Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
Book Icon
Chapter 9, Problem 41P
To determine

(a)

The best alternative using Benefit cost ratio.

Expert Solution
Check Mark

Answer to Problem 41P

Using cost benefit ratio alternative A is beneficial.

Explanation of Solution

Given:

A B
User benefits ($M/yr) 2.1 2.6
User dis-benefits ($M/yr) 1.2 2.1
First cost ($M) 6.9 9.9
Operations and maintenance ($M/yr) 0.75 0.825

Calculation:

Calculate the cost benefit ratio.

Cost-benefitratio=ΔEUABΔEUAC ...... (I)

Here, EUAB is annualised uniform benefits and EUAC is annualized uniform costs.

Calculate the EUAC for alternative A.

EUACA=(Firstcost+Userdisbenefits)(AP,8%,15years)+AnnualCost ...... (II)

Substitute 6.9 for first cost. 1.2 for user disbenefits and 0.75 for annual cost in Equation (II).

EUACA=($6.9+$1.2)(AP,8%,15years)+$0.75=($6.9+$1.2)(0.08(1+0.08)15(1+0.08)151)+$0.75=$0.946+$0.75=$1.696

EUAB is annual benefits which are $2.1million.

Calculate the EUAC of alternative B.

Substitute 9.9 for first cost. 2.1 for user dis-benefits and

0.825 for annual cost in Equation (II).

EUACB=($9.9+$2.1)(AP,8%,15years)+$0.825=($9.9+$2.1)(0.08(1+0.08)15(1+0.08)151)+$0.825=$1.4016+$0.825=$2.226million

EUAB is $2.6million.

Calculate the difference between the EUAC’s of two alternatives.

ΔEUAC=EUACBEUACA ...... (III)

Substitute $2.226million for EUACB and $1.696 for EUACA in Equation (III).

ΔEUAC=$2.226$1.696=0.53

Calculate the difference between the EUAB’s of two alternatives.

ΔEUAB=EUABBEUABA=$2.6$2.1=$0.5million

Calculate the benefit-cost ratio.

Substitute $0.5million for ΔEUAB and 0.53 for ΔEUAC in Equation (I).

BCratio=$0.5$0.53=$0.94

Thus the incremental cost ratio is less than 1 alternative A must be chosen.

Conclusion:

Using cost benefit ratio alternative A is beneficial.

To determine

(b)

The best alternative using Modified benefit cost ratio.

Expert Solution
Check Mark

Answer to Problem 41P

Using Modified cost benefit ratio alternative A is beneficial.

Explanation of Solution

Calculation:

In modified benefit cost ratio the salvage value is not added to the benefits. It is deducted from the costs. Since there is no salvage value in this case, thus, the answer will remain same as of part (a).

Conclusion:

Using Modified cost benefit ratio alternative A is beneficial.

To determine

(c)

The best alternative using the public/government version of the B/C ratio.

Expert Solution
Check Mark

Answer to Problem 41P

The best alternative using the public/government version of the B/C ratio is alternative B..

Explanation of Solution

Calculation:

Alternative A:

Benefits of public and government are calculated separately.

Calculate the present worth of the consumer’s benefits and dis-benefits.

PW=Userbenefits+Annualbenefits(PA,8%,15) ...... (IV)

Substitute 1.2 for User dis-benefits and $2.1 for Annual benefits in Equation (IV).

PW=$1.2+$2.1((1+0.08)1510.08(1+0.08)15)=$1.2+$2.1(8.559)=$16.7739million

Calculate the present worth of governments cost.

PW=Firstcost+Annualcost(PA,8%,15) ...... (V)

Substitute $6.9 for First cost and $0.75 for Annual cost in Equation (IV).

PW=$6.9+$0.75((1+0.08)1510.08(1+0.08)15)=$6.9+$0.75(8.559)=$13.319million

Calculate the benefit cost ratio.

