Please show work. You invest $25,000 now and receive $3,000 per year for 25 year
ID: 2612369 • Letter: P
Question
Please show work. You invest $25,000 now and receive $3,000 per year for 25 years starting at the end of the first year. What is the payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 8% annual rate compounded annually, and use the discounted payback approach (not Simple Payback). Discounted payback years answer A machine costs $50,000, and increases revenues by $18,000 per year. However, O&M; costs increase by $4,000 per year. The machine lasts 6 years and your MARR is 7% annual rate compounded annually. What is the Present Worth (or Net Present Value)? Should you purchase the machine? (One sentence answer why or why not)Explanation / Answer
1. Discounted Payback:
as can be seen from the table, the discounted payback is between 14 and 15 years.
= 14 + |-267.289|/945.725 = 14.28 years
2.
Yes, as the Present Worth is positive, the machine should be purchased
Year Cashflow Present Value factor = 1/1.08^year Discounted Cashflow Cumulative DCF 0 -25000 1 -25000 -25000 1 3000 0.925926 2777.778 -22222.2 2 3000 0.857339 2572.016 -19650.2 3 3000 0.793832 2381.497 -17268.7 4 3000 0.73503 2205.09 -15063.6 5 3000 0.680583 2041.75 -13021.9 6 3000 0.63017 1890.509 -11131.4 7 3000 0.58349 1750.471 -9380.89 8 3000 0.540269 1620.807 -7760.08 9 3000 0.500249 1500.747 -6259.34 10 3000 0.463193 1389.58 -4869.76 11 3000 0.428883 1286.649 -3583.11 12 3000 0.397114 1191.341 -2391.77 13 3000 0.367698 1103.094 -1288.67 14 3000 0.340461 1021.383 -267.289 15 3000 0.315242 945.7251 678.4361 16 3000 0.29189 875.6714 1554.107 17 3000 0.270269 810.8069 2364.914 18 3000 0.250249 750.7471 3115.661 19 3000 0.231712 695.1362 3810.798 20 3000 0.214548 643.6446 4454.442 21 3000 0.198656 595.9672 5050.409 22 3000 0.183941 551.8215 5602.231 23 3000 0.170315 510.9459 6113.177 24 3000 0.157699 473.098 6586.275 25 3000 0.146018 438.0537 7024.329