The preference of one alternative out of the three based on economic criteria by using the present worth, equivalent annual cost, benefit-cost ratio and rate of return methods.

Question

Want to see more full solutions like this?

Answer 1

Question

100%

Chapter 13, Problem 14P

To determine

The preference of one alternative out of the three based on economic criteria by using the present worth, equivalent annual cost, benefit-cost ratio and rate of return methods.

Expert Solution & Answer

Answer to Problem 14P

Alternative 3- Intersection widening

Explanation of Solution

Given:

Analysis period = 20 years

Annual interest rate = 15 percent

MindTap Engineering for Garber/Hoel's Traffic and Highway Engineering, 5th Edition, [Instant Access], 1 term (6 months), Chapter 13, Problem 14P

Calculation:

Determine the present worth of alternative 1 (Traffic signals):

PW1=−340,000−(10,000+450,000)(P/A−15−20)+25,000(P/F−15−20)(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26(P/F−15−20)=1 ( 1+i )n=1 ( 1+0.15 ) 20=0.0611PW1=−340,000−(10,000+450,000)(6.26)+25,000(0.0611) =$−3218072.50

Determine the present worth of alternative 2 (Intersection widening):

PW2=−850,000−(5,000+300,000)(P/A−15−20)+12,000(P/F−15−20)(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26(P/F−15−20)=1 ( 1+i )n=1 ( 1+0.15 ) 20=0.0611PW2=−850,000−(5,000+300,000)(6.26)+12,000(0.0611) =$−2758566.80

Determine the present worth of alternative 3 (Grade separation):

PW3=−2,120,000−(5,000+225,000)(P/A−15−20)(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26PW3=−2,120,000−(5,000+225,000)(6.26) =$−3559800

The project with the highest present worth is alternative 2.

Determine the equivalent annual cost of alternative 1 (Traffic signals):

EUAW=NPW[i ( 1+i ) n ( 1+i ) n−1]EUAW1=−3218072.50 [0.15 ( 1+0.15 ) 20 ( 1+0.15 ) 20−1]EUAW1=$−514891.60

Determine the equivalent annual cost of alternative 2 (Intersection widening):

EUAW=NPW[i ( 1+i ) n ( 1+i ) n−1]EUAW2=−2758566.80 [0.15 ( 1+0.15 ) 20 ( 1+0.15 ) 20−1]EUAW2=$−441370.688

Determine the equivalent annual cost of alternative 3 (Grade separation):

EUAW=NPW[i ( 1+i ) n ( 1+i ) n−1]EUAW3=−3559800 [0.15 ( 1+0.15 ) 20 ( 1+0.15 ) 20−1]EUAW3=$−569568

The project with the highest equivalent annual costis alternative 2.

Determine the benefit-cost ratioof alternative 1 (Traffic signals):

BCR1=−( 10,000+450,000)( P/A−15−20)+25,000( P/F−15−20)−340,000(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26(P/F−15−20)=1 ( 1+i )n=1 ( 1+0.15 ) 20=0.0611BCR1=−2878072.5−340,000=8.465

Determine the benefit-cost ratio of alternative 2 (Intersection widening):

BCR2=−( 5,000+300,000)( P/A−15−20)+12,000( P/F−15−20)−850,000(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26(P/F−15−20)=1 ( 1+i )n=1 ( 1+0.15 ) 20=0.0611BCR2=−1908566.8−850,000=2.245>1

Since BCR >1, we would select Alternative 2.

