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|CE361 Introduction to Transportation Engineering |Posted: Fri. 3 October 2008 |

|Homework 6 Solutions |Due: Wed. 15 October 2008 |

ECONOMIC EVALUATION AND RANKING OF ALTERNATIVES

Three or fewer CE361 students.

1. Vernita Lee, who is Oprah Winfrey’s mom, has a credit problem.

A. (5 points) If Mrs. Lee pays only the interest due on the $155,547 balance and the annual interest rate is 18.0 percent, how much will her next monthly payment be?

[pic]* $155,547 = $2333.21

B. (5 points) Actually, a cardholder must also pay at least 4 percent of the outstanding balance each month. How much will this add to Mrs. Lee’s monthly payment?

0.04*$155,547=$6221.88

C. (10 points) If Mrs. Lee pays the combined amount found in Parts A and B each month, how many months will it take her to pay off her debt to Valentina, Inc.? Assume that she makes no new charges to her account. (Using the Solver feature of a spreadsheet is acceptable, if you explain how your solution was found.)

Mrs. Lee needs to pay $2333.21+$6221.88=$8555.09 until balance of debt drops below zero. If i=0, n=[pic]= 18.18 months to retire the debt, but i=0.18/year and she must keep paying interest on the declining balance until the balance drops to zero. If P=$155,547 and A=$8555.09, [A|P] must be $8555.09/$155,547 = 0.055. [A|P,i=0.18/12=0.015,n]=[pic]= 0.055 when n=21.4 months. (Found using Solver feature of Excel.)

2. Choosing between two proposed traffic safety projects. The intersection of Renner Blvd and Dell Ave has a very high crash rate. Two solutions are proposed.

• Project A: Build a $5.57 million overpass to separate the two roadways. The estimated value of the crashes avoided will be $513,000 per year over the next 20 years.

• Project B: Improve the geometry and signal timing at the intersection, at a cost of $418,000. The estimated value of the crashes avoided will be $61,800 per year over the next 20 years.

A. (10 points) What are PWB and PWC for each project? Show your cash flow diagrams and calculations. The current government interest rate is 5.4 percent/year.

|[pic] |In cash flow diagram at left, replace “P” with “PWB”. There will be twenty “A” arrows, each |

| |$513,000 or $61,800, depending on the problem. Calcs are: |

PWB (A)= $513,000*[P|A,0.054,20]=$513,000*12.050

=$6,181,733

PWB (B)= $61,800*[P|A,0.054,20]=$61,800*12.050

=$744,700

PWC(A) = $5,570,000; PWC(B) = $418,000

B. (5 points) Using NPW, which project is better?

NPW(A) = PWB(A)-PWC(A) = $6,181,733-$5,570,000 = $611,733

NPW(B) = PWB(B)-PWC(B) = $744,700-$418,000 = $326,700

Project A has the higher NPW.

C. (5 points) Using BCR, which project is better?

BCR(A) = [pic]= 1.11

BCR(B) = [pic]= 1.78

Project B has the higher BCR.

3. Ranking alternatives. The PSR factor values in FTE Table 5.10 are not correct.

A. (10 points) What is the correct PSR Percentile value for each Segment A through K? Show your Percentile calculation for each of the five possible “raw” values – 1-5.

Using FTE (5.13), if PSR=5, the corresponding Percentile value = [pic]* 100 = 0.

If PSR=4, Percentile = [pic]* 100 = 10.

If PSR=3, Percentile = [pic]* 100 = 25.

If PSR=2, Percentile = [pic]* 100 = 71.

If PSR=1, Percentile = [pic]* 100 = 100.

B. (11 points) Recompute the CPI for all eleven segments.

See entries in CPI column in New Table 5.10 below.

Example calc: CPI(H) = [pic]+[pic]+[pic]= 63.3 versus 63.4 in Table. Spreadsheet used to produce Table 5.10 used unrounded percentile values.

Table 5.10 Priority ranking of highway segments

|Segment |PSR |AADT |HAZ |CPI |Dollars ($) |Cumulative ($) |

|H |71 |30 |89 |63.4 | 161,500 | $ 161,500 |

|J |100 |90 |0 |63.3 | 78,000 | $ 239,500 |

|D |71 |10 |100 |60.5 | 90,000 | $ 329,500 |

|C |71 |100 |0 |57.1 | 402,600 | $ 732,100 |

|A |100 |70 |0 |56.7 | 181,700 | $ 913,800 |

|E |25 |40 |89 |51.3 | 46,500 | $ 960,300 |

|B |25 |80 |0 |35.0 | 45,000 | $ 1,005,300 |

|K |71 |0 |0 |23.8 | 30,000 | $ 1,035,300 |

|F |0 |60 |0 |20.0 |0 | $ 1,035,300 |

|G |10 |50 |0 |20.0 | 22,000 | $ 1,057,300 |

|I |25 |20 |0 |15.0 | 64,000 | $ 1,121,300 |

C. (9 points) How many road segment projects can be undertaken, given the county’s $600,000 budget? Which road segments will get improvements?

Dollars/mile values have been converted to dollars/segment. Segments H, J, and D receive the three highest CPI scores. Together, those three road projects would cost $329,500. Adding the fourth neediest project (Segment C) would exceed the $600,000 budget specified in the problem.

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