Question

office in Ontario is considering buying a 3-D printing machine. The office is choosing hetween two 3-D printing inachines that use Fused Deposition Modeling (FDM) technology. The office has a MARR (Minimum Acceptable Rate of Return) of 7%. The salvage value for both machines at the end of their service lives is expected to he $400. Use the information in the table below to answer the following questions Price Running cost per year Maintenance cost Machine A S6,400 $1,200 $600 for the first year, increasing by S100/year thereafter 6 years Machine B $4,400 $1,400 $400 for the first year, increasing by $140/year thereafter 4 years Liſe a) State the necessary assumption to compare mutually exclusive alternatives of different lives. (4 Marls) b) Which alternative is more economic based on Annual Worth comparison? (6 Marks) c) Which alternative is more economic hased on Present Worth comparison? (6 Marks) d) For a four-year study period, what salvage value for machine A would take it the preferred choice? (6 Marks) e) Do both methods (Present Worth and Annual Worth) always yield to the same decision? (3 Marks)

Answer 1

Q.1 : Necessary assumption to compare mutually exclusive alternatives of different lives :

Answer :

1)The usage of machine are needed for the indefinite future.

2) The selected alternative will be repeated for succeeding life cycles in exactly the same manner as for the first life cycle.

3) All cash flows will have the same estimated values in every life cycle.

Q.2 : Which alternative is more economic based on Annual worth comparison

Machine A is more economic since Machine A Annual value cash outflow is $ 2210 whereas Machine B has $2336  

Machine-A Calculation

Running Cost	Maintenance Cost	Salvage Value	Total Cost
1,200	600		1,800
1,200	700		1,900
1,200	800		2,000
1,200	900		2,100
1,200	1,000		2,200
1,200	1,100	(400)	1,900
NPV			9,411
Price of Machine A			6,400
Total NPV of Machine A (a)			15,811
6 Year Annuity Value @ 7% (b)			7.1533
Annual Value Comparison (a/b)			2,210

Machine B Calculation

Running Cost	Maintenance Cost	Salvage Value	Total Cost
1,400	400		1,800
1,200	540		1,740
1,200	680		1,880
1,200	820	(400)	1,620
NPV			$5,973
Price of Machine B			4,400
Total NPV of Machine B (a)			$10,373
4 Year Annuity @ 7% (b)			4.4399
Annual Comparison (a/b)			$2,336

Q.3 Which alternative is more economic based on Present worth comparison

Present Worth means Net Present Value. Machine B is more economic based on Present worth comparison since it has $ 10,373 cash outflow whereas Machine A has $ 15,811

Q.4 For a four year study period, what salvage  value for machine A would make it preferred choice

Salvage value greater than 3415 will make Machine A preferred choice since at salvage value 3415 the annual comparison worth of both machine is $ 2336

Machine-A Calculation
Running Cost	Maintenance Cost	Salvage Value	Total Cost
1,200	600		1,800
1,200	700		1,900
1,200	800		2,000
1,200	900	(3,415)	(1,315)
NPV			3,971
Price of Machine A			6,400
Total NPV of Machine A (a)			10,371
6 Year Annuity Value @ 7% (b)			4.4399
Annual Value Comparision (a/b)			2,336
Machine B Calculation
Running Cost	Maintenance Cost	Salvabe Value	Total Cost
1,400	400		1,800
1,200	540		1,740
1,200	680		1,880
1,200	820	(400)	1,620
NPV			$5,973
Price of Machine B			4,400
Total NPV of Machine B (a)			$10,373
4 Year Annuity @ 7% (b)			4.4399
Annual Comparison (a/b)			$2,336

Q.5 Do the both method yield same result

No as evident from above both method yield different result. Present worth comparison yield same result when life of both machine is same however when life is different present worth comparison method is not useful and need to use annual worth comparison method.