BenefitCost Analysis

1
Chapter 9

• Benefit/Cost Analysis

2
Incremental B/C Multiple Projects

• Determine the total cost for all alternatives.
• Order the alternatives by total cost.
• The first alternative is called the defender and
  the second one the challenger.
• Calculate the incremental benefit (?B) and
  incremental cost (?C) for the defender and the
  challenger.
• If ?B/ ?C 1, eliminate the defender and the
  challenger becomes the new defender. Otherwise,
  eliminate the challenger and select the new
  alternative (new challenger).
• Repeat the procedure until only one alternative
  remains.
• Note in case of revenue-generating projects, you
  need to consider DN (Do nothing alternative) as
  well.

3
Example

• Four methods can be used to recover lubricant in
  an installed automated milling system. The
  investment costs and income associated with each
  are given below. Assuming that all methods have a
  10-year life with zero salvage value, determine
  which one should be selected using a MARR of 15
  per year and the B/C method. Consider operating
  costs as disbenefit.
• Cost 1
  2 3 4
• Fist Cost, 15,000 19,000
  25,000 33,000
• Annual operating 10,000 12,000 9,000
  11,000
• cost,
• Annual Income, 15,000 20,000 19,000
  22,000

4
Solution

• Order by cost
• DN?1?2?3?4
• 1 to DN
• ?C 15,000(A/P,15,10) - 0
• 15,000(0.19925)
• 2,988.75
• ?B (15,000 -10,000) (0)
• 5000
• ?B/ ?C 5000/2988.75
• 1.67 gt1
• Select 1 and eliminate DN.
• 1?2?3?4

5
Solution

• 2 to 1
• ?C(19,000 -15,000)(A/P, 15,10)
• 4000(0.19925)
• 797
• ?B(20,000 -12,000) (15,000 10,000)
• 3000
• ?B/?C 3000/797
• 3.76gt1
• Eliminate 1 and select 2.
• 2?3?4

6
Solution

• 3 to 2
• ?C(25,000 -19,000)(A/P, 15,10)
• 4000(0.19925)
• 1195.50
• ?B(19,000 -9,000) (20,000 12,000)
• 2000
• ?B/?C 2000/1195.50
• 1.67gt1
• Eliminate 2 and select 3.
• 3?4

7
Solution

• 4 to 3
• ?C(33,000 -25,000)(A/P, 15,10)
• 8000(0.19925)
• 1594
• ?B(22,000 -11,000) (19,000 9,000)
• 1000
• ?B/?C 1000/1594
• 0.63gt1
• Eliminate 4 and select 3

8
Example

• The four mutually exclusive alternatives below
  are being compared using the B/C method. What
  alternative, if any, should be selected?
• Alternative Initial B/C
  Incremental B/C
• Investment J
  K L M
• J 20,000,000 1.10 -
• K 25,000,000 0.96 0.40 -
• L 33,000,000 1.22 1.42 2.14
  - -
• M 45,000,000 0.89 0.72 0.80
  0.08 -

9
Solution

• DN? J?K?L?M
• J to DN
• B/C 1.1gt1 Select J
• J? K? L?M
• K to J
• B/C 0.4lt1 Select J.
• J?L?M.
• L to J
• B/C1.42gt1 Select L.
• L?M
• M to L.
• B/C 0.08lt1 select L.

10
Solution

• Eliminate K and M since their B/C ratio is
  smaller than 1.
• Compare L to J.
• B/C 1.42gt1 Select L.