Answer:
Techron I $ 84,403.55
Techron II $ 70,526.47
Explanation:
we will calculate the present worth for each millng machine and then the equivalent annual cost
Techron I
depreciation 261,000 - 47,000 = 214,000
214,000 / 3 = 71,333.33 depreciation per year
then we calcualte the tax shield:
71,333.33 x 35% = 24.966,67
70,000 operating cost:
tax shield for operating cost: 70,000 x 35% = 24,500
Annual cash outflow: 70,000 - 24,500 - 24,966.67 = 20,533.33
now we calculate the present value of a three years annuity of 20,533.33 discounted at 9%:
[tex]20533.33 \times \frac{1-(1+0.09)^{-3} }{0.09} = PV\\[/tex]
PV $51,975.9087
and the present value of the salvage value:
[tex]\frac{47000}{(1 + 0.09)^{3} } = PV[/tex]
PV 36,292.62
Present worth:
261,000 + 51,975.91 - 36,292.62 = 276,683.29
last, we claculate the PTM of an annuity which present value is 276,683.29
Equivalent Annual Cost
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $276,683.29
time 3
rate 0.09
[tex]276683.29 \div \frac{1-(1+0.09)^{-3} }{0.09} = C\\[/tex]
C $ 84,403.554
For Techron II we do the same:
net operaing cost:
depreciation tax shield: (455,000 - 47,000)/5 x 0.35 = 28,560)
operating cost after-tax 43,000 x (1-.35 ) = 27,950
net cash flow: 28,560 - 27,950 = 610 (is positive as the tax shield is greater than the operting cost)
present value of the cash inflow:
[tex]610 \times \frac{1-(1+0.09)^{-5} }{0.09} = PV\\[/tex]
PV $2,372.6873
present value of salvage value
[tex]\frac{47000}{(1 + 0.09)^{5} } = PV[/tex]
PV 30,546.78
Net Present value:
455,000 - 2,372.69 - 30,546,78 = 422080,53
Equivalent annual cost:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $422,080.53
time 5
rate 0.09
[tex]422080.53 \div \frac{1-(1+0.09)^{-5} }{0.09} = C\\[/tex]
C $ 70,526.473
