# Melbourne Transportation Engineering Questions

CVE 4000 – Transportation Engineering 05/25/2021 8:30a.m. Homework 1. [100 points] – Must submit as PDF file. (- 5% after 5 minutes of due time, – 20% per day of delay afterwards, correct answers receive full points only if the correct procedure is provided).

Challenge 1. [20 points] A lending institution charges a 6% interest rate compounded annually. A \$20,000 loan is given to a person with the possibility of paying \$5,000 at the end of the first year, \$10,000 at the end of the second year and the rest of the debt (principal + interests) at the end of the sixth year.

Question 1.1. (10 points) How much should the person pay at the end of the sixth year? Question 1.2. (10 points) Draw the corresponding cash flow diagram (borrower’s and lender’s).

Challenge 2 [20 points] A financial institution lends money to companies at an interest rate that compounds daily.

Question 2.a. (10 points) If a company borrows \$1.234 million today and pays \$4.321 million in 9 years. What is the nominal interest rate for that investment?

Question 2.b. (10 points) What is the effective interest rate for that investment?

Challenge 3 [20 points] A construction project can purchase concrete from two facilities. The transportation cost to bring materials to the project is \$0.40/m3 per mile. Facility Material Cost Sand content Distance to project A \$1.0/m3 25% 5.00 miles B \$1.5/m3 40% 7.25 miles

Question 3.a. (10 points) For each source facility, provide a mathematical function that computes the total cost of bringing concrete to the construction project.

Question 3b. (10 points) If least 31% sand content is required? What is the minimum cost of bringing to 110 m3 of concrete to the construction project? Indicate m3 from each facility and assume materials can be mixed at the construction project.

Challenge 4. [20 points] An engineering firm will commercialize units of certain product with the following production characteristics: Selling price \$167/unit Cost of materials and purchased parts \$25/unit Direct Labor Cost 2 hours per unit at \$20 per hour Fixed Costs \$1,400,000

Question 4.1. (5 points) If the overhead expenses are charged at 80% of labor cost, What is the manufacturing cost per unit?

Question 4.2. (5 points) What is the breakeven volume (in units) for this product?

Question 4.3. (5 points) What is the profit per unit if 30,000 units are sold?

Question 4.4. (5 points) To reduce the breakeven volume to 15,000 units, what should be the selling price?

Challenge 5 [20 points] A construction firm finished two projects today, both with very similar technical specifications. The first project involves the construction of a 2,100 square-feet facility and the total cost is \$480,000. The second project is a 8,300 square-feet facility with \$1,470,000.

Question 5.a. (10 points) Use the power-sizing model to determine the cost of a similar 5,500 square-feet project today?

Question 5.b. (10 points) If the construction cost index is expected to increase from 180 today to 600 in 10 years, what is the expected total construction cost for a 5,500 square-feet project 10 years from now? Equations and Factors that can be used to address the challenges 𝐹 = 𝑃(1 + 𝑖)𝑛 = 𝑃[𝐹 ⁄𝑃 , 𝑖, 𝑛] 𝑃 = 𝐹(1 + 𝑖)−𝑛 = 𝐹[𝑃/𝐹, 𝑖, 𝑛] 𝑖𝑎 = (1 + 𝑖)𝑚 − 1 𝐶𝑜𝑠𝑡(𝐴) 𝐶𝑜𝑠𝑡(𝐵) 𝐶𝑜𝑠𝑡(𝐴) 𝐶𝑜𝑠𝑡(𝐵) =( = 𝑆𝑖𝑧𝑒(𝐴) 𝑥 𝑃 Present value or present worth. 𝐹 Future value or future worth. 𝑖 Interest rate per time period. 𝑛: Number of time periods 𝑖𝑎 : Effective annual interest rate (𝑖𝑎 ). 𝑖 = 𝑟/𝑚 . 𝑟: Nominal interest rate (decimal). 𝑚: Number of compounding sub-periods (within the year) 𝑥: Power-sizing exponent (Adjustment for economies of scale) ) 𝑆𝑖𝑧𝑒(𝐵) 𝐼𝑛𝑑𝑒𝑥(𝐴) Cost and price index model 𝐼𝑛𝑑𝑒𝑥(𝐵) Total Cost(𝑥)= Total Revenue(𝑥) Factors 𝑥: Breakeven units. n: [F/P,6%, n]: 1 1.0600 2 1.1236 3 1.1910 4 1.2625 5 1.3382 6 1.4185

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