ENGINEERING ECONOMIC ENHANCED EBOOK
ENGINEERING ECONOMIC ENHANCED EBOOK
14th Edition
ISBN: 9780190931940
Author: NEWNAN
Publisher: OXF
Question
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Chapter D, Problem 80P
To determine

The interest rate that makes alternatives A and B equivalent is in what range.

Expert Solution & Answer
Check Mark

Answer to Problem 80P

Therefore, the correct option is (c)Greaterthan5%.

Explanation of Solution

Given:

Year Alternative I Alternative II
0 $1000 $3000
1 100 500
2 100 550
3 100 600
4 200 650
5 200 700

Concept used:

Write the expression to calculate the present worth.

PW=F( 1+i)n

Here, future amount is F, number of years is n and the interest rate is i.

Calculation:

Write the expression to calculate present worth of Alternative I.

PWA=[1000+100( 1 ( 1+i) 1)+100( 1 ( 1+i) 2)+100( 1 ( 1+i) 3)+200( 1 ( 1+i) 4)+200( 1 ( 1+i) 5)] ...... (I)

Write the expression to calculate present worth of Alternative II.

PWB=[3000+500( 1 ( 1+i) 1)+550( 1 ( 1+i) 2)+600( 1 ( 1+i) 3)+650( 1 ( 1+i) 4)+700( 1 ( 1+i) 5)] ...... (II)

Equate Equation (I) and Equation (II).

[1000+100( 1 ( 1+i) 1)+100( 1 ( 1+i) 2)+100( 1 ( 1+i) 3)+200( 1 ( 1+i) 4)+200( 1 ( 1+i) 5)]=[3000+500( 1 ( 1+i) 1)+550( 1 ( 1+i) 2)+600( 1 ( 1+i) 3)+650( 1 ( 1+i) 4)+700( 1 ( 1+i) 5)]8 ( 1+i )1+9 ( 1+i )2+10 ( 1+i )3+9 ( 1+i )4+10 ( 1+i )540=0 ...... (III)

Calculate the internal rate of return by hit and trial.

Substitute 4% for i in Equation (III) which is V1.

V1=8 ( 1+0.04 )1+9 ( 1+0.04 )2+10 ( 1+0.04 )3+9 ( 1+0.04 )4+10 ( 1+0.04 )540=7.6923+8.321+8.89+7.6932+8.219340=0.8158

Substitute 5% for i in Equation (III) which is V2.

V2=8 ( 1+0.05 )1+9 ( 1+0.05 )2+10 ( 1+0.05 )3+9 ( 1+0.05 )4+10 ( 1+0.05 )540=7.6190+8.1633+8.6384+7.4043+7.835240=0.3398

Calculate the internal rate of return by interpolating V1 and V2.

IRR=i1+(i2i1)×V1V1V2 ...... (IV)

Substitute, 4% for i1, 5% for i2, 0.8158 for V1 and 0.3398 for V2 in Equation (IV)

IRR=0.04+(0.050.04)( 0.8158 0.81580.3398)=0.057=5.7%.

Conclusion:

Therefore, the correct option is (c)Greaterthan5%.

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Chapter D Solutions

ENGINEERING ECONOMIC ENHANCED EBOOK

Ch. D - Prob. 11PCh. D - Prob. 12PCh. D - Prob. 13PCh. D - Prob. 14PCh. D - Prob. 15PCh. D - Prob. 16PCh. D - Prob. 17PCh. D - Prob. 18PCh. D - Prob. 19PCh. D - Prob. 20PCh. D - Prob. 21PCh. D - Prob. 22PCh. D - Prob. 23PCh. D - Prob. 24PCh. D - Prob. 25PCh. D - Prob. 26PCh. D - Prob. 27PCh. D - Prob. 28PCh. D - Prob. 29PCh. D - Prob. 30PCh. D - Prob. 31PCh. D - Prob. 32PCh. D - Prob. 33PCh. D - Prob. 34PCh. D - Prob. 35PCh. D - Prob. 36PCh. D - Prob. 37PCh. D - Prob. 38PCh. D - Prob. 39PCh. D - Prob. 40PCh. D - Prob. 41PCh. D - Prob. 42PCh. D - Prob. 43PCh. D - Prob. 44PCh. D - Prob. 45PCh. D - Prob. 46PCh. D - Prob. 47PCh. D - Prob. 48PCh. D - Prob. 49PCh. D - Prob. 50PCh. D - Prob. 51PCh. D - Prob. 52PCh. D - Prob. 53PCh. D - Prob. 54PCh. D - Prob. 55PCh. D - Prob. 56PCh. D - Prob. 57PCh. D - Prob. 58PCh. D - Prob. 59PCh. D - Prob. 60PCh. D - Prob. 61PCh. D - Prob. 62PCh. D - Prob. 63PCh. D - Prob. 64PCh. D - Prob. 65PCh. D - Prob. 66PCh. D - Prob. 67PCh. D - Prob. 68PCh. D - Prob. 69PCh. D - Prob. 70PCh. D - Prob. 71PCh. D - Prob. 72PCh. D - Prob. 73PCh. D - Prob. 74PCh. D - Prob. 75PCh. D - Prob. 76PCh. D - Prob. 77PCh. D - Prob. 78PCh. D - Prob. 79PCh. D - Prob. 80PCh. D - Prob. 81PCh. D - Prob. 82PCh. D - Prob. 83PCh. D - Prob. 84PCh. D - Prob. 85PCh. D - Prob. 86PCh. D - Prob. 87PCh. D - Prob. 88PCh. D - Prob. 89PCh. D - Prob. 90PCh. D - Prob. 91PCh. D - Prob. 92PCh. D - Prob. 93PCh. D - Prob. 94PCh. D - Prob. 95PCh. D - Prob. 96PCh. D - Prob. 97PCh. D - Prob. 98PCh. D - Prob. 99PCh. D - Prob. 100PCh. D - Prob. 101PCh. D - Prob. 102PCh. D - Prob. 103PCh. D - Prob. 104PCh. D - Prob. 105PCh. D - Prob. 106PCh. D - Prob. 107PCh. D - Prob. 108PCh. D - Prob. 109PCh. D - Prob. 110PCh. D - Prob. 111PCh. D - Prob. 112PCh. D - Prob. 113PCh. D - Prob. 114PCh. D - Prob. 115PCh. D - Prob. 116PCh. D - Prob. 117PCh. D - Prob. 118PCh. D - Prob. 119PCh. D - Prob. 120PCh. D - Prob. 121PCh. D - Prob. 122PCh. D - Prob. 123PCh. D - Prob. 124PCh. D - Prob. 125PCh. D - Prob. 126PCh. D - Prob. 127PCh. D - Prob. 128PCh. D - Prob. 129PCh. D - Prob. 130PCh. D - Prob. 131PCh. D - Prob. 132PCh. D - Prob. 133PCh. D - Prob. 134PCh. D - Prob. 135PCh. D - Prob. 136PCh. D - Prob. 137PCh. D - Prob. 138PCh. D - Prob. 139P
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