Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $290,000, has a three-year life, and has pretax operating costs of $67,000 per year. The Techron II costs $510,000, has a five-year life, and has pretax operating costs of $35,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $40,000. If your tax rate is 35 percent and your discount rate is 10 percent, compute the Equivalent Annual Cost for both machines. Which do you prefer? Why?

Answer 1

Answer:

EAC techron I =   130,996.7425

EAC techron II = 124,386.7141

I would prefer techron II as their annual cost is lower than techron I

Explanation:

The first step is calculate the NPV of each machine

Techron I

investment 290,000

Depreciation per year

acquisition - salvage value = depreciable amount

depreciable amount / useful life = depreciation per year

290,000 - 40,000 = 250,000

250,000/3 = 83,333

The depreication provides a tax-shield so it lowers the annual cost for the machine.

operating cost x (1-t) - depreciation x t = after-tax operating cost

-67,000 x (1-0.35) +83,333 x 0.35 = 14383.45

Now we calculate the present value of there cash outflow for 3 years

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

C -14383.45

time 3

rate 0.1

$14383.45 \times \frac{1-(1+0.1)^{-3} }{0.1} = PV$

PV -$35,769.51

Now the NPV of the machine Techron I

-290,000  -  35,769.51 = -325.769,51‬

We do the same for the second machine Techron II

after-tax cost:

depreciation per year:

(510,000-40,000)/5

-35,000 x (1-.035) +  94,000 x 0.35 = 10.150

The tax shield for the depreciation is high enough it makes cost savings rather than cost outflow.

Now we calculate the present value of this aannuity

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

C 10150

time 5

rate 0.1

$10150 \times \frac{1-(1+0.1)^{-5} }{0.1} = PV$

PV $38,476.49

And the NPV for Techron II

-510,000 + 38,476.49 = (471,523.51‬)

Now we are able to calcualte the EAC for each machine:

$EAC = \frac{NPV \times r}{1 - (1+r)^{-n} }$

First Machine Techron I

$EAC = \frac{-325.769,51 \times 0.10}{1 - (1+0.10)^{-3} }$

EAC techron I = 130996.7425

Second Machine Techron II

$EAC = \frac{-471,523.51 \times 0.10}{1 - (1+0.10)^{-5} }$

EAC techron II = 124386.7141