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 32P
To determine

The option which should be selected.

Expert Solution & Answer
Check Mark

Answer to Problem 32P

The option C the building with height of 10 stories should be selected.

Explanation of Solution

Given:

Cost of land is $100000 and the interest rate is 8%.

Concept used:

Write the expression for present worth of benefits.

PWB=A[(1+i)n1i(1+i)n] ...... (I)

Here, the annual payment is A, the interest rate is i and time period is n.

Write the expression for present worth of costs.

PWC=C+LS[1(1+i)n] ...... (II)

Here, the cost of building is C, the cost of land is L and the salvage value after 20 years is S.

Write the expression for benefit cost ratio.

B-C ratio=PWBPWC ...... (III)

Calculations:

Consider option A the building with height of 2 stories.

Calculate the present worth of benefits.

Substitute $70000 for A, 8% for i and 20 for n in Equation (I).

PWB=$70000[(1+0.08)2010.08(1+0.08)20]=$700000[(1.08)2010.08(1.08)20]=$70000(9.8181)=$687267

Calculate the present worth of costs.

Substitute $400000 for C, $100000 for L, $200000 for S, 8% for i and 20 for n in Equation (II).

PWC=$400000+$100000$200000[1(1+0.08)20]=$500000$200000(0.2145)=$500000$42900=$457100

Calculate the benefit cost ratio.

Substitute $457100 for PWC and $687267 for PWB in Equation (III).

B-C ratio=$687267$457100=1.5

Consider option B the building with height of 5 stories.

Calculate the present worth of benefits.

Substitute $105000 for A, 8% for i and 20 for n in Equation (I).

PWB=$105000[(1+0.08)2010.08(1+0.08)20]=$105000[(1.08)2010.08(1.08)20]=$105000(9.8181)=$1030901

Calculate the present worth of costs.

Substitute $800000 for C, $100000 for L, $300000 for S, 8% for i and 20 for n in Equation (II).

PWC=$800000+$100000$300000[1(1+0.08)20]=$900000$300000(0.2145)=$900000$64350=$8356500

Calculate the benefit cost ratio.

Substitute $8356500 for PWC and $1030901 for PWB in Equation (III).

B-C ratio=$1030901$8356500=1.23

Consider option C the building with height of 10 stories.

Calculate the present worth of benefits.

Substitute $256000 for A, 8% for i and 20 for n in Equation (I).

PWB=$256000[(1+0.08)2010.08(1+0.08)20]=$256000[(1.08)2010.08(1.08)20]=$256000(9.8181)=$2513434

Calculate the present worth of costs.

Substitute $800000 for C, $100000 for L, $300000 for S, 8% for i and 20 for n in Equation (II).

PWC=$2100000+$100000$400000[1(1+0.08)20]=$2100000$400000(0.2145)=$2200000$85800=$2114200

Calculate the benefit cost ratio.

Substitute $2114200 for PWC and $2513434 for PWB in Equation (III).

B-C ratio=$2513434$2114200=1.19

Consider incremental analysis for option B-A.

Calculate the value of A.

A=$105000$70000=$35000

Calculate the present worth of benefits.

Substitute $35000 for A, 8% for i and 20 for n in Equation (I).

PWB=$35000[(1+0.08)2010.08(1+0.08)20]=$350000[(1.08)2010.08(1.08)20]=$35000(9.8181)=$343634

Calculate the value of C.

C=$800000$400000=$400000

Calculate the value of L.

L=$100000$100000=0

Calculate the value of S.

S=$300000$200000=$100000

Calculate the present worth of costs.

Substitute Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  1for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  2Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  3for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  4Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  5for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  6Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  7for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  8and Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  9for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  10in Equation (II).

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  11

Calculate the benefit cost ratio.

Substitute Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  12for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  13and Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  14for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  15in Equation (III).

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  16

The benefit cost ratio is less than Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  17so option A is more preferable to B.

Consider incremental analysis for option C-A.

Calculate the present worth of benefits.

Calculate the value of A.

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  18

Substitute Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  19for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  20Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  21 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  22 and Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  23 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  24 in Equation (I).

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  25

Calculate the value of Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  26

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  27

Calculate the value of Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  28

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  29

Calculate the value of Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  30

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  31

Calculate the present worth of costs.

Substitute Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  32 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  33Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  34for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  35Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  36for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  37Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  38 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  39 and Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  40 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  41 in Equation (II).

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  42

Calculate the benefit cost ratio.

Substitute Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  43 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  44 and Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  45 for Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  46 in Equation (III).

Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  47

The benefit cost ratio is more than Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  48 so option C is more preferable to A.

The option C the building with height of Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  49 stories should be selected.

Conclusion:

The option C the building with height of Engineering Economic Analysis, Chapter 9, Problem 32P , additional homework tip  50 stories should be selected.

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