ENGINEERING ECONOMY DIGITAL ACCESS
ENGINEERING ECONOMY DIGITAL ACCESS
8th Edition
ISBN: 2810022611683
Author: Blank
Publisher: MCG
Question
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Chapter 8, Problem 23P

(a):

To determine

Calculate the rate of return.

(a):

Expert Solution
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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.

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