Homework Answers
Here, the each of 2 machines have an unequal useful lives, 7 Years for Machine-A and 5 Years for Machine-B. Therefore, the machine with lower Equivalent Annual Cost (EAC) should be acquired.
Equivalent Annual Cost (EAC) for MACHINE-A
|
Period |
Annual Cash Flow ($) |
Present Value factor at 8.00% |
Present Value of Cash Flow ($) |
|
1 |
-30,000 |
0.925926 |
-27,777.78 |
|
2 |
-30,000 |
0.857339 |
-25,720.16 |
|
3 |
-30,000 |
0.793832 |
-23,814.97 |
|
4 |
-30,000 |
0.735030 |
-22,050.90 |
|
5 |
-30,000 |
0.680583 |
-20,417.50 |
|
6 |
-30,000 |
0.630170 |
-18,905.09 |
|
7 |
-30,000 |
0.583490 |
-17,504.71 |
|
TOTAL |
5.206370 |
-1,56,191.10 |
|
Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment
= -$156,191.10 - $200,000
= -$356,191.10 (Negative)
Equivalent Annual Cost (EAC) for Machine-A = Net Present Value / [PVIFA 8.00%, 7 Years]
= -$356,191.10 / 5.206370
= -$68,414.48 (Negative)
Equivalent Annual Cost (EAC) for MACHINE-B
|
Period |
Annual Cash Flow ($) |
Present Value factor at 8.00% |
Present Value of Cash Flow ($) |
|
1 |
-25,000 |
0.925926 |
-23,148.15 |
|
2 |
-25,000 |
0.857339 |
-21,433.47 |
|
3 |
-25,000 |
0.793832 |
-19,845.81 |
|
4 |
-25,000 |
0.735030 |
-18,375.75 |
|
5 |
-25,000 |
0.680583 |
-17,014.58 |
|
TOTAL |
3.992710 |
-99,817.75 |
|
Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment
= -$99,817.75 - $150,000
= -$249,817.75 (Negative)
Equivalent Annual Cost (EAC) for Machine-B = Net Present Value / [PVIFA 8.00%, 5 Years]
= -$249,817.75 / 3.992710
= -$62,568.47 (Negative)
DECISION
Here, the MACHINE-B should be selected, since it has the lower Equivalent Annual Cost (EAC) of $62,568.47 as compared to the EAC of Machine-A.
NOTE
The Formula for calculating the Present Value Factor is [1/(1 + r)n], Where “r” is the Discount/Interest Rate and “n” is the number of years.
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