Question

Q.4 (25pts) Sandersen Meat Processors has asked its lead process engineer to evaluate two different types of conveyors for the beef cutting line. Type A has an initial cost of $82897 and a life of 4 years. Type B has an initial cost of $97452 and a life expectancy of 6 years. The annual operating cost (AOC) for type A is expected to be $8194, while the AOC for type B is expected to be $7056. If the salvage values are $5533 and $10555 for type A and type B, respectively, tabulate the incremental cash flow using their Least Common Multiple (LCM).

Answer 1

The life of the different conveyors for the beef cutting line is not equal. So, use the common multiple method and convert the unequal life to equal life. Type A has a life of 4 years and Type B has a life of 6 years. The LCM of 4 and 6 will be 12. So, the common life of both the alternatives will be 12 years.

Plan A – Is to be repeated for 3 times (0th, 4th and 8th year)

Plan B – Is to be repeated for 2 times (0th and 6th year)

The other information is as given

Plan A	Plan B
Initial Cost = -82897 Annual Operating Cost = -8194 Salvage Value = 5533	Initial Cost = -97452 Annual Operating Cost = -7056 Salvage Value = 10555

Now, tabulating the incremental cash flow using the least common multiple.

The incremental cash flow will be calculated for Plan B – Plan A

Years	Cash Flows of A	Cash Flows of B	ICF of B - A
1	-82897	-97452	-97452 – (-82897) = 14555
2	-8194	-7056	-7056 – (-8194) = 1138
3	-8194	-7056	-7056 – (-8194) = 1138
4	-82897 – 8194 + 5533 = -85558	-7056	-7056 – (-85558) = 78502
5	-8194	-7056	-7056 – (-8194) = 1138
6	-8194	-97452 – 7056 + 10555 =    -93953	-93953 – (-8194) =       -85759
7	-8194	-7056	-7056 – (-8194) = 1138
8	-82897 – 8194 + 5533 = -85558	-7056	-7056 – (-85558) = 78502
9	-8194	-7056	-7056 – (-8194) = 1138
10	-8194	-7056	-7056 – (-8194) = 1138
11	-8194	-7056	-7056 – (-8194) = 1138
12	-8194 + 5533 = -2661	-7056 + 10555 = 3499	3499 – (-2661) = 6160