Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $261,000, has a three-year life, and has pretax operating costs of $70,000 per year. The Techron II costs $455,000, has a five-year life, and has pretax operating costs of $43,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $47,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines

Answer 1

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%:

$20533.33 \times \frac{1-(1+0.09)^{-3} }{0.09} = PV$

PV $51,975.9087

and the present value of the salvage value:

$\frac{47000}{(1 + 0.09)^{3} } = PV$  

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

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $276,683.29

time 3

rate 0.09

$276683.29 \div \frac{1-(1+0.09)^{-3} }{0.09} = C$

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:

$610 \times \frac{1-(1+0.09)^{-5} }{0.09} = PV$

PV $2,372.6873

present value of salvage value

$\frac{47000}{(1 + 0.09)^{5} } = PV$  

PV   30,546.78

Net Present value:

455,000 - 2,372.69 - 30,546,78 = 422080,53

Equivalent annual cost:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $422,080.53

time 5

rate 0.09

$422080.53 \div \frac{1-(1+0.09)^{-5} }{0.09} = C$

C  $ 70,526.473