Question

*"About 1.2 million additional advanced robots are expected to be deployed in the U.S. by 2025, Boston Consulting Group says. Four industries will lead the shift — computer and electronics products; electrical equipment and appliances; transportation; and machinery — largely because more of their tasks can be automated and they deliver the biggest cost savings." (Davidson, Paul. “More robots coming to U.S. factories” USA TODAY, February 9, 2015)

The systems (Robot X and Robot Y) shown below are under consideration for an improvement to an automated packaging process. Determine which should be selected on the basis of an Annual Worth Analysis using an interest rate of 10% per year.

	Robot X	Robot Y
First cost, $	–350,000	–250,000
Annual cost, $/year	–4,000	–3,000
Salvage value, $	25,000	40,000
Life, years	3	2

**The answers presented below were calculated using the appropriate factors from interest tables including all their decimal places**

Question 14 options:

	Select Robot X with AWx= $-125,000
	Select Robot Y with AWy= $-128,000
	Select Robot Y with AWy= $-141,186
	Select Robot X with AWx= $-137,186

Answer 1

Annual Worth Analysis – ROBOT X

Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of annul Cash Flow ($)
1	-4,000.00	0.90909	-3,636
2	-4,000.00	0.82645	-3,306
3	21,000.00 [-4,000 + 25,000]	0.75131	15,778
TOTAL		2.48685	8,835

Net Present Value (NPV) = Present value of annual cash flows – Initial Cost

= $8,835 - $350,000

= -$3,41,165

Equivalent Annual Worth = Net Present Value / (PVIFA 10%, 3 Years)

= -$3,41,165 / 2.4685

= -$137,186

Annual Worth Analysis – ROBOT Y

Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of annul Cash Flow ($)
1	-3,000.00	0.90909	-2,727
2	37,000.00 [-3,000 + 40,000]	0.82645	30,579
TOTAL		1.73554	27,851

Net Present Value (NPV) = Present value of annual cash flows – Initial Cost

= $27,851 - $250,000

= -$222,149

Equivalent Annual Worth = Net Present Value / (PVIFA 10%, 2 Years)

= -$222,149 / 1.73554

= -$128,000

DECISION

“Select Robot Y with AWy= $-128,000”.

The Robot Y with AWy= $-128,000 should be selected, since it has lowest annual worth of -$128,000”

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.