ENGR.ECONOMY CUSTOM FOR TAMU ISEN 667
ENGR.ECONOMY CUSTOM FOR TAMU ISEN 667
8th Edition
ISBN: 9781307584394
Author: Blank
Publisher: MCG/CREATE
Question
Book Icon
Chapter 8, Problem 23P

(a):

To determine

Calculate the rate of return.

(a):

Expert Solution
Check Mark

Explanation of Solution

Alternative X: First cost (F) is $84,000. Annual maintenance cost (AC) is $31,000 per year. Salvage value (SV) is $40,000. Annual revenue (AR) is $96,000per year.

Alternative Y: First cost (F) is $146,000. Annual maintenance cost (AC) is $28,000 per year. Salvage value (SV) is $47,000. Annual revenue (AR) is $119,000per year.

MARR is 15%. Time period (n) is 3.

Rate of return of alternative X (i) can be calculated as follows:

FX=(ARXACX)((1+i)n1i(1+i)n)+SVX(1+i)n84,000=(96,00031,000)((1+i)31i(1+i)3)+40,000(1+i)384,000=65,000((1+i)31i(1+i)3)+40,000(1+i)3

Substitute the rate of return as 65% by trial-and-error method in the above equation.

84,000=65,000((1+0.65)310.65(1+0.65)3)+40,000(1+0.65)384,000=65,000(4.49212510.65(4.492125))+40,0004.49212584,000=65,000(3.4921252.91988125)+8,904.4784,000=65,000(1.19598)+8,904.4784,000=77,738.7+8,904.4784,000<86,643.17

The calculated value is greater than the present value of the first cost. Thus, increase the rate of return to 67.85%.

84,000=65,000((1+0.6785)310.6785(1+0.6785)3)+40,000(1+0.6785)384,000=65,000(4.72894310.6785(4.728943))+40,0004.72894384,000=65,000(3.7289433.208588)+40,0004.72894384,000=65,000(1.162176)+8,458.5584,000=75,541.44+8,458.5584,00083,999.99

The calculated value is nearly equal to the present value of the first cost. Thus, it is confirmed that the rate of return is 67.85%.

Rate of return of alternative Y (i) can be calculated as follows:

FY=(ARYACY)((1+i)n1i(1+i)n)+SVY(1+i)n146,000=(119,00028,000)((1+i)31i(1+i)3)+47,000(1+i)3146,000=91,000((1+i)31i(1+i)3)+47,000(1+i)3

Substitute the rate of return as 47% by trial-and-error method in the above equation.

146,000=91,000((1+0.47)310.47(1+0.47)3)+47,000(1+0.47)3146,000=91,000(3.17652310.47(3.176523))+47,0003.176523146,000=91,000(2.1765231.49296581)+47,0003.176523146,000=91,000(1.457852)+14,796.05146,000=132,664.53+14,796.05146,000<147,460.58

The calculated value is greater than the present value of the first cost. Thus, increase the rate of return to 47.78%.

146,000=91,000((1+0.4778)310.4778(1+0.4778)3)+47,000(1+0.4778)3146,000=91,000(3.22735710.4778(3.227357))+47,0003.227357146,000=91,000(2.2273571.542031)+47,0003.227357146,000=91,000(1.444431)+14,796.05146,000=131,443.22+14,563146,000146,006.22

The calculated value is nearly equal to the present value of the first cost. Thus, it is confirmed that the rate of return is 47.78%.

Both the rates of returns are greater than MARR. Since the rate of return for X is greater, alternate X should be selected.

(b):

To determine

Calculate incremental rate of return.

(b):

Expert Solution
Check Mark

Explanation of Solution

Incremental rate of return of alternatives Y and X can be calculated as follows:

(FYFX)=((ARYARX)+(ACYACX))((1+i)n1i(1+i)n)+SVYSVX(1+i)n(146,00084,000)=((119,00096,000)(28,00031,000))((1+i)31i(1+i)3)+47,00040,000(1+i)362,000=(23,000(3,000.))((1+i)31i(1+i)3)+7,000(1+i)362,000=26,000((1+i)31i(1+i)3)+7,000(1+i)3

Substitute the incremental rate of return as 16% by trial-and-error method in the above equation.

62,000=26,000((1+0.16)310.16(1+0.16)3)+7,000(1+0.16)362,000=26,000(1.56089610.16(1.560896))+7,0001.56089662,000=26,000(0.5608960.24974336)+7,0001.56089662,000=26,000(2.24589)+4,484.662,000=58,393.14+4,484.662,000<62,877.74

The calculated value is greater than the present value of the incremental first cost. Thus, increase the incremental rate of return to 16.83%.

62,000=26,000((1+0.1683)310.1683(1+0.1683)3)+7,000(1+0.1683)362,000=26,000(1.59464210.1683(1.594642))+7,0001.59464262,000=26,000(0.5946420.268378)+7,0001.59464262,000=26,000(2.215688)+4,389.762,000=57,607.89+4,389.762,00061,997.59

The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is 16.83%. Since the incremental rate of return is greater than MARR, alternate Y must be selected.

(c):

To determine

Calculate incremental rate of return.

(c):

Expert Solution
Check Mark

Explanation of Solution

The procedure used in subpart (b) is correct (Incremental rate of return). Since the procedure used in subpart (a) is incorrect, Project X should not be selected.

Incremental rate of return of alternatives Y and X can be calculated as follows:

(FYFX)=((ARYARX)+(ACYACX))((1+i)n1i(1+i)n)+SVYSVX(1+i)n(146,00084,000)=((119,00096,000)(28,00031,000))((1+i)31i(1+i)3)+47,00040,000(1+i)362,000=(23,000(3,000.))((1+i)31i(1+i)3)+7,000(1+i)362,000=26,000((1+i)31i(1+i)3)+7,000(1+i)3

Substitute the incremental rate of return as 16% by trial-and-error method in the above equation.

62,000=26,000((1+0.16)310.16(1+0.16)3)+7,000(1+0.16)362,000=26,000(1.56089610.16(1.560896))+7,0001.56089662,000=26,000(0.5608960.24974336)+7,0001.56089662,000=26,000(2.24589)+4,484.662,000=58,393.14+4,484.662,000<62,877.74

The calculated value is greater than the present value of the incremental first cost. Thus, increase the incremental rate of return to 16.83%.

62,000=26,000((1+0.1683)310.1683(1+0.1683)3)+7,000(1+0.1683)362,000=26,000(1.59464210.1683(1.594642))+7,0001.59464262,000=26,000(0.5946420.268378)+7,0001.59464262,000=26,000(2.215688)+4,389.762,000=57,607.89+4,389.762,00061,997.59

The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is 16.83%. Since the incremental rate of return is greater than MARR, alternate Y must 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!
Students have asked these similar questions
Use a game tree to illustrate why an aircraft manufacturer may price below the current marginal cost in the short run if it has a steep learning curve.   ​(Hint​: Show that learning by doing lowers its cost in the second​ period.) Part 2 Assume for simplicity the game tree is illustrated in the figure to the right. Pricing below marginal cost reduces profits but gives the incumbent a cost advantage over potential rivals. What is the subgame perfect Nash​ equilibrium?
Answer
M” method  Given the following model, solve by the method of “M”. (see image)
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