A five year old machine cost $15,000 when new and is being depreciated on a a st

Question

A five year old machine cost $15,000 when new and is being depreciated on a a straight line basis to a zero salvage value in 5 more years ( 10 years total life.) the operating expenses for this machine are $2500 as of the end of each year. At the end of its life it will be replaced by a new machine that costs $22,000, will last 10 years and have operating costs of $1500 a year. Should we replace it now instead of waiting 5 years? The interest rate is 10% a year and the tax rate 50%. What is the current book value of the old machine ?

Explanation / Answer

Depriciation of existing machine=15000/10 1500 Depriciation of new machine=22000/10 2200 Depriciation Tax shield=0.50*(2200-1500) for 5 years 350 PV of Annuity(350,10%,5)=3.7908*350 (A) 1326.78 Savings from Opearating Cost=(2500-1500) 1000 Savings from Opearating Cost after tax shield=0.5*1000 for 5years 500 PV of Annuity(1000,10%,5)=3.7908*1000 (B) 3790.8 Total Savings =A+B (X) 5117.58 Current Book value of the macchine=15000-5*1500 7500 Extra cost for new machine=22000-7500 (Y) 14500 Since Y>X , we should postpone purchase of the new machine

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