BC=Presentworthofcustomer'sbenefitsPresentworthofGovernment'scost ...... (VI)

Substitute $16.7739million for Presentworthofcustomer'sbenefits and $13.319million for PresentworthofGovernment'scost in Equation (VI).

BC=$16.7739million$13.319million=1.259

Thus, alternative can be accepted.

Alternative B:

Benefits of public and government are calculated separately.

Calculate the present worth of the consumer’s benefits and dis-benefits.

Substitute 2.1 for User dis-benefits and $2.6 for Annual benefits in Equation (IV).

PW=$2.1+$2.6((1+0.08)1510.08(1+0.08)15)=$2.1+$2.6(8.559)=$20.1534million

Calculate the present worth of governments cost.

Substitute $9.9 for First cost and $0.825 for Annual cost in Equation (IV).

PW=$9.9+$0.825((1+0.08)1510.08(1+0.08)15)=$9.9+$0.825(8.559)=$16.9612million

Calculate the benefit cost ratio.

Substitute $20.1534million for Presentworthofcustomer'sbenefits and $16.9612million for PresentworthofGovernment'scost in Equation (VI).

BC=$20.1534million$16.9612million=1.188

Project B is also acceptable.

To chose between alternatives incremental analysis is performed.

Calculate the difference between the present worth of consumer’s benefits and disbenefits.

PWAB=[(DifferenceinUserbenefits)+Differenceinannualbenefits(PA,8%,15)]=(1.22.1)+(2.12.6)((1+0.08)1510.08(1+0.08)15)=0.94.2795=$3.3795

Calculate the difference between the present worth of government’s cost.

PWAB=[(DifferenceinFirstcost)+Differenceinannualcost(PA,8%,15)]=(6.99.9)+(0.750.825)((1+0.08)1510.08(1+0.08)15)=30.642=$3.642million

Calculate the benefit cost ratio.

BC=Presentworthofcustomer'sbenefitsPresentworthofgovernment'scost=$3.3795$3.642=0.927

Since the ratio is less than 1 so alternative B is selected.

Conclusion:

The best alternative using the public/government version of the B/C ratio is alternative B.

To determine

(d)

The best alternative using present worth index.

Expert Solution
Check Mark

Answer to Problem 41P

The best alternative using present worth index is alternative A..

Explanation of Solution

Calculation:

Alternative A:

Calculate the present worth of A.

Write the expression to calculate the present worth for the alternative expand.

PW=P+A((1+i)n1i(1+i)n)AOM((1+i)n1i(1+i)n)D ...... (VII)

Here, the present worth is, PW, the initial cost is P, the annual benefit is A, the annual operation and maintenance cost is AOM and the user dis-benefit is D.

Substitute $6.9 for, P, $2.1 for A, $0.75 for AOM, 1.2 for D. 8% for, i and 15 for n in Equation (VII).

PW=$6.9+$2.1((1+0.08)1510.08(1+0.08)15)$0.75((1+0.08)1510.08(1+0.08)15)$1.2=$6.9+$2.1(8.559)$0.75(8.559)$1.2=3.45

Calculate the present worth of B.

Substitute $9.9 for, P, $2.6 for A, $0.825 for AOM, 2.1 for D. 8% for, i and 15 for n in Equation (VII).

PW=$9.9+$2.6((1+0.08)1510.08(1+0.08)15)$0.825((1+0.08)1510.08(1+0.08)15)$2.1=$9.9+$2.6(8.559)$0.825(8.559)$2.1=3.16

Since the present worth of A is more thus, project A should be selected.

Conclusion:

The best alternative using present worth index is alternative A.

To determine

(e)

The consistency of data from a to d and the largest value.

Expert Solution
Check Mark

Explanation of Solution

The result remains consistent in all options except in the public/government version of B/C ratio.

The alternative A must be chosen as the highest value of modified B/C ratio is obtained. Because in this method all the operation and the maintenance cost and user dis-benefit are included as a deduction in Benefits.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 9 Solutions

Engineering Economic Analysis

Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education