engg 401 x2 fundamentals of engineering management spring 2008 chapter 7: other analysis techniques...

ENGG 401 X2ENGG 401 X2Fundamentals of Engineering ManagementFundamentals of Engineering Management

Spring 2008Spring 2008

Chapter 7:Chapter 7:

Other Analysis TechniquesOther Analysis Techniques

Dave LudwickDave Ludwick

Dept. of Mechanical EngineeringDept. of Mechanical Engineering

University of AlbertaUniversity of Albertahttp://members.shaw.ca/dave_ludwick/

Dave Ludwick, Dept. of Mech. Eng.Ch 7 – Other Analysis Techniques

Summer 20082

ENGG 401 X2 – Fundamentals of Engineering Management

Benefit-Cost Ratio AnalysisBenefit-Cost Ratio Analysis

• Benefit-cost ratio analysisBenefit-cost ratio analysis compares the value gained from a project to the cost of the project.– We expect the benefits to outweigh the costs (i.e., the total value of

the benefits should be greater than the total value of the costs).

• The idea is that a project with a large benefit-cost ratiobenefit-cost ratio (BCR) will be a good project (but bigger isn’t always better).

• Benefit-cost ratio analysis is frequently used for analyzing pubic sector projects.– and can include costs or benefits that may not necessarily be

considered if it was a private investment

cosbenefits tsPW PW cos

1benefits

ts

PWBCR

PW


Summer 20083


Benefit-Cost Ratio ExampleBenefit-Cost Ratio Example

• You can select between the Baseline model or Gold Standard model for a new piece of equipment your company needs. The equivalent uniform annual costs and benefits of each are as follows:– Baseline model: EUAC = $50k, EUAB = $75k– Gold Standard model: EUAC = $125k, EUAB = $140k

• Which model should you choose?– Since the BCR of each is greater than one, then each is individually

acceptable, so calculate the incremental BCR:

– Since ∆BCR < 1, the extra benefits we get from the Gold Standard model isn’t worth the extra costs. Choose the Baseline model.Choose the Baseline model.

$140 $75 $651

$125 $50 $75

BBCR

C


Summer 20084


Benefit-Cost Ratio In-Class Problem #1Benefit-Cost Ratio In-Class Problem #1

• You can consider two types of equipment for your company, each with different costs, net annual benefits, salvage values, and useful lives:

#1 #2

Purchase cost $ 200k $ 700k

Annual benefit $ 95k $ 120k

Salvage value $ 50k $ 150k

Useful life 6 years 12 years

• Assuming a 10% interest rate, what are their benefit-cost ratios?

• Which would you choose? Why?


Summer 20085


Benefit-Cost Ratio Analysis with Multiple OptionsBenefit-Cost Ratio Analysis with Multiple Options

• When comparing more than one alternative project, we don’t necessarily want to choose the one with the largest BCR.– For reasons similar to those for not automatically selecting the

project with the largest IRR.

• The method is to calculate incremental costs (∆C) and incremental benefits (∆B) for each progressively more expensive pair, which will allow us to calculate incremental benefit-cost ratios (∆BCR) for those pairs.– If ∆BCR ≥ 1, then the more expensive project is worthwhile, since

the incremental benefit is worth more than the incremental cost.


Summer 20086


Benefit-Cost Ratio In-Class Problem #2Benefit-Cost Ratio In-Class Problem #2

• Consider that you can choose one of six alternatives, each with the same useful life and with no salvage value:

A B C D E F

PWcost $4000 $2000 $6000 $1000 $9000 $10000

PWbenefit $7330 $4700 $8730 $1340 $9000 $9500

BCR 1.83 2.35 1.46 1.34 1.00 0.95

• Question:Question: Which alternative should you select?

– Note: We don’t need to know i in this case because we’re given the PW of all of our cash flows. But if all we had were the actual cash flows, we’d need to calculate the PWcost and PWbenefit ourselves, so we’d need to know i.


Summer 20087


Payback PeriodPayback Period

• Payback period is the amount of time that elapses before the net benefits of an investment equal its cost.– For projects with high uncertainty, payback period becomes very

important.

• Two main types of payback period analysis:– Discounted payback

• Uses the specified discount rate, MARR, interest rate, etc.

– Simple payback• Doesn’t use any discount rate at all (i.e., i = 0, or FV = PV)

• There are other versions payback:– can consider depreciation, inflation, taxes, etc.


