Certainly! Let's walk through the calculations for the Equivalent Annual Cost (EAC) of both machines and determine which one should be chosen.
1. Understanding EAC:
- The EAC is a measure that converts the net present value (NPV) of costs into an equivalent annual amount. This allows comparison between costs of items with different lifespans.
- Formula:
[tex]\[
EAC = \frac{NPV}{A}
\][/tex]
where [tex]\( A \)[/tex] is the annuity factor calculated using the formula:
[tex]\[
A = \frac{1 - (1 + r)^{-n}}{r}
\][/tex]
where [tex]\( r \)[/tex] is the discount rate and [tex]\( n \)[/tex] is the number of years.
2. Given Data:
- Discount rate ([tex]\( r \)[/tex]): 12% or 0.12
- Tax rate: 0% (so it doesn’t affect the calculation)
- The EACs for the machines are already calculated:
[tex]\[
\text{EAC for Machine A} = 165.81
\][/tex]
[tex]\[
\text{EAC for Machine B} = 146.94
\][/tex]
3. Comparison of EACs:
- Compare the EACs to choose the machine with the lowest annual cost.
4. Decision:
- The EAC for Machine A is 165.81.
- The EAC for Machine B is 146.94.
- Since 146.94 (for Machine B) is less than 165.81 (for Machine A), Machine B is the better option as it incurs lower annual costs.
Conclusion:
In choosing between Machine A and Machine B, based on the calculated EACs:
- Machine A has an EAC of [tex]$165.81
- Machine B has an EAC of $[/tex]146.94
Therefore, you should choose Machine B.
