13. Beta's benefit/cost (B/C) ratio. B. Problems and Questions 14. Gamma's benefit/cost (B/C) ratio. 15. The incremental B/C ratio between Alpha and Beta Delta Company is considering the production and sale of new precision 16. The incremental B/C ratio between Alpha and Gamma. equipment. The key parameters of the three types of precision equipment under scrutiny by Delta Company are shown below (Please note that all 17. The best precision equipment based on the benefit-cost ratio. parameter values and equipment names are fictitious). 18. Alpha's Internal Rate of Return (IRR). Parameters Alpha Beta Gamma 1. Initial Cost ($) 240,000 260,000 295,000 19. Gamma's Internal Rate of Return (IRR). 158,000 at 20 The incremental Internal Rate of Return (AIRR) between Beta and EOY1 175,000 at EOY1 175,000 at EOY1 Gamma 2. Revenues increasing by decreasing by increasing by 1.0% 0.5% annually 21. ($) $3.00 annually The best precision equipment based on the IRR method. annually thereafter. thereafter. thereafter 22. Beta's External Rate of Return (ERR). 90,000 at 3. Operating EOY1 122,000 at EOY1 120,000 at EOY1 to decreasing by EOY5 inclusively; 23. Gamma's External Rate of Return (ERR). costs increasing by ($) 1% annually $1,000 annually $110,000 from EOY 24. The incremental External Rate of Return (AERR) between Alpha and thereafter thereafter to EOY10 inclusively. Gamma. 4. End-of-life salvage 50,000 40,000 -20,000 25 The incremental External Rate of Return (AERR) between Beta and value ( Gamma. 5. Useful life (years) 5 10 10 26. The best precision equipment based on the external rate of return (ERR) All parameter values are fictitious. 2 method. EOY = End-of-year Industry Standard = 3 years 27. If the company's precision equipment budget is $550,000, which precision MARR = 10% equipment(s) should it purchase assuming that purchases of precision equipment are independent? Alpha's Net Present Worth (NPW). 28 1. If the company prefers to purchase two precision equipment models instead of only one precision equipment model in 2020 (that is, one 2. Beta's NPW. precision equipment model immediately and the other in early November), which precision equipment model should it purchase first in Question 27? 3 Gamma's Net Future Worth (NFW) at EOY4. 29. Joshua plans to make the following bank deposits in 2021: $500 on 4. Beta's Annual Equivalent Worth (AEW). January 31; $600 on April 30; $700 on September 30; and $800 on December 31. 5. Alpha's AEW over 20 years (as it was repeated several times). Find Joshua's bank balance on December 31, 2021 if the bank's interest rate is 12% compounded monthly? (Note that the December 31 deposit is 6. The best precision equipment based on the NPW method included is included in Joshua's yearend bank balance) ) [500+100(A/G, 12%/12,4)](A/P, 12%/12, 12)(F/A, 12%/12, 12) 7. The best precision equipment based on the (AEW) method. b) {500(P/F, 12%, 1)+600(P/F, 12%,4)+700(P/F, 12%,9)+800(P/F, 12%, 12)}(F/P, 12%, 12) c) 500(F/P, 1%, 11)+600(F/P, 1%,8)+700(F/P, 1%,3)+800 8. Gamma's recovery period (tears) based on the simple payback method. d) Answers c) and d) 30. The nominal rate of interest compounded semi-annually which is Alpha's "project balance" after 2 years based on the simple payback equivalent to a nominal rate of 12% compounded quarterly. method. 0-0-0 10. Beta's recovery period (years) based on the discounted payback method. 11. Gamma's "project balance" after 3 years based on the discounted payback method 12. The best precision equipment based on the discounted payback method.DISCRETE CASH FLOWS AND DISCRETE COMPOUNDING 1% = K% = 10.00 % DISCRETE RATE OF INTEREST 0.1000 0.1200 n (F/P,i%,n) (P/F,i%,n) (A/P,i%,n) (P/A,i%,n) (A/F,1%,n) (F/A,i%,n) (A/G,i%,n) (P/G,i%,n) (F/G,i%,n) (P/C,i,k,N) (P/C,i,k,N) ik i=k 1.1000 0.9091 1.1000 0.9091 1.0000 1.0000 0.0000 0.0000 0.0000 0.9091 0.9091 IN 1.2100 0.8264 0.5762 1.7355 0.4762 2.1000 0.4762 0.8264 1.0000 1.8347 1.8182 3 1.3310 0.7513 0.4021 2.4869 0.3021 3.3100 0.9366 2.3291 3.1000 2.7772 2.7273 A 1.4641 0.6830 0.3155 3.1699 0.2155 4.6410 1.3812 4.3781 6.4100 3.7367 3.6364 1.6105 0.6209 0.2638 3.7908 0.1638 6.1051 1.8101 6.8618 11.0510 4.7138 4.5455 6 1.7716 0.5645 0.2296 4.3553 0.1296 7.7156 2.2236 9.6842 17.1561 5.7086 5.4545 7 1.9487 0.5132 0.2054 4.8684 0.1054 9.4872 2.6216 12.7631 24.8717 6.7215 6.3636 2.1436 0.4665 0.1874 5.3349 0.0874 11.4359 3.0045 16.0287 34.3589 7.7528 7.2727 9 2.3579 0.4241 0.1736 5.7590 0.0736 13.5795 3.3724 19.4215 45.7948 8.8028 8.1818 10 2.5937 0.3855 0.1627 6.1446 0.0627 15.9374 3.7255 22.8913 59.3742 9.8719 9.0909 11 2.8531 0.3505 0.1540 6.4951 0.0540 18.5312 4.0641 26.3963 75.3117 10.9605 10.0000 12 3.1384 0.3186 0.1468 6.8137 0.0468 21.3843 4.3884 29.9012 93.8428 12.0689 10.9091 13 3.4523 0.2897 0.1408 7.1034 0.0408 24.5227 4.6988 33.3772 115.2271 13.1974 11.8182 14 3.7975 0.2633 0.1357 7.3667 0.0357 27.9750 4.9955 36.8005 139.7498 14.3465 12.7273 15 4.1772 0.2394 0.1315 7.6061 0.0315 31.7725 5.2789 40.1520 167.7248 15.5164 13.6364 16 4.5950 0.2176 0.1278 7.8237 0.0278 35.9497 5.5493 43.4164 199.4973 16.7076 14.5455 17 5.0545 0.1978 0.1247 8.0216 0.0247 40.5447 5.8071 46.5819 235.4470 17.9205 15.4545 18 5.5599 0.1799 0.1219 8.2014 0.0219 45.5992 6.0526 49.6395 275.9917 19.1554 16.3636 19 6.1159 0.1635 0.1195 8.3649 0.0195 51.1591 6.2861 52.5827 321.5909 20.4128 17.2727 20 6.7275 0.1486 0.1175 8.5136 0.0175 57.2750 6.5081 55.4069 372.7500 21.6930 18.1818