Solution manual engineering economic analysis 9th edition ch16

Chapter 16: Economic Analysis in the Public Sector16-1 Public decision-making involves the use of public money and resources to fund public projects.. Often there are those who are advoc

Chapter 16: Economic Analysis in the Public Sector

16-1

Public decision-making involves the use of public money and resources to fund public projects Often there are those who are advocating for particular projects, those who oppose projects, those who will be immediately affected by such project, and those who may be affected in the future There are those who represent their own stated interests, and those who are representing others’ interests Thus the “multi-actor” aspect of the phrase refers to the varied and wide group of “stakeholders” who are involved with, affected by, or place some concern on the decision process

16-2

Public decision-making is focused on promoting the general welfare of the aggregate public

There is an explicit recognition in promoting the good of the whole, in some cases, that individual’s goals must be subordinate (e.g eminent domain) Private decision making, on the other hand, is generally focused on increasing stakeholder wealth or investment This is not to say that private decision-making is entirely focuses on financials, clearly private decision-making focuses on non-monetary issues However, the goal and objective of the enterprise is economic survival and growth and thus the primary objective is financial in nature (for without success financially all other objectives are moot is the firm dissolves)

16-3

The general suggestion is that the viewpoint should be at least as broad as those who pay the costs and/or receive the benefits This approach balances local decisions, which may sub-optimize decision making if not taken Example 16-1 describes this dilemma for a municipal project funded partly by federal money (50%) In this example, it still made sense

to approve the project from the municipality’s viewpoint but not the federal government, after the benefit estimate was revised

16-4

This phrase refers to the fact that most benefits are confined locally for government

investments As the authors state, “Other than investments in defense and social programs, most benefits provided by government are realized at the local or regional levels.” This is true for projects funded with full or partial government money The conflict arises when some regions, states, municipalities perceive that they are consistently passed over for projects that would benefit their region, state, municipality Powerful members in congress, and state legislatures, with key committee/subcommittee appointments can influence

government spending in their districts Politics have an effect in this regard However, many projects, including the US parks system, the interstate highway, and others reach many beyond even regional levels

Students will pull elements from the discussion of this topic in the textbook In the text the concepts discussed include (1) No Time Value of Money, (2) Cost of Capital, and (3)

Opportunity Cost The Recommended Concept is to select the largest of the cost of capital, the government opportunity cost, or the taxpayer opportunity cost

16-6

The conventional benefit-cost ratio has net benefits to the users in the numerator and cost to the sponsor in the denominator The modified B-C ratio takes the project operating and

maintenance costs paid by the sponsor, and subtracts these from the net benefits to the users This quantity is all in the numerator These leaves only the projects initial costs in the denominator

The conventional and modified versions of the B-C ratio use different algebra/math to

calculate the ration, but the resulting recommendation will always be the same That is, for any problem, both ratios will either be greater than or less than 1.0 at the same time

16-7

This is a list of potential costs, benefits, and disbenefits for a nuclear power plant

Land Acquisition

Site Preparation

Cooling System

- Reservoir dams

- Reservoir cooling

Construction

- Reactor vessel/core

- Balance of plant

- Spent fuel storage

- Water cleaning

Environment

- No greenhouse gas

- No leakage

- No combustion Jobs & Economy

- At enrichment plants

- At power plant

- Increase tax base Increase Demand

- Uranium plants

Fission product material to contend with forever Not in my backyard Risk of Reactor

- Real

- Psychological Loss to Economy

- Coal

- Electric

16-8

(a) The conventional and modified versions of the B/C Ratio will always give consistent

recommendations in terms of “invest” or “do not invest” However, the magnitude of the B/C Ratio will be different for the two methods Advocates of a project may use the method with the larger ratio to bolster their advocacy

(b) Larger interest rates raise the “cost of capital” or “lost interest” for public projects

because of the sometimes quite expensive construction costs A person favoring a

$200 M turnpike project would want to use lower i% values in the B/C Ratio

calculations to offset the large capital costs

(c) A decision-maker in favor of a particular public project would advocate the use of a

longer project in the calculation of the B/C ratio Longer durations spread the large initial costs over a greater number of years

