414.3
3. You are trying to decide between two computer
systems for your firm, both of which perform the same function.
The first one lasts 4 years and the present value of all of its
costs is $50,000. The second one lasts for 3 years and the
present value of all of its costs is $40,000. You plan to commit
to one of the systems for the next 12 years (thus you will have
to replace which ever system you choose with an identical one at
the end of its life). If the correct discount rate for this
project is 6%, which should you choose? (2)
This is an EAC question because the projects have different lives and will have to be repeated.
The first step in calculating an EAC is to get the PV of all of the relevant cash flows. The two computers perform the same function, so the benefits are the same over the 12 years. The question is which has lower costs. In order to compare something that costs $50000 over 4 years with something that costs $40000 over 3 years, you must put them on equal footing--per year. The way to do this is to compute the EAC, which is just the smooth annual cash flow with the same present value as the actual cash flows of the project.
\( \Large 50000 = EAC(A) \left [ \frac{1}{.06} - \frac{1}{.06\left(1+.06 \right )^{4} } \right ] \)
\( \LARGE EAC(A) = \frac{50{,}000} { \left [ \frac{1}{.06} - \frac{1}{\left(1+.06 \right )^{4} } \right ]} = 14{,}429.57 \)
\( \Large 40000 = EAC(B) \left [ \frac{1}{.06} - \frac{1}{.06\left(1+.06 \right )^{3} } \right ] \)
\( \LARGE EAC(B) = \frac{40{,}000} { \left [ \frac{1}{.06} - \frac{1}{\left(1+.06 \right )^{3} } \right ]} = 14{,}964.39 \)
We would take the 4 year system. It costs more, but you get 4 years of use out of it, and on a per-year basis, it actually ends up costing less.