ENGINEERING ECO ANALYSIS W/STUDY GUIDE
ENGINEERING ECO ANALYSIS W/STUDY GUIDE
13th Edition
ISBN: 9780190693053
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 10, Problem 2P
To determine

The Equivalent uniform cost for 10000miles, 15000 miles, and 5000 miles.

Expert Solution & Answer
Check Mark

Answer to Problem 2P

The EUAC for 10000miles is, $4725.6.

The EUAC for 15000miles is, $6669.1.

The EUAC for 5000miles is, $2782.1.

Explanation of Solution

Given:

Purchasing cost of used pickup is $14000.

Fuel cost is $1500 per year.

The drop of salvage value after 5 year is 10% per mile.

The number of miles truck has driven is 10000miles.

Rate of interest is 6%.

Calculation:

Case I: Truck is driven 10000 miles.

Calculate the salvage value.

Salvagevalue=(Purchaseprice)(0.10×(Milesdrivenin5years)) ...... (I)

Substitute $14000 for Purchase price, 10000miles for Miles driven in 5 years in Equation (I).

Salvagevalue=$14000(0.10×(10000miles)×5)=$14000$5000=$9000

Calculate the Equivalent uniform annual cost.

EUAC=[Yearlyfuelcost+Yearlyothercosts+Purchaseprice[i(1+i)n(1+i)n1]Salvagevalue[i(1+i)n1]] ...... (II)

Here, the Equivalent uniform annual cost is EUAC, interest rate is i, and number of year is n.

Substitute $1500 for Yearly fuel cost and Yearly other cost, $14000 for Purchase price, $9000 for the Salvage value, 6% for i, and 5 year for n in Equation (II).

EUAC=[$1500+$1500+$14000[0.06(1+0.06)5(1+0.06)51]$9000[0.06(1+0.06)51]]=$3000+($14000×0.2373)($9000×0.1774)=$3000+$3322.2$1596.6=$4725.6

Case II: Truck is driven 15000 miles.

Calculate the fuel cost.

Fuelcost=$1500$10000×$15000=$2250

Calculate the salvage value.

Substitute $14000 for Purchase price, 15000miles for miles driven in 5 year in Equation (I).

Salvagevalue=$14000(0.10×(15000miles)×5)=$14000$7500=$6500

Calculate the Equivalent uniform annual cost.

Substitute $2250 for Yearly fuel cost and Yearly other cost, $14000 for Purchase price, $6500 for the Salvage value, 6% for i, and 5 year for n in Equation (II).

EUAC=[$2250+$2250+$14000[0.06(1+0.06)5(1+0.06)51]$6500[0.06(1+0.06)51]]=$4500+($14000×0.2373)($6500×0.1774)=$4500+$3322.2$1153.1=$6669.1

Case III: Truck is driven 5000 miles.

Calculate the fuel cost.

Fuelcost=$1500$10000×$5000=$750

Calculate the salvage value.

Substitute $14000 for Purchase cost, 15000miles for miles driven in 5 year in Equation (I).

Salvagevalue=$14000(0.10×(5000miles)×5)=$14000$2500=$11500

Calculate the Equivalent uniform annual cost.

Substitute $750 for Yearly fuel cost and Yearly other cost, $14000 for Purchase price, $11500 for the Salvage value, 6% for i, and 5 year for n in Equation (II).

EUAC=[$750+$750+$14000[0.06(1+0.06)5(1+0.06)51]$11500[0.06(1+0.06)51]]=$1500+($14000×0.2373)($11500×0.1774)=$1500+$3322.2$2040.1=$2782.1.

Conclusion:

Therefore, the EUAC for 10000miles is, $4725.6.

The EUAC for 15000miles is, $6669.1.

The EUAC for 5000miles is, $2782.1.

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