(d) Benefits, costs and disbenefits are quantities that have various amounts of

“certainty” associated with them Although this is true for all engineering economy estimates it is particularly true for public projects It is much easier to estimate labor savings in a production environment than it is to estimate the impact on local hotels

of new signage along a major route through town Because benefits, costs, and disbenefits tend to have more uncertainty it is therefore easier to manipulate their values to make a B/C Ratio indicate a decision with your position

16-9

The time required to initiate, study, fund and construct public projects is generally several years (or even decades) Because of this it is not uncommon for there to be turnover in public policy makers Politicians, who generally strive to maintain a positive public image, have been known to “stand up and gain political capital” from projects that originally began many years before they took office

16-10

Benefit- Cost Ratio = PW of Benefits/PW of Cost

= [$20,000 (P/A, 7%, 9) (P/F, 7%, 1)]/[$100,000

+ $50,000 (P/F, 7%, 1)]

= [$20,000 (6.515) (0.9346)]/[$100,000

+ $50,000 (0.9346)]

= 0.83

16-11

The problem requires the student to use calculus The text points out in Example 8-9 (of Chapter 8) that one definition of the point where ∆B = ∆C is that of the slope of the benefits curve equals the slope of the NPW = 0 line

2

01

81

61

41

21

08

6

4

2

0

2 4 6 8 10 12 14

16 18 20PW of Cost

Values for the graph:

PW of Cost (x) PW of Benefits (y)

Let x = PW of Cost and y = PW of Benefits

y2 – 22x + 44 = 0 or y = (22x – 44)1/2

dy/dx = ½ (22x – 44)(-1/2) (22) = 1

(Note that the slope of the NPW = 0 line is 1)

22x – 44 = [(1/2) (22)]2

x = (112 + 44)/22= 7.5 = optimum PW of cost

16-12

Since we have a 40-year analysis period, the problem could be solved by any of the exact analysis techniques Here the problem specifies a present worth analysis The annual cost solution, with a 10% interest rate, is presented in problem 6-44

Gravity Plan

PW of Cost = $2,800,000 + $10,000 (P/A, 8%, 40)

= $2,800,000 + $10,000 (11.925) = $2,919,250

Pumping Plan

PW of Cost = $1,400,000 + $200,000 (P/F, 8%, 10)

+ ($25,000 + $50,000) (P/A, 8%, 40) + $50,000 (P/A, 8%, 30) (P/F, 8%, 10)

= $1,400,000 + $200,000 (0.4632)

+ ($25,000 + $50,000) (11.925) + $50,000 (11.258) (0.4632)

= $2,647,700

To minimize PW of Cost, choose pumping plan

16-13

(a) Conventional B/C Ratio

= [PW (Benefits – Disabilities)]/[PW (1st Cost + Annual Cost)]

= [($500,000-$25,000) (P/A, 10%, 35)]/[($1,200,000

+ $125,000) (P/A, 10%, 35)]

= 1.9

(b) Modified B/C Ratio

= [PW (Benefits – Disbenefits – Cost)]/[PW (1st Cost)]

= [($500,000 - $25,000 - $125,000) (P/A, 10%, 35)]/$1,200,000

= 2.8

16-14

Using the Conventional B/C Ratio

(i) Using PW B/C Ratio = 1.90 (as above)

(ii) Using AW B/C Ratio = ($500,000 - $25,000)/[$1,200,000 (A/P,10%,35)

+ $125,000]

= 1.90 (iii) Using FW B/C Ratio = [($500,000 - $25,000) (F/A,10%,35)]

/[$1,200,000 (F/P, 10%, 35) + $125,000 (F/A, 10%, 35)]

= 1.90

16-15

(a) B/C Ratio = [($550 - $35) (P/A, 8%, 20)]/[($750 + $2,750)

+ $185 (P/A, 8%, 20)]

= 0.95 (b) Let’s find the breakeven number of years at which B/C = 1.0

1.0= [($550 - $35) (P/A, 8%, x)]/[($750 + $2,750)

