4. (Challenge) Replacement Decisions And now for something completely different. This question is based on a published paper: Al-Chalabi, H., Lundberg, J., Alireza, A. & Jonsson, A. (2015). Case Study: Model for Economic Lifetime of Drilling Machines in the Swedish Mining Industry. The Engineering Economist, 6012 138-154 You may find it useful to read the paper. I have simplified the case study slightly for this project. In particular, I've approximated their Lorentzian cost equations by geometric sequences calibrated to their estimates for months 75 - 120, to make it easier to use the DCFA. Sam has been hired by a Swedish mining company to determine how often they should replace their drilling machines. Currently, they are replacing them every 120 months, but recently it's been suggested that they could save money by choosing a slightly different replacement period. The situation is as follows: The machines cost $6,000 in month 0. Once the company is done with the machines, it sells them. Immediately (less than one second) after purchase, the machine's resale value falls to 90% of its purchase price. This is the 'driving the car off the lot' depreciation familiar to car owners. After this immediate drop in value, the machines lose d% of their resale value each month. If the resale value is $V in month N, it's (1 -d%)XV in month N+1. Sam's company contact isn't sure what the value of d is, but they know that the machine's resale value is $50 in month 50. The machine is subject to ongoing operating and maintenance costs. Operating costs grow by 4.043% per month. Maintenance costs grow by 3.895% per month. Sam's company contact only has operating & maintenance values for month 75 on hand. In month 75, operating costs for the month are $9.89, and maintenance costs for the month are $24.20. The mining company's MARR is 10% per year. Help Sam out by doing the following: a. (3 marks) Write the EACIN) equation for the drilling machine using DCFA notation (e.g. (P/F,6%,N)). You will probably want to use (P/A&i.N) and (A/P.I.N). b. (4 marks) Use your answer for part a. to calculate the economic lifetime of the drilling machine to the nearest month. Back up your answer (explain your reasoning) with one or more of a graphs, a table or a step-by-step analytical solution. (I recommend a graph and a table, if you're comfortable with Excel.) Economic lifetime: months Work backing up your answer: c. |(3 marks) Sam's company contact wants to know how much money they are losing per machine each year by replacing the machines every 120 months, instead of at the economic lifetime. Calculate this amount, and show your work. (If we wanted the amount lost per month, it would just be the difference between EAC(120 months) and the EAC at the economic lifetime.) Money lost each year: (Show your work, using appropriate notation] 4. (Challenge) Replacement Decisions And now for something completely different. This question is based on a published paper: Al-Chalabi, H., Lundberg, J., Alireza, A. & Jonsson, A. (2015). Case Study: Model for Economic Lifetime of Drilling Machines in the Swedish Mining Industry. The Engineering Economist, 6012 138-154 You may find it useful to read the paper. I have simplified the case study slightly for this project. In particular, I've approximated their Lorentzian cost equations by geometric sequences calibrated to their estimates for months 75 - 120, to make it easier to use the DCFA. Sam has been hired by a Swedish mining company to determine how often they should replace their drilling machines. Currently, they are replacing them every 120 months, but recently it's been suggested that they could save money by choosing a slightly different replacement period. The situation is as follows: The machines cost $6,000 in month 0. Once the company is done with the machines, it sells them. Immediately (less than one second) after purchase, the machine's resale value falls to 90% of its purchase price. This is the 'driving the car off the lot' depreciation familiar to car owners. After this immediate drop in value, the machines lose d% of their resale value each month. If the resale value is $V in month N, it's (1 -d%)XV in month N+1. Sam's company contact isn't sure what the value of d is, but they know that the machine's resale value is $50 in month 50. The machine is subject to ongoing operating and maintenance costs. Operating costs grow by 4.043% per month. Maintenance costs grow by 3.895% per month. Sam's company contact only has operating & maintenance values for month 75 on hand. In month 75, operating costs for the month are $9.89, and maintenance costs for the month are $24.20. The mining company's MARR is 10% per year. Help Sam out by doing the following: a. (3 marks) Write the EACIN) equation for the drilling machine using DCFA notation (e.g. (P/F,6%,N)). You will probably want to use (P/A&i.N) and (A/P.I.N). b. (4 marks) Use your answer for part a. to calculate the economic lifetime of the drilling machine to the nearest month. Back up your answer (explain your reasoning) with one or more of a graphs, a table or a step-by-step analytical solution. (I recommend a graph and a table, if you're comfortable with Excel.) Economic lifetime: months Work backing up your answer: c. |(3 marks) Sam's company contact wants to know how much money they are losing per machine each year by replacing the machines every 120 months, instead of at the economic lifetime. Calculate this amount, and show your work. (If we wanted the amount lost per month, it would just be the difference between EAC(120 months) and the EAC at the economic lifetime.) Money lost each year: (Show your work, using appropriate notation]
