ENGR.ECONOMIC ANALYSIS W/DASHBOARD
ENGR.ECONOMIC ANALYSIS W/DASHBOARD
14th Edition
ISBN: 9780190063467
Author: NEWNAN
Publisher: OXF
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Chapter 9, Problem 51P
To determine

(a)

The best alternative based on payback period.

Expert Solution
Check Mark

Answer to Problem 51P

The Alternative- B should be selected.

Explanation of Solution

Calculation:

Write the equation for Payback period.

Paybackperiod=CostAnnualBenefit ...... (I)

Calculate the Payback period for Alternative-A.

Substitute $50 for Cost, and $30 for Annual Benefit in Equation (I).

Paybackperiod=$50$30=1.67Years

Calculate the Payback period for Alternative-B.

Substitute $150 for Cost, and $45 for Annual Benefit in Equation (I).

Paybackperiod=$150$45=3.33Years

Calculate the Payback period for Alternative-C.

Substitute $110 for Cost, and $45 for Annual Benefit in Equation (I).

Paybackperiod=$110$45=2.44Years

The alternative that has minimum value of payback period should be selected.

Conclusion:

Therefore, the Alternative- B should be selected.

To determine

(b)

The best alternative based on future worth analysis.

Expert Solution
Check Mark

Answer to Problem 51P

The Alternative- B should be selected.

Explanation of Solution

Calculation:

Calculate the net future worth for alternative-A.

NFW=$30(FA,10%,3)$50(FP,10%,3) ...... (II)

Here, the net future worth is NFW, the future value is F, the Annual benefit is A and the initial cost is P.

Calculate the factor (FA,10%,3).

(FA,10%,3)=[(1+0.10)310.10]=3.31

Calculate the factor (FP,10%,3).

(FP,10%,3)=(1+0.10)3=1.331

Substitute $3.31 for (FA,10%,3), and 1.331 for (FP,10%,3) in Equation (II).

NFW=$30×3.31$50×1.331=$99.3$66.55=$32.75

Calculate the net future worth (NFW) for alternative-B.

NFW=$45(FA,10%,9)$150(FP,10%,9) ...... (III)

Calculate the factor (FA,10%,9).

(FA,10%,9)=[(1+0.10)910.10]=$13.58

Calculate the factor (FP,10%,9).

(FP,10%,9)=(1+0.10)9=2.36

Substitute $13.58 for (FA,10%,9), and 2.36 for (FP,10%,9) in Equation (III).

NFW=$45×13.58$150×2.36=$611.1$354=$257.1

Calculate the net future worth (NFW) for alternative-C.

NFW=$45(FA,10%,6)$110(FP,10%,6) ...... (IV)

Calculate the factor (FA,10%,6).

(FA,10%,6)=[(1+0.10)610.10]=$7.715

Calculate the factor (FP,10%,6).

(FP,10%,6)=(1+0.10)6=1.772

Substitute $7.715 for (FA,10%,6), and 1.772 for (FP,10%,6) in Equation (IV).

NFW=$45×7.715$110×1.772=$347.175$194.92=$152.255

The Alternative that has maximum value of future worth should be selected.

Conclusion:

Therefore, the Alternative- B should be selected.

To determine

(c)

The best alternative based on B/C ratio analysis.

Expert Solution
Check Mark

Answer to Problem 51P

The Alternative- C should be selected.

Explanation of Solution

Calculation:

Calculate the factor (PA,10%,3).

(PA,10%,3)=[(1+0.10)310.10(1+0.10)3]=2.49

Write the equation for B/C ratio.

B/Cratio=EUABEUAC ...... (V)

Calculate EUAB for Alternative-A.

EUAB=$30(PA,10%,5) ...... (VI).

Substitute 2.49 for (PA,10%,3) in Equation (VI).

EUAB=$30×2.49=$74.7

Calculate the B/C ratio for Alternative-A.

Substitute $74.7 for EUAB, and $50 for EUAC in Equation (V).

B/Cratio=$74.7$50=1.494

Calculate the factor (PA,10%,9).

(PA,10%,9)=[(1+0.10)910.10(1+0.10)9]=5.759

Write the Equation for B/C ratio.

B/Cratio=EUABEUAC ...... (VII)

Calculate EUAB for Alternative-B.

EUAB=$30(PA,10%,9) ...... (VIII).

Substitute 5.759 for (PA,10%,9) in Equation (VIII)

EUAB=$45×5.759=$259.155

Calculate the B/C ratio for Alternative-B.

Substitute $259.155 for EUAB, and $150 for EUAC in Equation (VII).

B/Cratio=$259.155$150=1.73

Calculate the factor (PA,10%,6).

(PA,10%,6)=[(1+0.10)610.10(1+0.10)6]=4.355

Write the Equation for B/C ratio.

B/Cratio=EUABEUAC ...... (IX)

Calculate EUAB for Alternative-B.

EUAB=$30(PA,10%,6) ...... (X).

Substitute 4.355 for (PA,10%,6) in Equation (X).

EUAB=$45×4.355=$195.975

Calculate the B/C ratio for Alternative-B.

Substitute $195.975 for EUAB, and $150 for EUAC in Equation (VII).

B/Cratio=$195.975$110=1.78.

Conclusion:

Therefore, the Alternative- C should be selected.

To determine

(d)

The reason behind the difference in answer in parts (a), (b), and (c).

Expert Solution
Check Mark

Answer to Problem 51P

Explanation of Solution

In this case, there are three alternatives and rate of return accounts from 10%. Since, each alternative generates uniform annual benefits in excess of the cost, during the useful life and the payback period analysis ignores time value of money and only concentrates on time required to recover the investment. Therefore, payback period pertaining to each alternative is less than the alternative's useful life.

Since, least time is taken by alternative A for recovering the cost, however according to part (b), Alternative B is favorable for long-term economic efficiency and Alternative C is favorable according to part (c). Hence, it is ascertained that the answers in part (c), (a) and (b) differs from each other.

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ENGR.ECONOMIC ANALYSIS W/DASHBOARD

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