18. Apple's Internal Rate of Return (IRR) (first decimal; no rounding) is a) 49.3%; b) 55.9%; C) 64.1%; d) 67.8%. 19. HP's Internal Rate of Return (IRR) (first decimal; no rounding) is a) 43.4%; b) 48.6%; C) 53.1%; d) 59.9%. 20. The incremental Internal Rate of Return (AIRR) between the Apple and Dell computers (first decimal; no rounding) is a) Negative; b) 8.7%; c) 21.1%; d) 22.6%. Dell's External Rate of Return (ERR) (first decimal; no rounding) is a) 20.7%; b) 23.1%; c) 25.8%; d) 28.3%. 22. HP's External Rate of Return (ERR) (first decimal; no rounding) is a) 13.9%; b) 18.2%; c) 22.4%; d) 26.4%. 23. The incremental External Rate of Return (AERR) between the Apple and Dell computers (first decimal; no rounding) is a) 5.9%; b) 6.4%; c) 6.9%; d) 7.2%. 24. The incremental External Rate of Return (AERR) between the Apple and HP computers is a) 5.3%; b) 5.7%; c) 6.0%; d) 6.5%. 25. The best computer based on the external rate of return method is a) Apple; b) Dell; c) HP; d) None of the computers is valid. B. Problems and Questions An architectural company must replace one of its super computers. The key parameters (all arbitrary values) of the three computers under scrutiny are provided below. Parameters 1. Initial Cost ($) 2. Revenues ($) Apple Dell 15,000 22,000 45,000 at EOY1 43,000 at EOY1 increasing by increasing by $5,000 2.0% annually annually thereafter thereafter 41,000 at EOY1 38,000 at EOY1 increasing by decreasing by 1% annually 2% annually thereafter thereafter 400 HP 26,000 46,000 at EOY1 increasing by $500 annually thereafter 33,000 at EOY1 increasing by 0.5% annually thereafter 900 3. Operating costs ($) 0 4. End-of-life salvage value ($) 5. Useful life (years) 10 EOY = End-of-year Industry standard for backhoes = 4 years MARR = 10% DISCRETE CASH FLOWS AND DISCRETE COMPOUNDING 10.00 % DISCRETE RATE OF INTEREST 1% = 0.1000 k% = 0.1200 (F/P.1%,n) (P/F /%,n) (A/P,1%,n) (P/A,1%,n) (A/F,1%,n) (FIA,1%,n) (ANG,1%,n) (PIG,1%,n) 1.1000 0.9091 1.2100 0.8264 1.3310 0.7513 1.4641 0.6830 1.6105 0.6209 1.7716 0.5645 1.9487 0.5132 2.1436 0.4665 2.3579 0.4241 2.5937 0.3855 2.8531 0.3505 3.1384 0.3186 3.4523 0.2897 3.7975 0.2633 4.1772 0.2394 4.5950 0.2176 0.0046 | 0.1978 | 5.5599 0.1799 0.1169 0.16351 6.72751 0.1486 1.1000 0.9091 0.5762 1.7355 0.4021 2.4869 0.3155 3.1699 0.2638 3.7908 0.2296 4.3553 0.2054 4.8684 0.1874 5.3349 0.1736 5.7590 0.1627 6.1446 0.1540 6.4951 0.1468 6.8137 0.1408 7.1034 0.13577.3667 0.1315 7.6061 0.1278 7.8237 0.1247| 8.0216 0.1219 8.2014 0.1196 | 8.3649 0.1175 8.5136 1.0000 0.4762 0.3021 0.2155 0.1638 0.1296 0.1054 0.0874 0.0736 0.0627 0.0540 0.0468 0.0408 0.0357 0.0315 0.0278 0.0247 0.0219 0.0195 0.0175 1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 18.5312 21.3843 24.5227 27.9750 31.7725 35.9497 40.5447 45.5992 51.1591 57.2750 0.0000 0.0000 0.4762 0.8264 0.9366 2.3291 1.3812 4.3781 1.8101 6.8618 2.2236 9.6842 2.6216 12.7631 3.0045 16.0287 3.3724 19.4215 3.7255 22.8913 4.0641 26.3963 4.3884 29.9012 4.6988 33.3772 4.9955 36.8005 5.2789 40.1520 5.5493 43.4164 5.807146.5819 6.0526 49.6395 6.286162.6827 6.5081 55.4069 (FIG.1%,n) (PCLN (PIC.LKN) ik i=k 0.0000 0.9091 0.9091 1.0000 1.8347 1.8182 3.1000 2.7772 2.7273 6.4100 3.7367 3.6364 11.0510 4.7138 4.5455 17.1561 5.7086 5.4545 24.87176.7215 6.3636 34.3589 7.7528 7.2727 45.7948 8.8028 8.1818 59.3742 9.8719 9.0909 75.3117 10.9605 10.0000 93.8428 12.0689 10.9091 115.2271 13.1974 11.8182 139.7498 14.3465 12.7273 167.7248 15.5164 13.6364 199.4973 16.7076 14.5455 235.4470 17.9205 15.4545 275.9917 19.1554 16.3636 321.590920.4128 17.2727 372.7500 21.6930 18.1818 17 18 19 20 18. Apple's Internal Rate of Return (IRR) (first decimal; no rounding) is a) 49.3%; b) 55.9%; C) 64.1%; d) 67.8%. 