ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 6, Problem 29P
To determine

The equivalent annual cost of owning a car.

Expert Solution & Answer
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Answer to Problem 29P

The equivalent annual cost of owning a car is, $7150.485.

Explanation of Solution

Given:

Vehicle down payment is $2200.

Vehicle payments is $5500 for period 14.

Prepaid insurance is, $1500, which is increased by 8% per year.

Gas, oil, and maintenance cost is, $2000 that increases by 10% per year.

New tires cost is $650 during period 4 and 800 during period 8.

Major maintenance overhaul at period five is, $2400.

Salvage of vehicle at period 9 is, $3750.

Calculation:

Tabulate the values for calculation of total cost/benefits.

Time Down payment Annual payments (a) Prepaid insurance(b) Wear and Tear (c) Tires(d) Salvage Total costs/benefits (a + b + c + d)
0 $2200 $2200
1 $5500 $1500 $2000 $9000
2 $5500 $1620 $2200 $9320
3 $5500 $1749.6 $2420 $9670
4 $5500 $1889.57 $2662 $650 $10701.57
5 $2040.7 $2928.20 $4969
6 $2204 $3221.02 $5425
7 $2380.3 $3543.12 $5923.42
8 $2570.74 $3897.43 $800 $7268.17
9 $3750 $3750

Write the equation for equivalent annual unit cost.

EUAC=[$2200(AP,0.05,9)+$9000(PF,0.05,1)(AP,0.05,9)+$9320(PF,0.05,2)(AP,0.05,9)+$9670(PF,0.05,3)(AP,0.05,9)+$10701.57(PF,0.05,4)(AP,0.05,9)+$4969(PF,0.05,5)(AP,0.05,9)+$5425(PF,0.05,6)(AP,0.05,9)+$5923.42(PF,0.05,7)(AP,0.05,9)+$7268.17(PF,0.05,8)(AP,0.05,9)$3750(AF,0.05,9)] ...... (I)

Here, the equivalent uniform cost is EUAC, the down payment is D, salvage value is S, present worth is P, future worth is F, annual amount is A, interest rate is i, and number of year is n.

Calculate the factor (AP,i,n) for 9 years.

(AP,i,n)=[i(1+i)n(1+i)n1] ...... (II)

Substitute 5% for i, and 9years for n in Equation (II).

(AP,i,n)=[0.05( 1+0.05)9( 1+0.05)91]=0.1407

Calculate the factor (AF,i,n)

(AF,i,n)=[i(1+i)n1] ...... (III)

Substitute 5% for i, and 9years for n in Equation (III).

(AF,i,n)=[0.05( 1+0.05)91]=0.0907

Calculate the factor (PF,i,n)

(PF,i,n)=1(1+i)n ...... (IV)

Calculate the factor (PF,i,n) for 1 year.

Substitute 5% for i, and 1years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)1=0.9524

Substitute 5% for i, and 2years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)2=0.9070

Substitute 5% for i, and 3years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)3=0.8638

Substitute 5% for i, and 4years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)4=0.8227

Substitute 5% for i, and 5years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)5=0.7835

Substitute 5% for i, and 6years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)6=0.7462

Substitute 5% for i, and 7years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)7=0.7107

Substitute 5% for i, and 8years for n in Equation (IV).

(PF,i,n)=1( 1+0.05)8=0.6768

Substitute all the factors in Equation (I).

EUAC=[$2200×0.1407+$9000×0.9524×0.1407+$9320×0.9070×0.1407+$9670×0.8638×0.1407+$10701.57×0.8227×0.1407+$4969×0.7835×0.1407+$5425×0.7462×0.1407+$5923.42×0.7107×0.1407+$7268.17×0.6768×0.1407$3750×0.0907]=[$309.54+$1206.02+$1189.37+$1175.25+$1238.75+$517.68+$569.57+$592.31+$692.12$340.125]=$7150.485.

Conclusion:

Therefore, the Equivalent annual cost of owning a car is, $7150.485.

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