Two financial choices are available. We will compare them using the standard cri
ID: 2461573 • Letter: T
Question
Two financial choices are available. We will compare them using the standard criteria that the Annual Worth of one is greater than the annual worth than the other. (A) The first choice has an initial investment of 20,000. It generates a yearly revenue of 10000 and at the end of three years has a salvage value of 2000. (B) The second choice has an initial investment of 30,000. It generates a yearly revenue of 12000 and at the end of 6 years has a salvage value of 4000. The interest rate environment is 3%. The management wishes the Time Horizon to be 24 years and assume exact repetition of the choice after each time period is completed. Analyze the two choices using Annualized Worth.Explanation / Answer
A) First Option Years nvestment Annual Revenue Salvage Net Worth PV factor @3% PV of Benefits Year 1 (20,000) 10,000 (10,000) 0.971 (9,709) Year 2 10,000 10,000 0.943 9,426 Year 3 10,000 2,000 12,000 0.915 10,982 Year 4 (20,000) 10,000 (10,000) 0.888 (8,885) Year 5 10,000 10,000 0.863 8,626 Year 6 10,000 2,000 12,000 0.837 10,050 Year 7 (20,000) 10,000 (10,000) 0.813 (8,131) Year 8 10,000 10,000 0.789 7,894 Year 9 10,000 2,000 12,000 0.766 9,197 Year 10 (20,000) 10,000 (10,000) 0.744 (7,441) Year 11 10,000 10,000 0.722 7,224 Year 12 10,000 2,000 12,000 0.701 8,417 Year 13 (20,000) 10,000 (10,000) 0.681 (6,810) Year 14 10,000 10,000 0.661 6,611 Year 15 10,000 2,000 12,000 0.642 7,702 Year 16 (20,000) 10,000 (10,000) 0.623 (6,232) Year 17 10,000 10,000 0.605 6,050 Year 18 10,000 2,000 12,000 0.587 7,049 Year 19 (20,000) 10,000 (10,000) 0.570 (5,703) Year 20 10,000 10,000 0.554 5,537 Year 21 10,000 2,000 12,000 0.538 6,451 Year 22 (20,000) 10,000 (10,000) 0.522 (5,219) Year 23 10,000 10,000 0.507 5,067 Year 24 10,000 2,000 12,000 0.492 5,903 16.9355 64,057 NPV of Net Annual Worth 64,056.88 Annuity Factor = 16.9355 Annualized Worth=64056.88/16.9355 $ 3,782.39 B) Second Option Years nvestment Annual Revenue Salvage Net Worth PV factor @3% PV of Benefits Year 1 (30,000) 12,000 (18,000) 0.971 (17,476) Year 2 12,000 12,000 0.943 11,311 Year 3 12,000 12,000 0.915 10,982 Year 4 12,000 12,000 0.888 10,662 Year 5 12,000 12,000 0.863 10,351 Year 6 12,000 4,000 16,000 0.837 13,400 Year 7 (30,000) 12,000 (18,000) 0.813 (14,636) Year 8 12,000 12,000 0.789 9,473 Year 9 12,000 12,000 0.766 9,197 Year 10 12,000 12,000 0.744 8,929 Year 11 12,000 12,000 0.722 8,669 Year 12 12,000 4,000 16,000 0.701 11,222 Year 13 (30,000) 12,000 (18,000) 0.681 (12,257) Year 14 12,000 12,000 0.661 7,933 Year 15 12,000 12,000 0.642 7,702 Year 16 12,000 12,000 0.623 7,478 Year 17 12,000 12,000 0.605 7,260 Year 18 12,000 4,000 16,000 0.587 9,398 Year 19 (30,000) 12,000 (18,000) 0.570 (10,265) Year 20 12,000 12,000 0.554 6,644 Year 21 12,000 12,000 0.538 6,451 Year 22 12,000 12,000 0.522 6,263 Year 23 12,000 12,000 0.507 6,080 Year 24 12,000 4,000 16,000 0.492 7,871 16.9355 122,643 NPV of Net Annual Worth 122,643.20 Annuity Factor = 16.9355 Annualized Worth=122643.20/16.9355 $ 7,241.76 So the second option has more annualised worth.
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