19. HP's Internal Rate of Return (IRR) (first decimal; no rounding) is a) 43.4%; b) 48.6%; C) 53.1%; d) 59.9%. 20. The incremental Internal Rate of Return (AIRR) between the Apple and Dell computers (first decimal; no rounding) is a) Negative; b) 8.7%; c) 21.1%; d) 22.6%. Dell's External Rate of Return (ERR) (first decimal; no rounding) is a) 20.7%; b) 23.1%; c) 25.8%; d) 28.3%. 22. HP's External Rate of Return (ERR) (first decimal; no rounding) is a) 13.9%; b) 18.2%; c) 22.4%; d) 26.4%. 23. The incremental External Rate of Return (AERR) between the Apple and Dell computers (first decimal; no rounding) is a) 5.9%; b) 6.4%; c) 6.9%; d) 7.2%. 24. The incremental External Rate of Return (AERR) between the Apple and HP computers is a) 5.3%; b) 5.7%; c) 6.0%; d) 6.5%. 25. The best computer based on the external rate of return method is a) Apple; b) Dell; c) HP; d) None of the computers is valid. B. Problems and Questions An architectural company must replace one of its super computers. The key parameters (all arbitrary values) of the three computers under scrutiny are provided below. Parameters 1. Initial Cost ($) 2. Revenues ($) Apple Dell 15,000 22,000 45,000 at EOY1 43,000 at EOY1 increasing by increasing by $5,000 2.0% annually annually thereafter thereafter 41,000 at EOY1 38,000 at EOY1 increasing by decreasing by 1% annually 2% annually thereafter thereafter 400 HP 26,000 46,000 at EOY1 increasing by $500 annually thereafter 33,000 at EOY1 increasing by 0.5% annually thereafter 900 3. Operating costs ($) 0 4. End-of-life salvage value ($) 5. Useful life (years) 10 EOY = End-of-year Industry standard for backhoes = 4 years MARR = 10% DISCRETE CASH FLOWS AND DISCRETE COMPOUNDING 10.00 % DISCRETE RATE OF INTEREST 1% = 0.1000 k% = 0.1200 (F/P.1%,n) (P/F /%,n) (A/P,1%,n) (P/A,1%,n) (A/F,1%,n) (FIA,1%,n) (ANG,1%,n) (PIG,1%,n) 1.1000 0.9091 1.2100 0.8264 1.3310 0.7513 1.4641 0.6830 1.6105 0.6209 1.7716 0.5645 1.9487 0.5132 2.1436 0.4665 2.3579 0.4241 2.5937 0.3855 2.8531 0.3505 3.1384 0.3186 3.4523 0.2897 3.7975 0.2633 4.1772 0.2394 4.5950 0.2176 0.0046 | 0.1978 | 5.5599 0.1799 0.1169 0.16351 6.72751 0.1486 1.1000 0.9091 0.5762 1.7355 0.4021 2.4869 0.3155 3.1699 0.2638 3.7908 0.2296 4.3553 0.2054 4.8684 0.1874 5.3349 0.1736 5.7590 0.1627 6.1446 0.1540 6.4951 0.1468 6.8137 0.1408 7.1034 0.13577.3667 0.1315 7.6061 0.1278 7.8237 0.1247| 8.0216 0.1219 8.2014 0.1196 | 8.3649 0.1175 8.5136 1.0000 0.4762 0.3021 0.2155 0.1638 0.1296 0.1054 0.0874 0.0736 0.0627 0.0540 0.0468 0.0408 0.0357 0.0315 0.0278 0.0247 0.0219 0.0195 0.0175 1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 18.5312 21.3843 24.5227 27.9750 31.7725 35.9497 40.5447 45.5992 51.1591 57.2750 0.0000 0.0000 0.4762 0.8264 0.9366 2.3291 1.3812 4.3781 1.8101 6.8618 2.2236 9.6842 2.6216 12.7631 3.0045 16.0287 3.3724 19.4215 3.7255 22.8913 4.0641 26.3963 4.3884 29.9012 4.6988 33.3772 4.9955 36.8005 5.2789 40.1520 5.5493 43.4164 5.807146.5819 6.0526 49.6395 6.286162.6827 6.5081 55.4069 (FIG.1%,n) (PCLN (PIC.LKN) ik i=k 0.0000 0.9091 0.9091 1.0000 1.8347 1.8182 3.1000 2.7772 2.7273 6.4100 3.7367 3.6364 11.0510 4.7138 4.5455 17.1561 5.7086 5.4545 24.87176.7215 6.3636 34.3589 7.7528 7.2727 45.7948 8.8028 8.1818 59.3742 9.8719 9.0909 75.3117 10.9605 10.0000 93.8428 12.0689 10.9091 115.2271 13.1974 11.8182 139.7498 14.3465 12.7273 167.7248 15.5164 13.6364 199.4973 16.7076 14.5455 235.4470 17.9205 15.4545 275.9917 19.1554 16.3636 321.590920.4128 17.2727 372.7500 21.6930 18.1818 17 18 19 20