3360 unit 09 2014-i-01

ENGR 3360U Winter 2014Unit 9

Other Choosing Techniques

Dr. J. Michael Bennett, P. Eng., PMP, UOIT,

Version 2014-I-01

Unit 9 Other Choosing Analyses

Change Record

• 2014-I-01 Initial Creation• Text Chapter 9

2014-I-019-2 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco


Course Outline1. Engineering Economics2. General Economics

1. Microeconomics2. Macroeconomics3. Money and the Bank of

Canada3. Engineering Estimation4. Interest and Equivalence5. Present Worth Analysis6. Annual Cash Flow7. Rate of Return Analysis8. Picking the Best Choice9. Other Choosing Techniques

10. Uncertainty and Risk11. Income and Depreciation12. After-tax Cash Flows13. Replacement Analysis14. Inflation15. MARR Selection16. Public Sector Issues17. What Engineering should know

about Accounting18. Personal Economics for the

Engineer

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco1-3


Learning Objectives

• 9.1 Future Worth Analysis• 9.2 Benefit–Cost Ratio• 9.3Payback Period Analysis• 9.4 Sensitivity Analysis• 9.5 Break-even Analysis



-• In contrast to present worth analysis, one might

want to know the situation of a set of alternatives at any point in time in the future.

• Future worth analysis is very similar to present worth analysis but the analysis exists at some future point in time.

• As in present worth analysis, the evaluation of alternatives must be over the same time period.– This implies that the use of LCM or a specified

time period is needed.



Example 9.1

Ron is a 20-year old UOIT student who smokes a carton of ciggies a week. If he stops smoking and places this money in a savings account which earns 5% compounded semi-annually, what is his future worth at 65 if a carton costs $85?



Answer

Semi-savings = 85x26 = 2,210FW = (F/A, 2.5%, 90) = 2210(329.2)

= $727, 532 (at least)



9.2 Benefit-Cost Ratio Analysis• At a given MARR an alternative that would be

acceptable when:PW of benefits – PW of costs >= 0orEUAB – EUAC >= 0

• This makes sense as the benefits outweigh the costs for a net positive benefit at MARR over a specified lifetime.

• This could also be stated as a ratio:PW of benefits/PW of costs >= 1

• Called the Benefit–Cost Ratio



Benefit-Cost Ratio Analysis cont.

• In the public sector it is common that:– The numerator includes all consequences to the

user or public (Benefits – Disbenefits).– The denominator includes the consequences to

the government or sponsor.• The ratios may differ in exact value by this

method, but, more importantly, the decision point (> or < 1) does not.

• The conclusions remain the same.



Example 9-2

Two machines have a life of 5 years. A costs $1000 and will earn $300 annually. B costs $1350 and will earn $300, the first year, $350 the second and so on. At 7%, which machine should be selected?



Solution

Incremental B-APWcosts = 1350 – 1000 = 350

PWbenefits = (0-0) + 50(P/G, 7%, 5) = 382

B/C = 382/350 = 1.09

Note that direct calculation gives the wrong answer.



Example 9.3

Here are 6 mutually exclusive alternatives. They have a 20 year life. At 6%, using B/C ratio, which would you pick?

A B C D E FCost 4K 2K 6K 1K 9K 10KPW 7.3K 4.7K 8.7K 1.3K 9K 9.5KB/C 1.8 2.4 1.5 1.3 1.0 0.95



Benefit-Cost Ratio Analysis

• Graphed individual project points from Example 9-5• The slopes indicate B/C ratios of the increments between projects.

Example(s): B – D slope is greater than 1.0 A – C slope is less than 1.0 F is not considered (B/C ratio is less <1)



Solution

Discard F (B/C < 1)



Solution

Δ B-D Δ A-B Δ C-A Δ E-AΔ Cost 1K 2K 2K 5KΔ Benefit 3.4K 2.6K 1.4K 1.7KB/C 3.4 1.3 0.7 0.341) Chose B over D2) Chose A over B3) Chose A over C4) Chose A over E



9.3 Payback Period• Payback period is:

– The period of time required for the profit or Other Choosing benefits of a project to equal the cost.

– Note: Interest Rate is NOT considered• Four important points:

1) This is an approximate calculation.2) Costs/benefits/savings are included with no consideration

of timing differences.2) All economic consequences beyond the payback are

ignored, including salvage!3) Due to its approximate nature, it may not select the correct

alternative.



Example 9.4

A firm is trying to decide which of 2 scales it should buy. If both have a 6-year life, which should be selected at 8%, using PB?

Choice Cost UAB Salvage A 2K 450 100 B 3K 600 700



Payback Period Example



Solution

Ignore Salvage and interest ratePBA = cost/UAB = 2000/450 = 4.4 years

PBB = 3000/600 = 5 years



9.4 Sensitivity Analysis

• Since economic problem solving often considers future consequences, there is uncertainty regarding accuracy.

• To better evaluate the impact of estimates, we can compute how much an estimate can change and the effect on a particular decision.

• This is ‘Sensitivity Analysis’.



9.5 Break-Even Analysis

• Break-Even Analysis is a form of sensitivity analysis.

• Typically presented as a break-even chart.• It indicates the point at which two

alternatives are equal to each Other Choosing.– The point of indifference



Example 9-5Consider a project that may be constructed to full

capacity now or may be built in 2 stages. Assume 40 year life at 8%, no SV.Costs

2-Stage first stage now 100,0002nd stage n years out 120,000

Full capacitydo it now 140,000



Solution

Full Cap = 140,0002-Stage

PW = 100000 + 120000(P/F, 8%, n) n=05 PW = 182,700 n=10 PW = 155,600 n=20 PW = 125,700 n=40 PW = 111,900



Break-Even Analysis, cont’d.• Example 9-11

– Shows present worth of building both stages now versus building a second stage at a later date.

– The point at which they are equal is when the second stage is built in year 15.



Summary

• Future Worth Analysis– Comparisons between alternatives made based

on a future time• Benefit-Cost Ratio Analysis

– Analyses the ratio of benefits to costs through present worth or annual worth.

– Incremental benefit-cost ratios are used for multiple alternatives when neither input nor output are fixed.

– Often used in various levels of government.



Summary, cont’d.

• Payback Period Analysis– The period of time required for profit or Other

Choosing benefits to equal the cost of the investment.

– A poor method for ranking alternatives because interest rate is NOT considered.

– Simply measures the time it takes to recover the investment in original dollars.



Summary, cont’d.

• Sensitivity Analysis– Used to determine how sensitive a decision is

to estimates and parameters.– Examination of the range of values to

determine their effect on a decision.

• Break-Even Analysis– To locate the condition where alternatives are

equivalent.– Often uses a break-even chart.


3360 unit 09 2014-i-01

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