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Benefit Cost Analysis

Typical ly used fo r publ ic pro jects

The goal is to determine if benefi ts exceed

costs :

Benefi t / Cost Ratio > 1

The goal is NOT to maxim ize B/C Ratio.

Interest rates u sed are typically low er than

those used by businesses. Typ ical ly 4% - 8% (6.5% is typic al)

OMB requires 10% (except w ater p roj .)

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Benefit Cost Analysis

The chal lenge is to quant i fy the

benef i ts and cos ts.

The equation

B/C = (Benefits Disbenefi ts)to the publ ic

(Costs)to sponsor ing agency

You can use NPW, EAW, even NFW

which ever is easier in a part icular prob lem .

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3

Benefit Cost Analysis

Steps:1. Def ine the p lann ing hor izon .

2. Spec i fy the Discoun t Rate (MARR) to be used .

3. Deve lop the cost and benef it -d isbenefi t pro f iles in

monetary terms.

4. Compare the benef it s to cos ts using a spec i fied

measu re of worth , su ch as annual equivalent or

present wor th.

5. If th e B /C rat io is :

> 1 project is just i f ied= 1 barely jus ti f ied pol i t ical

< 1 no t just i f ied

6. Repeat steps 3 5 for al ternat ive viewpo ints

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Example

A ci ty l ibrary is to be expanded to includ e meeting room s,

more electronic volum es, compu ter facil i t ies, and electroniccheck- in and check-out.

The cos t of the expansio n w il l be $700,000 and the new

equipm ent w il l cos t anoth er $175,000.

Maintenance and renewal of the new addi t ion and equipm entw il l run app rox imately $100,000/year.

The l ibrary is pro jected to be in operation f or 20 years, w ith a

residual value of 40% of first co st for th e ph ysic al faci l i t ies.

There is no salvage value for the equ ipment. Disco un t is 8%.An estimated 150,000 people w il l visi t the l ibrary each year.

How much addi t ional benef i t per person, per year, must the

l ibrary vis i to rs perceive in o rder to just i fy the expansion?

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Perspective Matters

Suppose the l ibrary charged an annual

fee

Suppose the ent i re county sponsored

The equation

B/C = (Benefits Disbenefi ts)to pub l ic

(Init ial Investment)by sponsor

What is the viewpo int of a user?

What is the viewpoint o f a non-user?

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Incremental B/C Analysis

MUST be used when there are mu lt ip le

al ternat ives to choose from !

The equation is still

B/C = (Benefits Disbenefi ts)to the publ ic

(Costs)to sponsor ing agency

You can useIncr. NPW o rIncr. EAW

which ever is easier in a part icular prob lem .

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Incremental B/C Analysis

Steps:1. Def ine the set of feas ib le, mu tual ly exc lus ive, pub l ic

sector al ternat ives to be compared.

2. Def ine the p lann ing hor izon .

3. Deve lop the cost and benef it -d isbenefi t pro f iles in

monetary terms for each alternat ive.

4. Spec if y the MARR to be used .

5. Order the al ternat ives f rom smal les t to largestCost

6. Compare the al ternat ives us ing a spec if ied measure

of worth, suc h as annual equiv alent, capital izedcost, or present wo rth (w ith matchin g l i fet imes).

I f the B/C ratio is :

> 1 higher cost project is just i f ied

1 lower cost project is st i l l just i f ied

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Incremental Benefit Cost Analysis Example

A B C D E F G

Benefits 174 180 136 80 136 178 89

Disbenefits 4 60 10 8 10 2 14

Costs 100 120 90 80 70 110 50

B D

C

1.7 1.0 1.4 0.9 1.8 1.6 1.5

NotFeasible

Cost Order: G E C A F B

E G:

G DN:

C E:

A E:

(136 89) (10 14) = 51 = 2.55

(70 50) 20Upgrade to E

(136 136) (10 10) = 0 = 0

(90 70) 20

Keep Proj. E

(174 136) (4 10) = 44 = 1.47

(100 70) 30

Upgrade to A

(From feasibility, (B D) / C = 1.5 Upgrade to G

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Incremental Benefit Cost Analysis Example

A B C D E F G

Benefits 174 180 136 80 136 178 89

Disbenefits 4 60 10 8 10 2 14

Costs 100 120 90 80 70 110 50

B D

C

1.7 1.0 1.4 0.9 1.8 1.6 1.5

NotFeasible

Cost Order: G E C A F B

F A:

B A:

(178 174) (2 4) = 6 = 0.6

(110 100) 10Keep Proj. A

(180 174) (60 4) = 50 = 2.5

(120 100) 20

Best is Proj A

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Bonus Problem: B/C Build-Up Example

Snack Frid ge Viabi l i tyData:

110 IE & EngM students

48% w i l l use snack fr idge instead of go ing home

Users average (2) drin ks & (1) snack each week

Mark-up i s 10%, dr ink p rice is $.50, sn acks $.75School year averages 32 weeks

Fridge costs $495, lasts 8 yr s, 8% cpd annu al ly

If they save t ime & $$ on snacks & dr ink s, they

can buy book s , study more, and expect one of

them to wina$5 500 national sch olarsh ip every4 years.But the vending company wi l l qui t

do nating $300 per year to their Tech Society

Perform a B/C analysis IE student perspect ive