EBK ENGINEERING ECONOMY
EBK ENGINEERING ECONOMY
8th Edition
ISBN: 8220103675437
Author: Blank
Publisher: YUZU
Question
Book Icon
Chapter 8, Problem 24P

(a):

To determine

Calculate the incremental rate of return.

(a):

Expert Solution
Check Mark

Explanation of Solution

Table-1 shows the cash flow.

Table -1

Alternative12
First cost (F)-15,000-25,000
AOC (AC) per year-1,600-400
Salvage value (SV)3,0004,000
Time period (n)24

MARR is 20%.

Incremental rate of return of alternatives Y and X can be calculated as follows: Since alternative 1 has 2-year life time, which is less than alternative 2, its cash flow has to be repeated for two years.

(F2F1)=(AC2AC1)((1+i)n21i(1+i)n2)(SV1+F1)(1+i)n1+SV2SV1(1+i)n2(25,000(15,000))=(400(1,600))((1+i)41i(1+i)4)(3,000+(15,000))(1+i)2+(4,0003,000)(1+i)n210,000=1,200((1+i)41i(1+i)4)+12,000(1+i)2+1,000(1+i)4

Substitute the incremental rate of return as 30% by trial-and-error method in the above equation.

10,000=1,200((1+0.3)410.3(1+0.3)4)+12,000(1+0.3)2+1,000(1+0.3)410,000=1,200(2.856110.3(2.8561))+12,0001.69+1,0002.856110,000=1,200(1.85610.85683)+7,100.59+350.1310,000=1,200(2.1662)+7,100.59+350.1310,000=2,599.44+7,100.59+350.1310,000<10,050.16

The calculated value is greater than the present value of the incremental first cost. Thus, increase the incremental rate of return to 30.31%.

10,000=1,200((1+0.3031)410.3031(1+0.3031)4)+12,000(1+0.3031)2+1,000(1+0.3031)410,000=1,200(2.883410.3031(2.8834))+12,0001.6981+1,0002.883410,000=1,200(2.1549)+7,066.72+346.8110,000=2,585.88+7,066.72+346.8110,000=9,999.41

The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is 30.31%. Since the incremental rate of return is greater than MARR, select the alternative 2.

(b):

To determine

Calculate incremental rate of return.

(b):

Expert Solution
Check Mark

Explanation of Solution

Alternative 2 has 4 years. Thus, time period (n) is 4. Incremental rate of return of alternatives Y and X can be calculated as follows:

(F2F1)=(AC2AC1)((1+i)n1i(1+i)n)+SV2SV1(1+i)n(25,000(15,000))=(400(1,600))((1+i)41i(1+i)4)+(4,0003,000)(1+i)n210,000=1,200((1+i)41i(1+i)4)+1,000(1+i)4

Substitute the incremental rate of return as -17% by trial-and-error method in the above equation.

10,000=1,200((10.17)410.17(10.17)4)+1,000(10.17)410,000=1,200(0.47458310.17(0.474583))+1,0000.47458310,000=1,200(0.5254170.080679)+2,107.1110,000=1,200(6.5124)+2,107.1110,000=7,814.88+2,107.1110,000>9,921.99

The calculated value is less than the present value of the incremental first cost. Thus, decrease the incremental rate of return to -17.22%.

10,000=1,200((10.1722)410.1722(10.1722)4)+1,000(10.1722)410,000=1,200(0.46957110.1722(0.469571))+1,0000.46957110,000=1,200(0.5304290.08086)+1,0000.46957110,000=1,200(6.5598)+2,129.610,000=7,871.66+2,107.1110,0009,978.87

The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is -17.22%. Since the incremental rate of return is negative, select the initial alternative 1.

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!
Students have asked these similar questions
Not use ai please
Not use ai please
Not use ai please
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
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