)^{-10}) P V = 0.10 50 , 000 ​ ∗ ( 1 − ( 1 + 0.10 ) − 10 ) PV = $380,773  The net advantage of replacing the old machine is:  P V − ( C o s t o f n e w m a c h i n e − S a l v a g e v a l u e o f o l d m a c h i n e ) PV - (Cost of new machine - Salvage value of old machine) P V − ( C os t o f n e w ma c hin e − S a l v a g e v a l u eo f o l d ma c hin e ) = $380,773 - ($500,000 - $20,000) = $15,773

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