Question

The management of Brawn Engineering is considering 3 alternatives to satisfy an OSHA requirement for safety gates in the machine shop. Each gate will completely satisfy the requirement, so no combinations need to be considered. The first costs, operating costs, and salvage values over a 5-year planning horizon are shown below. Using an annual worth analysis with a MARR of 20%/year, determine (a) the preferred gate. Show the annual worth for each gate: (b) Gate 1, (c) Gate 2, (d) Gate 3

End of Year	Gate 1	Gate 2	Gate 3
0	-$15,000	-$19,000	-$24,000
1	-$6,500	-$5,600	-$4,000
2	-$6,500	-$5,600	-$4,000
3	-$6,500	-$5,600	-$4,000
4	-$6,500	-$5,600	-$4,000
5	-$6,500 + $0	-$5,600 + $2,000

Answer 1

Annual worth (AW) of each gate is shown as follows.

AW, Gate 1 ($) = - 15,000 x A/P(20%, 5) - 6,500 = - 15,000 x 0.3344** - 6,500 = - 5,016 - 6,500 = - 11,516

AW, Gate 2 ($) = - 19,000 x A/P(20%, 5) - 5,600 + 2,000 x P/F(20%, 5) x A/P(20%, 5)

= - 19,000 x 0.3344** - 5,600 + 2,000 x 0.4019** x 0.3344** = - 6,353.6 - 5,600 + 268.79 = - 11,684.81

AW, Gate 3 ($) = - 24,000 x A/P(20%, 5) - 4,000 + 4,000 x P/F(20%, 5) x A/P(20%, 5)^##

= - 24,000 x 0.3344** - 4,000 + 4,000 x 0.4019** x 0.3344** = - 8,025.6 - 4,000 + 537.58 = - 11,488.02

Sine Gate 3 has lowest negative AW, this should be selected.

**From A/P and P/F Factor tables

##Gate 3 has no cash flow in year 5 but we are considering a planning period of 5 years. So, to make cash flow in year 5 zero, we add $4,000 as a positive cash flow in year 5 so that net cash flow = -$4,000 + $4,000 = 0.