1. Engineering Economic Analysis
Chapter 6
ANNUAL CASH FLOW ANALYSIS
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

2. Annual Cash Flow Calculations Resolving a Present Cost to an Annual Cost
Simplest case is to convert the PV to a series of EUAW (equivalent uniform annual worth) cash flows – [also known as A].
In Excel, we can take advantage of the PMT function
PMT(rate, nper, pv, [fv])
Rate: interest rate per time period
Nper: number of time periods (rate and nper have same time units)
pv: cash flow in time period 0 only
fv: cash flow in time period nper only
Annual cash flow analysis is exactly the same idea as present worth analysis, except use the equivalent uniform annual cost benefit or the difference of the two. Simplest method is to find the present worth and the find uniform series.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

3. Annual Cash Flow Four Essential Points
EUAW = PW(A/P,i,n)
EUAW is
Decreased by a cost
Increased by a benefit
In Excel use “PMT” to calculate EUAW
For an irregular cash flow over the analysis period, first determine the PW then convert to EUAW
Since the equivalent uniform annual worth is just the present worth multiplied by the uniform series capital recovery amount the alternative that is the best under present worth analysis will also be the best under annual cash flow analysis.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

4. Annual Cash Flow Analysis
Situation
Criterion
Fixed input
Amount of capital available fixed
Maximize EUAW
Fixed output
$ amount of benefit is fixed
Neither fixed
Neither capital nor $ benefits are fixed
We see the situations and the criterion for annual cash flow analysis
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

5. Example 1
You buy $1,000 worth of furniture that you expect to last for 10 years. If the interest rate is 7%, what is the EUAC?
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

6. Example 1
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

7. Example 1: Excel Since the $1000 is a cost, it is entered as -1000
To ensure the result has the right side, use -PMT
I have used the title “EAU Worth”.
If it is negative, it is a cost.
If it is positive, it is a benefit.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

8. Example 2
If you think you will be able to sell the furniture at a yard sale at the end of 10 years for $200, what is your EUAC?
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

9. Example 2
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

10. Example 2: Excel
By being able to sell the furniture, your annual cost is reduced from $142 per year to $128
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

11. Common Situations
A common situation is a cost at time 0, and a salvage value at the end of period n
3 Shortcuts for this are:
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

12. Example 3
Over 5 years the following maintenance and repair costs are incurred per year:
Year
Cost 1
$45 2
$90 3
$135 4
$180 5
$225
What is the EUAC if the interest rate is 7%?
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

13. Example 3
This is another almost arithmetic gradient. If we subtract out a uniform series of $45 from each period and use that as A one then A two will be an arithmetic gradient.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

14. Example 3
If we subtract out a uniform series of $45 from each period and use that as A one then the second part will be an arithmetic gradient.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

15. Example 3
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

16. Example 3: Excel Here, we can use the NPV function.
Be careful with signs to ensure your result matches the direction
Excel can use parentheses and red to indicate negative
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

17. Example 4 Consider the following four alternatives: A B C D
Cost to install
$15,000
$25,000
$33,000 $0
Savings Per Year
$14,000
$9,000
Annual Operating Cost
$8,000
$6,000
Salvage Value
$1,500
$2,500
$3,300
If we have an interest rate of 8% and alternatives A, B, and C have lifespans of 10 years, which alternative do you choose using annual cash flow analysis?
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

18. Example 4 What is our goal for this problem?
Since neither the benefits nor the costs are fixed our goal is to maximize the difference between EUAB and EUAC
Here, we include a “do-nothing” option
This option is really always an option, but often not explicitly considered
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

19. Example 4
What elements are benefits and what should we do to them to get them into an annual cash flow
Savings per year – Since this is already a per year number we don’t need to do anything to it.
Salvage value – Since this is a future cost we need to annualize it using:
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

20. Example 4
What elements are costs and what should we do to them to get them into an annual cash flow
Annual Operating Cost – Since this is an annual cost we do not need to do anything to it to make it an annual cost
Cost to Install – Since this is a present cost we need to annualize it using:
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

21. Example 4 Here is the table of costs with the annualization done: A B
EUA Cost to Install
-$2,235
-$3,725
-$4,917 $0
EUA Savings
$14,000
$9,000
EUA Operating Cost
-$8,000
-$6,000
EUA Salvage
$104
$172
$228
EUAB – EUAC
$3,869
-$553
$3,311
Clearly our best choice is alternative A.
Notice that B is worse than the “do-nothing” option
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

22. Example 4: Excel
In Excel, I would use the same format as for Present Worth Analysis
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

23. Analysis Period Considerations
Analysis period equal to alternative lives
Analysis period a common multiple of alternative lives
Analysis period for a continuing requirement
Infinite analysis period
Some other period such as project life
For annual cash flow analysis there are 5 different analysis considerations
Equal useful lives for all alternatives
Different useful lives, analysis period is the least common multiple
Different useful lives for a continuing requirement
Infinite analysis period
Another analysis period
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

24. Analysis Period Equal to Alternative Lives
Base the comparison on the life of the alternatives
This is the case we have most often considered in our examples
This is rarely the case in “real-life” organizations
For this we just find the equivalent uniform values
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

25. Analysis Period a Common Multiple of Alternative Lives
When the lives of the equipment in the two alternatives varies, use a common multiple of the two lives.
Assume consider replacement with identical item, just compare the equivalent uniform values
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

26. Analysis Period for a Continuing Requirement
Where the project will last forever (nothing does) use an infinite time period.
In most analyses, organizations often use a representatively long time period to get a reasonable estimate.
Just compare equivalent uniform values
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

27. Infinite Analysis Period
Alternative has a finite life
Find equivalent uniform value
Alternative has an infinite life
EUAC = P·i + other annual costs
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

28. Some Other Period Such As Project Life
Physical equipment usually has a useful life that is different from the project life.
In this case, use the project life as the analysis period.
This is the most common case in “real-life” organizations.
Need to be given the analysis period and any required terminal values
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

29. Example 5
Consider two pumps, where we have a 7% interest rate, use annual cash flow analysis to decide between the two A B
Initial Cost
$7,000
$5,000
Salvage Value
$1,500
$1,000
Useful Life (in years) 12 6
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

30. Example 5 Cash flow diagram for pump A
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

31. Example 5 Find EUAB – EUAC for pump A
So EUAB – EUAC for pump A is -$797.45
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

32. Example 5 For pump B there are two things we can do
Translate year 6 amounts to 0 then do the same as we did for pump A
Look only at 6 years
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

33. Example 5 Translate year six amount to year 0 then solve
The present worth and year 6 costs translated to time 0
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

34. Example 5 Translate year six amount to year 0 then solve
Find EUAB – EUAC for pump B
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

35. Example 5 Look only at 6 years Find EUAB – EUAC for pump B
We see that both give the same value and either way you should pick pump A
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

36. Example 5: Excel
When you are figuring out the number of periods (nper), use COUNT to count the number of periods – use the cells in the Cash Flows area
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

37. Example 6
Compare 2 plans for an aqueduct that must go through or around a mountain. We assume that the aqueduct must supply water forever. Choose the better aqueduct plan with an interest rate of 6%
Tunnel Through Mountain (A)
Pipeline Around Mountain (B)
Initial Cost
$5,500,000
$5,000,000
Maintenance Cost $0
Useful Life ∞
50 years
Salvage Value
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

38. Example 6 Compare EUAC for each alternative
For the lower annual cost pick plan B the pipeline around the mountain
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.