Summer 20088


Payback Period ExamplePayback Period Example

Year FV PV NPV PV NPV

0 -10,000$ -10,000$ -10,000$ -10,000$ -10,000$ 1 2,000$ 2,000$ -8,000$ 1,739$ -8,261$ 2 2,500$ 2,500$ -5,500$ 1,890$ -6,371$ 3 3,000$ 3,000$ -2,500$ 1,973$ -4,398$ 4 3,500$ 3,500$ 1,000$ 2,001$ -2,397$ 5 4,000$ 4,000$ 5,000$ 1,989$ -408$ 6 4,000$ 4,000$ 9,000$ 1,729$ 1,321$ 7 4,000$ 4,000$ 13,000$ 1,504$ 2,825$ 8 4,000$ 4,000$ 17,000$ 1,308$ 4,133$ 9 4,000$ 4,000$ 21,000$ 1,137$ 5,270$

10 4,000$ 4,000$ 25,000$ 989$ 6,258$

Simple Discounted (15%)

Payback of 4 years(actually 3.71 years)

Payback of 6 years(actually 5.24 years)


Summer 20089


Payback Period – In-Class ProblemPayback Period – In-Class Problem

• What is the payback period for the following two investment options?

Year Cash Flow Year Cash Flow

1 -212,000$ 12 108,000$ 2 -461,000$ 13 110,000$ 3 90,000$ 14 112,000$ 4 92,000$ 15 114,000$ 5 94,000$ 16 116,000$ 6 96,000$ 17 119,000$ 7 97,000$ 18 121,000$ 8 99,000$ 19 124,000$ 9 101,000$ 20 126,000$

10 103,000$ 21 129,000$ 11 105,000$ 22 131,000$

Early OptionYear Cash Flow Year Cash Flow

1 -212,000$ 12 228,000$ 2 -461,000$ 13 232,000$ 3 12,000$ 14 237,000$ 4 15,000$ 15 242,000$ 5 20,000$ 16 247,000$ 6 30,000$ 17 252,000$ 7 50,000$ 18 257,000$ 8 70,000$ 19 262,000$ 9 100,000$ 20 267,000$

10 120,000$ 21 272,000$ 11 150,000$ 22 278,000$

Late Option


Summer 200810


Sensitivity and Break-Even AnalysisSensitivity and Break-Even Analysis

• Sensitivity and break-even analysisSensitivity and break-even analysis is used to determine which value of a particular parameter will result in a break-even scenario (and which parameters a decision is sensitive to).– At break-even, costs will equal revenues, NPV equals zero, two

options are equivalent, etc.

• Example uses:– What cost do we set for a particular project so that it is equivalent to

another project?– What timing should be used to build a multi-phase projects?– How will the useful life of a piece of equipment impact a decision?


Summer 200811


Sensitivity and Break-Even Analysis ExampleSensitivity and Break-Even Analysis Example

• Your company needs to build a new plant.– Option A is to build all at once:

• The plant has the capacity you will need years from now, at a cost of $140k.

– Option B is to build in two phases:• Phase 1 provides the capacity you need for the first few years at a cost

of $100k.

• Phase 2 provides the remaining additional capacity at a cost of $120k.

– Both options have the same total useful lifetime, the same operation and maintenance costs, and no salvage value.

• With a WACC of 8%, at what time will the cost of both options be equivalent?– What does this mean?


Summer 200812


Sensitivity and Break-Even Analysis Example (2)Sensitivity and Break-Even Analysis Example (2)

$100,000

$120,000

$140,000

$160,000

$180,000

$200,000

$220,000

0 5 10 15 20 25 30

Year when Option B's Phase 2 constructed

NP

V o

f C

os

ts

both options equivalent here (between 14 & 15 years out)

Option BOption B

Option AOption A

The decision of which option to use is only sensitive to the timing if the range of estimates is in the area of 15 years.


Summer 200813



$100,000

$120,000

$140,000

$160,000

$180,000

$200,000

$220,000

0 5 10 15 20 25 30


NP

V o

f C

os

ts

with i = 10%, options are

equivalent here (13 years)

Option BOption B

Option AOption A

The decision will also depend on our WACC, or the interest rate we use to calculate our discounted cash flows.


Summer 200814



$100,000

$120,000

$140,000

$160,000

$180,000

$200,000

$220,000

0 5 10 15 20 25 30


NP

V o

f C

os

ts

with i = 6%, options are

equivalent here (19 years)

Option BOption B

Option AOption A


Summer 200815


Break-Even – In-Class Problem #1Break-Even – In-Class Problem #1

• Suppose you can choose between two options. – Option A has a cost that is known with some precision to be $5000,

and will provide an net annual benefit of $700.– Option B has an unknown cost, but we know it will provide an net

annual benefit of $639.– Both options have a 20-year useful life with no salvage value.

• With a WACC of 6%, which option should we choose?


Summer 200816


Break-Even – In-Class Problem #2Break-Even – In-Class Problem #2

• You need to replace a component in a piece of equipment used in an environment highly conducive to corrosion. An ordinary part has a cost of $350, a useful life of only 6 years, and no salvage value. How long a useful life must a more expensive ($500) corrosion resistant part have if it is preferred over the ordinary part?

• Assume a WACC of 10%.

engg 401 x2 fundamentals of engineering management spring 2008 chapter 7: other analysis techniques...

Documents

large benefitcost ratio

purchase cost

benefitcost ratiothe

analysis techniques

incremental bcr

ludwick slide

baseline model

incremental benefits