Please help me solve this question. Thank you so much! Replacement of equipment.
ID: 2613377 • Letter: P
Question
Please help me solve this question. Thank you so much!
Replacement of equipment. I own an old car that is worth about $3,000. As long as I keep fixing it, that salvage value is constant. It costs $5,000/year to maintain and fuel the car. Elon Musk just tweeted this: The Tesla 3 will cost $35,000, but has much lower fuel and maintenance costs of only $500/year. All these figures are real dollars. Suppose the resale value of the Tesla after 7 years is $10,000. Use a 10% real discount rate. Spreadsheet: What is the 7-year present value of costs for my old car? (include final salvage) What is the 7-year present value of costs for the Tesla 3 replacement? (include initial salvage and final resale) On a 7-year horizon, what is the annual lease equivalent for each car? In other words, convert the cash flows to a 7-year annuity. On a spreadsheet you can use guess-and-check (or goal seek, or PMT function); on paper use the A(7,10%)=4.868 annuity factor. Try all of these methods. Perhaps the Tesla also approaches a constant resale value. Since the Tesla generates $4,500/year of operating savings versus the old car (not including initial price), we could estimate a terminal valuation using a "multiple" of annual savings. Use a 4X multiple, plus the old-car base salvage, to re-estimate the constant resale. What is the 7-year annual lease equivalent now?Explanation / Answer
a. What is the 7-year present value of costs for old car? Year Fuel and Car Maintainers PV@10% Present value of Cash flow 1 5000 0.935 4675 2 5000 0.873 4365 3 5000 0.816 4080 4 5000 0.763 3815 5 5000 0.713 3565 6 5000 0.666 3330 7 5000 0.623 3115 7 -3000 0.623 -1869 Total cost of the car 25076 b.What is the 7-year present value of costs for the tesla 3 replacement ?( include initial salvage and final resale) Year Fuel and Car Maintainers PV@10% Present value of Cash flow 1 32000 1 32000 1 500 0.935 467.5 2 500 0.873 436.5 3 500 0.816 408 4 500 0.763 381.5 5 500 0.713 356.5 6 500 0.666 333 7 500 0.623 311.5 7 -10000 0.623 -6230 Total cost of the car 28464.5 c. on a 7 year horizon,what is the annual lease equivalent for each car ? In the other word, convert the cash flows to a 7 year annuity. On a spreadsheet you can use guess and check (Or goal seek, or PMT function ) on Paper use the A(7,10%) =4.868 annuity factory try all of these method Total Lease amount annuity Factor Old Cars = 25076 5151 7 year annuity fctory = 4.868 We can take the car on lease for amount of $5151 for seven years. d Ans) New Car = 28465 5847 7 year annuity fctory = 4.868 If we consider second method then total lease value is $28465, then total sale