7. You are considering the possibility of replacing an existing machine that has a book value of $500,000, a remaining depreciable life of five years, and a salvage value of $300,000. The replacement machine will cost $2 million and have a ten-year life. Assuming that you use straight-line depreciation and that neither machine will have any salvage value at the end of the next ten years, how much would you need to save each year to make the change (the tax rate is 40 percent)

 $221344.48

Explanation:

Book value of existing machine = $500,000

remaining depreciable life = 5 years

salvage value = $300,000

cost of replacement machine = $2 million

depreciable life = 10 years

Tax rate = 40 %

Difference in the cost of new machine and salvage value of existing machine

= 2,000,000 - 300,000 = $1,700,000

Calculate the depreciation tax benefit of new machine = ( 500,000 / 5 ) * 0.4 = $40,000

next calculate the present value of this tax benefit

=  $40000,PVAF(1.10,5years)^5 ( 1 )

where the Annuity of 5 years at 10% = 1/(1.10)5  = 3.7907)

Insert value into equation 1 (to calculate the present value of the tax benefit

=  40000*3.79078676 = $1,51,631.47 ( present value of tax benefit )

Determine the Annual depreciation tax advantage of the new machine  

=  (2,000,000/10)*0.40 = $80,000

Determine present value of this annuity

= $80,000,PVAF(1.10,10years)^10 ( 2 )

where the Annuity of 5 years at 10% = 1/(1.10)^10 ) = 6.144567

Insert value into equation2 ( to calculate the present value of this annuity )

= 80000 * 6.144567 = $491565.36

Therefore the Net cost of the new machine will be

=   $491565.36  -  $151631.47  -  $1,700,000  = $1,360,066

Annual savings on the new machine in 10 years

= 1,360,066 /  6.144567  =  $221344.48

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