Answer:
$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