+ $185 (P/A, 8%, x)]

By trial and error:

x B/C

ratio

24 years 0.995

25 years 1.004

26 years 1.031

One can see how Big City Carl arrived at his value of “at least” 25 years for the project duration This is the minimum number of years at which the B/C ratio is greater than 1.0 (nominally)

16-16

Annual Travel Volume = (2,500) (365) = 912,500 cars/year

The High Road

Annual Benefits = 0.015 ($912,500) 35) = $479,063

Annual O & M Cost = $2,000 (35) = $70,000

The Low Road

1st Cost = $450,000 (10) = $4,500,000

Annual Benefits = 0.045 ($912,500) (10) = $410,625

Annual O & M Cost = $10,000 (10) = $100,000

These are two mutually exclusive alternatives; we use an incremental analysis process Rank Order based on denominator = Low Road, High Road

Do Nothing-vs.-Low Low-vs.-High

∆ Annual O & M

Costs

Recommend investing in the Low road, it is the last justified increment

a [($410,625 - $100,000) ($15,456)]/$4,500,000 = 1.07

b [($68,438 + $30,000) ($15,456)]/$2,500,000 = 0.61

16-17

(a) PW of Benefits = $60,000 (P/A, 5%, 10)

+ $64,000 (P/A, 5%, 10) (P/F, 5%, 10) + $66,000 (P/A, 5%, 20) (P/F, 5%, 20) + $70,000 (P/A, 5%, 10) (P/F, 5%, 40)

= $60,000 (7.722)

+ $64,000 (7.722) (0.6139) + $66,000 (12.462) (0.3769) + $70,000 (7.722) (0.1420)

= $1,153,468 For B/C ratio = 1, PW of Cost = PW of Benefits

Justified capital expenditure

= $1,153,468 - $15,000 (P/A, 5%, 5)

= $1,153,468 - $15,000 (18.256)

= $879,628 (b) Same equation as on previous page except use 8% interest

PW of Benefits = $60,000 (6.710) + $64,000 (6.710) (0.4632)

+ $66,000 (9.818) (0.2145) + $70,000 (6.710) (0.0460)

= $762,116 Justified Capital Expenditure

= $762,116 - $15,000 (12.233)

= $578,621

Plan A

Plan B

Differences between Alternatives A and B

n = 15

$25,000

$200,000

$125,000

$150,000

$150,000

$300,000

$150,000

$100,00

$450,000

$50,000

$75,000

$125,000

$250,000

$300,000

$250,000

$300,000

An examination of the differences between the alternatives will allow us to quickly determine which plan is preferred

* This is sum of -$150 – 15 ($25) + $200 …

(a) When the Present Worth of the B- A cash flow is computed at 7%, the NPW = -142

The increment is not desirable at i = 7%

Choose Plan A

(b) For Plan B to be chosen, the increment B- A must be desirable The last column in

the table above shows that the B- A increment has a 5% rate of return In other words, at all interest rates at or below 5%, the increment is desirable and hence Plan

B is the preferred alternative The value of MARR would have to be 5% or less

16-19

Overpass Cost = $1,800,000 Salvage Value = $100,000 n = 30 i = 6%

Benefits to Public

Time Saving for 100 vehicles per day

400 trucks x (2/60) x ($10/hr) = $240 per day

600 others x (2/60) x ($5/hr) = $100 per day

Total = $340 per day

Benefits to the State

Saving in accident investigation costs= $2,000 per year

Combined Benefits

Benefits to the Public + Benefits to the State

= $340/day (365 days) + $6,000 = $130,100 per year

Benefits to the Railroad

Saving in crossing guard expense = $48,000 per year

Saving in accident case expense = $60,000 per year

Total = $108,000 per year

Should the overpass be built?