Determine the benefit-cost ratio of alternative 3 (Grade separation):

BCR3=−( 5,000+225,000)( P/A−15−20)−2,120,000(P/A−15−20)= ( 1+i )n−1i ( 1+i )n= ( 1+0.15 ) 20−10.15 ( 1+0.15 ) 20=6.26BCR3=−1439800−2,120,000=0.68<1

Since BCR is less than 1, we would not select Alternative 3

Determine the benefit-cost ratio of alternative 2 with respect to 1:

BCR2−1=1,908,566.8−2,878,072.5850,000−340,000 =1.9

We reachthe same conclusion as previously, which is to select Alternative 2

Determine the rate of return (ROR)of alternative 1versus 2:

NPW=0=(850,000−340,000)−(5,000+150,000)(P/A−i−20)+(25,000−12,000)(P/F−i−20)

It is very difficult to solve this explicitly for i. By trial and error, we can easily find the i that makes the right side of the equation equal to the left side.

510,000=−155,000(P/A−i−20)+13,000(P/F−i−20)

Try i=30 %,

−155,000(P/A−30−20)+13,000(P/F−30−20)=513911.62

For i=31 %

−155,000(P/A−31−20)+13,000(P/F−31−20)=497684.2512

Then, we can try i=30.5 % and by interpolation 30.237 % is the rate of return to make the left side to equal to the right side.

Since ROR is greater than 15 percent, we select Alternative 2

Determine the rate of return (ROR) of alternative 3 versus 1:

NPW=0=(2,120,000−340,000)−(5,000+225,000)(P/A−i−20)+(25,000−0)(P/F−i−20)

By trial and error, we can easily find the i that makes the right side of the equation equal to the left side.

1,780,000=−230,000(P/A−i−20)+25,000(P/F−i−20)

Try i=11 %,

−230,000(P/A−11−20)+25,000(P/F−11−20)=1828464.62

For i=12 %

−230,000(P/A−12−20)+25,000(P/F−12−20)=1715277.50

By interpolation 11.428 % is the rate of return to make the left side to equal to the right side.

Since the ROR is lower than 15 percent, we discard Alternative 3.

Conclusion:

The second alternative i.e. Intersection widening is selected by using the three economic methods.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Three designs have been proposed to improve traffic flow at a major intersection in a heavily traveled suburban area. The first alternative involves improved traffic signaling. The second alternative includes traffic-signal improvements and intersection widening for exclusive left turns. The third alternative includes extensive reconstruction, including a grade separation structure. The construction costs, as well as annual maintenance and user costs, are listed in the following table for each alternative. Determine which alternative is preferred based on economic criteria if the analysis period is 20 years and the annual interest rate is 15%. Show that the result is the same using the present worth, equivalent annual cost, benefit–cost ratio, and rate-of-return methods.

Three designs have been proposed to improve traffic flow at a major intersection in a heavily traveled suburban area. The first alternative involves improved traffic signaling. The second alternative includes traffic-signal improvements and intersection widening for exclusive left turns. The third alternative includes extensive reconstruction, including a grade separation structure. The construction costs, as well as annual maintenance and user costs, are listed in the following table for each alternative. Determine which alternative is preferred based on economic criteria if the analysis period is 20 years and the annual interest rate is 15%. Show that the result is the same using the present worth, equivalent annual cost, benefit–cost ratio, and rate-of-return methods. Alternatives Capital Cost ($) Annual Maintence ($) Annual User Cost ($) Salvage Value ($) Present Condition 0 15,000 600,000 0 Traffic Signal 340,000 10,000 450,000 25,000 Intersection Widening 850,000 5,000…

Identify and briefly discuss at least 3 risks that may be associated with this project. Highway 410/Steeles Road Project- Highway 410 currently has 4 lanes of traffic in each direction, i.e., northbound and southbound, with a 12-ft median between the northbound and southbound lanes- Steeles Road has 3 lanes of traffic in each direction, i.e., eastbound and westbound, with 4-ft median between the eastbound and westbound lanes- For this project the requirement is to: Build two off-ramps from Highway 410 to Steeles Road to, i.e., eastbound and westbound ramps Build two on-ramps from Steeles Road to Highway 410, i.e., northbound and southbound ramps Build a bridge overpass on Highway 410 over Steeles Road

Answer 2