ENGR.ECONOMIC ANALYSIS W/DASHBOARD
ENGR.ECONOMIC ANALYSIS W/DASHBOARD
14th Edition
ISBN: 9780190063467
Author: NEWNAN
Publisher: OXF
Question
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Chapter 16, Problem 23P
To determine

The plan which should be chosen.

Expert Solution & Answer
Check Mark

Answer to Problem 23P

The benefit to cost ratio using PW method is 0.66 which is less than 1 then plan A is chosen.

Explanation of Solution

Given:

The table for data given is shown below.

Year Cash flow A Cash flows B
0 $300 $450
115(A1) $75 $100
15(F1) $250 $50
1630(A2) $125 $125
30(F2) $300 $0
3140(A3) $250 $125
40(F3) $0 $150

Table (1)

All the amounts are in thousands.

Concept used:

Write the expression for present worth of benefits.

PWB=F3[1(1+i)n] ...... (I)

Here, the present worth is PW, final cash flow at stage 3 is F3, interest rate is i and time period is n.

Write the expression for present worth of costs.

PWC=[P+A1[(1+i)n1i(1+i)n]F1[1(1+i)n]F2[1(1+i)n]A3[(1+i)n1i(1+i)n][1(1+i)n]] ...... (II)

Here, first cost is P, annual maintenance at stage 1 is A1,, annual maintenance at stage 3 is A3, final cost at stage 1 is F1 and final cost at stage 3 is F3.

Write the expression for incremental benefit to cost ratio using PW method.

Incremental B-C ratio=(PWBPWC) ...... (III)

If the value for incremental benefit to cost ratio is greater than 1 then plan B is chosen otherwise the plan A is chosen.

Calculations:

Calculate the difference between cash flows A and cash flow B.

Year Cash flow A Cash flows B Incremental analysis (BA)
0 $300 $450 $150
115(A1) $75 $100 $25
15(F1) $250 $50 $200
1630(A2) $125 $125 $0
30(F2) $300 $0 $300
3140(A3) $250 $125 $125
40(F3) $0 $150 $150

Table (2)

Calculate the present worth of benefits.

Substitute $150000 for F3, 7% for i and 40 for n in Equation (I).

PWB=$150000[1(1+0.07)40]=$150000[1(1.07)40]=$150000(0.0668)=$10020

Calculate the present worth of costs.

Substitute $150000 for P, $25000 for A1, $200000 for F1, $300000 for F2, $125000 for A3, 7% for i in Equation (II).

PWC=[$150000+$25000[(1+0.07)1510.07(1+0.07)15]$200000[1(1+0.07)15]$300000[1(1+0.07)30]$125000[(1+0.07)1010.07(1+0.07)10][1(1+0.07)30]]=[$150000+$25000(9.108)$200000(0.3624)$300000(0.1314)$125000(7.024)(0.1314)]=($150000+$227700$72480$39420$115369.2)=$150430.8

Calculate the incrementalbenefit to cost ratio using PW method.

Substitute $10020 for PWB, $150430.8 for PWC in Equation (III).

Incremental B-C ratio=($10020$150430.8)=0.66

The benefit to cost ratio using PW method is 0.66 which is less than 1 then plan A is chosen.

Conclusion:

Thus, the benefit to cost ratio using PW method is 0.66 which is less than 1 ; hence plan A is chosen.

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