Benefit- Cost Ratio Analysis

Annual Cost (EUAC) = $1,700,000 (A/P, 6%, 30) + $100,000 (0.06)

= $1,700,000 (0.0726) + $6,000

= $129,420 Annual Benefit (EUAB) = $130,100 + $108,000

= $238,100 B/C= EUAB/EUAC = $238,100/$129,420 = 1.84

With a B/C ratio > 1, the project is economically justified

Allocation of the $1,800,000 cost

The railroad should contribute to the project in proportion to the benefits received

PW of Cost = $1,800,000 - $100,000 (P/F, 6%, 30)

= $1,800,000 - $100,000 (0.1741)

= $1,782,590 The railroad portion would be

($108,000/$238,100) ($1,782,590) = $808,570

The State portion would be

($130,100/$238,100) ($1,782,590) + $100,000 (P/F, 6%, 30)

= ($130,100/$238,100) ($1,782,590) + $100,000 (0.1741)

= $991,430

Note that $808,570 + $991,430 = $1,800,000

While this problem is a simplified representation of the situation, it illustrates a realistic statement of benefits and an economic analysis solution to the allocation of costs

16-20

Average ADT

Autos

Trucks

20,000 19,000 1,000

20,000 19,000 1,000

20,000 19,000 1,000

20,000 19,000 1,000 Time Savings (minutes)

Autos

1 3 4

Annual Maintenance per

Total Annual Maintenance $30,000 $50,000 $40,000 $41,200 EUAC of Initial Cost = (P x

miles) (A/P, 5%, 20)

Total Annual Cost of EUAC

+ Maintenance

Annual Incremental Operating Costs due to distance

None for Plans A and B, as they are the same length as existing road

Plan C Autos 19,000 x 365 x 0.3 mi x $0.06 = $124,830

Trucks 1,000 x 365 x 0.3 mi x $0.18 = $19,710

Total = $144,540/yr

Annual Accident Savings compared to Existing Highway

Plan A: (4.58 – 2.50) (10-6) ( 10 mi) (365 days) (20,000 ADT) ($1,200)

= $182,200

Plan B: (4.58 – 2.40) (10-6) ( 10 mi) (365 days) (20,000 ADT) ($1,200)

= $190,790

Plan C: (4.58 – 2.30) (10-6) ( 10.3 mi) (365 days) (20,000 ADT) ($1,200)

= $205,720

Time Savings Benefits to Road Users compared to Existing Highway

Plan A:

Autos 19,000 x 365 days x 2 min x $0.03 = $416,100

Trucks 1,000 x 365 days x 1 min x $0.15 = $54,750

Plan B:

Autos 19,000 x 365 days x 3 min x $0.03 = $624,150

Trucks 1,000 x 365 days x 3 min x $0.15 = $164,250

Plan C:

Autos 19,000 x 365 days x 5 min x $0.03 = $1,040,250

Trucks 1,000 x 365 days x 4 min x $0.15 = $219,000

Summary of Annual Costs and Benefits

Annual Highway Costs $30,000 $410,900 $561,300 $702,050 Annual Benefits

Accident Savings $182,200 $190,970 $205,720

* User costs are considered as disbenefits

Benefit-Cost Ratios

A rather than Existing: B/C = $653,050/($410,900 - $30,000)

B rather than A: B/C = ($979,370 - $653,050)/($561,300 - $410,900)

= 2.17

C rather than B: B/C = ($1,320,430 - $979,370)/($702,050 - $561,300

= 2.42 Plan C is preferred

16-21

Compute X for NPW = 0

NPW = PW of Benefits – PW of Costs

= X (P/A, 6%, 15) + $2,000 (P/G, 6%, 15) - $275,000 = $0

= X (9.712) + $2,000 (57.555) - $275,000 = $0

X = [$275,000 - $2,000 (57.555)]/9.712 = $16,463

Therefore, NPW at yr 0 turns positive for the first time when X is greater than $16,463 This indicates that construction should not be done prior to 19x5 as NPW is not positive The problem thus reduces to deciding whether to proceed in 2005 or 2006 The appropriate criterion is to maximize NPW at some point If we choose the beginning of 2005 for

convenience,

$275,00

0

G = $2,000

n = 15 yrs

i = 6%

x