Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
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Chapter 13, Problem 28P
To determine

(a)

The minimum cost life and the minimum EUAC if the new car is bought.

Expert Solution
Check Mark

Answer to Problem 28P

The minimum cost of life is $2300.

The minimum equivalent uniform annual cost is $19700.

Explanation of Solution

Given:

The annual cost of new car is $22000.

The depreciation rate for new as well as old car is 10%.

The maintenance cost is $100 per year during 2 years warranty period.

The maintenance cost after the warranty period is $600 per year with an annual increase of $400 per year.

The rate of interest is 10%.

Concept used:

Write the expression for minimum cost of life.

CL=D+M ...... (I)

Here, depreciation is D and maintenance cost is M.

Write the expression for minimum equivalent uniform annual cost.

EUACmin=ACL ...... (II)

Here, annual cost of car is A and minimum cost of life is CL.

Calculations:

Calculate the depreciation for the new car.

D=10%×$22000=10100×$22000=$2200

Calculate the minimum cost of life.

Substitute $2200 for D and $100 for M in Equation (I).

CL=$2200+$100=$2300

The minimum cost of life is $2300.

Calculate the minimum equivalent uniform annual cost.

Substitute $22000 for A and $2300 for CL. in Equation (II).

EUACmin=$22000$2300=$19700

The minimum equivalent uniform annual cost is $19700.

Conclusion:

Thus, the minimum cost of life is $2300.

The minimum equivalent uniform annual cost is $19700.

To determine

(b)

The minimum cost life and the minimum EUAC when 2 years old car is bought.

Expert Solution
Check Mark

Answer to Problem 28P

The minimum cost of life is $2382.

The minimum equivalent uniform annual cost is $15438.

Explanation of Solution

Given:

He buys the car after it is 2 years old.

Calculations:

Calculate the cost of car after 2 years.

A=$22000(10%×$22000)(10%×90%×$22000)=$22000(10100×$22000)(10100×90100×$22000)=$22000$2200$1980=$17820

Calculate the depreciation for the car.

D=(10%)×$17820=10100×$17820=$1782

Calculate the minimum cost of life.

Substitute $1782 for D and $600 for M in Equation (I).

CL=$1782+$600=$2382

The minimum cost of life is $2382.

Calculate the minimum equivalent uniform annual cost.

Substitute $17820 for A and $2382 for CL. in Equation (II).

EUACmin=$17820$2382=$15438

The minimum equivalent uniform annual cost is $15438.

Conclusion:

Thus, the minimum cost of life is $2382.

The minimum equivalent uniform annual cost is $15438.

To determine

(c)

The minimum cost life and the minimum EUAC when 4 years old car is bought.

Expert Solution
Check Mark

Answer to Problem 28P

The minimum cost of life is $3043.42.

The minimum equivalent uniform annual cost is $11390.78.

Explanation of Solution

Given:

He buys the car after it is 4 years old.

Calculations:

Calculate the cost of car after 4 years.

A=$17820(10%×$17820)(10%×90%×$17820)=$17820(10100×$17820)(10100×90100×$17820)=$17820$1782$1603.8=$14434.2

Calculate the depreciation for the car.

D=(10%)×$14434.2=10100×$14434.2=$1443.42

Calculate the minimum cost of life.

Substitute $1443.42 for D and ($600+$1000) for M in Equation (I).

CL=$1443.42+($600+$1000)=$3043.42

The minimum cost of life is $3043.42.

Calculate the minimum equivalent uniform annual cost.

Substitute $14434.2 for A and $3043.42 for CL. in Equation (II).

EUACmin=$14434.2$3043.42=$11390.78

The minimum equivalent uniform annual cost is $11390.78.

Conclusion:

Thus, the minimum cost of life is $3043.42.

The minimum equivalent uniform annual cost is $11390.78.

To determine

(d)

The minimum cost life and minimum EUAC when 6 years old car is bought.

Expert Solution
Check Mark

Answer to Problem 28P

The minimum cost of life is $5969.1.

The minimum equivalent uniform annual cost is $5721.9.

Explanation of Solution

Given:

He buys the car after it is 6 years old.

Calculations:

Calculate the cost of car after 6 years.

A=$14434.2(10%×$14434.2)(10%×90%×$14434.2)=$14434.2(10100×$14434.2)(10100×90100×$14434.2)=$14434.2$1443.42$1299.08=$11691

Calculate the depreciation for new car.

D=(10%)×$11691=10100×$11691=$1169.1

Calculate the minimum cost of life.

Substitute $1169.1 for D and ($600+$1000+$1400+$1800) for M in Equation (I).

CL=$1169.1+($600+$1000+$1400+$1800)=$5969.1

The minimum cost of life is $5969.1.

Calculate the minimum equivalent uniform annual cost.

Substitute $11691 for A and $5969.1 for CL. in Equation (II).

EUACmin=$11691$5969.1=$5721.9

The minimum equivalent uniform annual cost is $5721.9.

Conclusion:

Thus, the minimum cost of life is $5969.1.

The minimum equivalent uniform annual cost is $5721.9.

To determine

(e)

The strategy that should be recommended.

Expert Solution
Check Mark

Answer to Problem 28P

The best strategy recommended is to buy the car after it is 6years old.

Explanation of Solution

The strategy which gives minimum equivalent uniform annual cost is considered the best one.

The minimum cost of life when 6 years old car is bought is $5969.1 and the minimum equivalent uniform annual cost is $5721.9.

Thus, it is considered as the best strategy as it yields the minimum equivalent uniform annual cost.

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