Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
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Chapter 10, Problem 27P
To determine

(a)

The expected value of equivalent uniform annual cost.

Expert Solution
Check Mark

Answer to Problem 27P

The expected value of equivalent uniform annual cost is $7021.35.

Explanation of Solution

Given:

Optimistic probability is 20%, most likely probability is 50% and pessimistic probability is 30%.

From question number 2 obtain equivalent uniform annual cost (EUAC) for optimistic, most likely and pessimistic case.

The values are:

Cases EUAC
Pessimistic (5000miles/year) $3783.50
Most likely (10000miles/year) $6727
Optimistic (15000miles/year) $9670.50

Concept used:

The expected value of equivalent uniform annual cost can be calculated by the summation of the product of equivalent uniform cost and their probabilities in optimistic, most likely and in pessimistic case.

Calculation:

Let expected value in optimistic case be (E)O.

Calculate the expected value in optimistic case (E)O.

(E)O=(EUACo×Po)

Here, probability is Po and EUACo in optimistic case.

Substitute $3783.50 for EUACo and 0.20 for Po.

(E)O=($3783.50×0.20)=$756.70

Let expected value in most likely case be (E)M.

Calculate the expected value in most likely case (E)M.

(E)M=(EUACm×Pm)

Here, probability is Pm and EUACm in most likely case.

Substitute, $6727 for EUACm and 0.50 for Pm.

(E)M=($6727×0.50)=$3363.50

Let expected value in pessimistic case be (E)P

Calculate the expected value in pessimistic case (E)P.

(E)P=(EUACp×Pp)

Here, probability is Pp and EUACp in pessimistic case.

Substitute $9670.50 for EUACp and 0.30 for Pp.

(E)P=($9670.50×0.30)=$2901.15

Calculate the expected value of equivalent uniform of annual cost.

Let the expected value of equivalent uniform of annual cost denoted by (E)EUAC.

(E)EUAC=(E)O+(E)M+(E)P

Substitute $756.70 for (E)O, $3363.50 for (E)M and $2901.15 for (E)P.

(E)EUAC=$756.70+$3363.50+$2901.15=$7020.35.

Conclusion:

Thus, the expected value of equivalent uniform of annual cost is $7021.35.

To determine

(b)

The expected value for number of miles and their corresponding annual cost.

Expert Solution
Check Mark

Answer to Problem 27P

The expected value for number of miles are 10500.

The corresponding annual cost is $7373.54.

Explanation of Solution

Given:

Fuel cost is $1500.

Cost for oil, repair, tires is $1500 per year.

Initial investment is $14000.

Drop in cent per mile is 10cent.

Interest rate is 6%.

Number of years is 5.

Concept used:

The expected of number of miles is determined by the summation of the product of number of miles in different situations and their respective probabilities.

Calculation:

Calculate the expected number of miles in optimistic case (EM)O.

(EM)O=(NM×P)O

Here, probability is P and number of miles in optimistic case is NM.

Substitute, 5000 for NM and 0.20 for P.

(EM)O=(5000×0.20)=1000

Let expected number of miles in most likely case be (EM)M.

Calculate the expected number of miles in most likely case.

(EM)M=(NM×P)M

Substitute, 10000 for NM and 0.50 for P.

(EM)M=(10000×0.50)=5000

Let expected number of years in pessimistic case be (EM)P.

Calculate the expected number of miles in pessimistic case.

(EM)P=(NM×P)P

Substitute, 15000 for NM and 0.30 for P.

(EM)P=(15000×0.30)=4500

Calculate the expected number of miles (E)r.

(E)r=(EM)O+(EM)M+(EM)P

Substitute, 1000 for (EM)O, 5000 for (EM)M, 4500 for (EM)P.

(E)r=1000+5000+4500=10500miles

The annual cost is the sum of fuel cost and oil, repair and tires cost per year.

Calculate the annual cost (a).

a=f+t

Here, fuel cost is f and oil, repair and tires cost is t.

Substitute, $1500 for f and $1500 for t.

a=$1500+$1500=$3000

Calculate the salvage value per year (S).

S=(EM)×d100

Here, expected number of miles per year is (EM) and drop in cent per mile is d.

Substitute, 10500 for (EM) and 10 for d.

S=10500×10100=$1050

The total annual cost is the sum of salvage cost and annual cost.

Calculate the total annual cost (A).

A=a+S

Substitute, $3000 for a and $1050 for S.

A=$3000+$1050=$4050

Calculate the equivalent annual cost. (A)e.

(A)e=Annualcost+(r×initialinvestemnt11 ( 1+r) n)

Here, interest rate is r and number of years is n.

Substitute, $4050 for Annualcost, 0.06 for r, $14000 for Initialinvestemnt and 5 for n.

(A)e=$4050+(0.06×$140001 1 ( 1+.06) 5)=$7373.54.

Conclusion:

Thus, the expected value for number of miles are 10500.

The corresponding annual cost is $7373.54.

To determine

(c)

If the answers in part (a) and part (b) match.

Expert Solution
Check Mark

Answer to Problem 27P

Answer in part (a) and part (b) are approximately the same.

Explanation of Solution

Answer in part (a) and part (b) are approximately the same.

This is because in part (a), the expected value of equivalent uniform annual cost is calculated with each possible mileage which is adjusted in accordance to their probability.

In part (b), the annual cost is calculated by first adjusting with their probability and then is calculated for possible mileage.

The same equation is obtained in both the parts. Therefore, answers are approximately same.

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