ENMG 400 Problems, Spring 2008

te ENMG400 Assigned Problems Chapters 1 > 9 Fag & Arch. Librar Fall 05-06 1.9 Rate of return = (45/966)(100) = 4.65% 1.17 Equivalent cost now: P + 0.1P = 16,000 1.1P = 16,000 P = $14,545.45 1.22 Simple: 1,000,000 = 500,000 + 500,000()(5) i= 20% per year simple Compound: 1,000,000 = 500,000(1 + iy (1 +i)° =2.0000 (1 + i) = (2.0000)°? i= 14.87% 1.39 The cash flow diagram is: $3000 $10,000 2.9 F = 1,700,000(F/P,18%,1) = 1,700,000(1.18) = $2,006,000 2.31 (a) CF3 = 280,000 — 2(50,000) = $180,000 (b) A = 280,000 — 50,000(A/G,12%,5) = 280,000 — 50,000(1.7746) = $191,270 2.40 For g=i, P = 60,000(0.1)[15/(1 + 0.04)] = $86,538 2.54 400,000 = 320,000 + 50,000(A/G,i,5) (A/G,i,5) = 1.6000 Interpolate between i = 22% and i = 24% i= 22.6% 3.4 P = 100,000(P/A,15%,3) + 200,000(P/A, 15%,2)(P/F,15%,3) = 100,000(2.2832) + 200,000(1.6257)(0.6575) = $442,100 Eng, & Arch. Library ENMG400 Assigned Problems Fall 05-06 Chapters 1 > 9 3.17 A=600(A/P,12%,5) + 4000(P/A,12%,4)(A/P,12%,5) = 600(0.27741) + 4000(3.0373)(0.27741) = $3536.76 3.27 Move all cash flows to year 9. 0 = -800(F/A,14%,2)(F/P, 14%,8) + 700(F/P,14%,7) + 700(F/P,14%,4) —950(F/A, 14%,2)(F/P,14%,1) + x — 800(P/A, 14%,3) 0 = -800(2.14)2.8526) + 700(2.5023) + 700(1.6890) —950(2.14)(1.14) + x — 800(2.3216) x = $6124.64 4.9 i/6months = 0.14/2 = 7% 423 P = 5000(P/F,4%,16) = 5000(0.5339) = $2669.50 445 i =e"P_] = 12.75% 453 P = 150,000(P/F,12%,2)(P/F,10%,3) = 150,000(0.7972)(0.75 13) = $89,840 5.9 PWa = -80,000 — 30,000(P/A,12%,3) + 15,000(P/F,12%,3) = -80,000 — 30,000(2.4018) + 15,000(0.7118) = $-141,377 5.15 PWotastic = -75,000 - 27,000(P/A,10%,6) - 75,000(P/F,10%,2) - 75,000(P/F,10%,4) = -75,000 - 27,000(4.3553) - 75,000(0.8264) - 75,000(0.6830) = $-305,798 PWoatuminum = -125,000 — 12,000(P/A,10%,6) — 95,000(P/F,10%,3) + 30,000(P/F,10%,6) = -125,000 — 12,000(4.3553) — 95,000(0.7513) + 30,000(0.5645) = $-231,702 Use aluminum case 5.21 FW, = -300,000(F/P,12%,10) — 900,000(F/A, 12%,10) = -300,000(3.1058) — 900,000(17.5487) Eng. & Arch. Library ENMG400 Assigned Problems Fall 05-06 Chapters 1 > 9 = $-16,725,570 FWe = -1,200,000(F/P, 12%, 10) — 200,000(F/A, 12%, 10) — 150,000(F/A,12%,10) = -1,200,000(3.1058) — 200,000(17.5487) — 150,000(17.5487) = $-9,869,005 Select Plan B 5.33 CCr = [-200,000(A/P,3%,8) + 30,000 + 50,000(A/F,3%,8)]/0.03 = [-200,000(0.14246) + 30,000 + 50,000(0.11246)]/0.03 = $237,700 CCr = [-300,000(A/P,3%,16) + 10,000 + 70,000(A/F,3%, 16)}/0.03 = [-300,000(0.07961) + 10,000 + 70,000(0.04961)]/0.03 = $-347,010 CCg = -900,000 + 40,000/0.03 = $433,333 Select alternative G. 6.7 AWyx =-85,000(A/P,12%,3) — 30,000 + 40,000(A/F,12%,3) = -85,000(0.41635) — 30,000 + 40,000(0.29635) = $-53,536 AWy = -97,000(A/P,12%,3) — 27,000 + 48,000(A/F,12%,3) = -97,000(0.41635) — 27,000 + 48,000(0.29635) = $-53,161 Select robot Y by a small margin. 6.13 AWhang = -110,000(A/P,12%,3) —95,000 + 15,000(A/F,12%,3) = -110,000(0.41635) —95,000 + 15,000(0.29635) = $-136,353 A Wincin = -800,000(A/P,12%,6) 60,000 + 250,000(A/F,12%,6) = -800,000(0.24323) -60,000 + 250,000(0. 12323) = $-223,777 AWeontract = $-190,000 Use land application. 6.21 P., = 1,000,000(P/A,10%, 11) + 100,000(P/G,10%,11) = 1,000,000(6.4951) + 100,000(26.3963) = $9,134,730 Eng. & Arch. Libran: ENMG400 Assigned Problems Fall 05-06 Chapters 1 > 9 Amt in yr 10 = 9,134,730(F/P,10%,11) = 9,134,730(2.8531) = $26,062,298 AW = 26,062,298(0.10) = $2,606,230 7.8 0=-130,000 —49,000(P/A,i%,8) + 78,000(P/A,i%,8) + 1000(P/G,i%,8) + 23,000(P/F.i%,8) Solve by trial and error or Excel i=19.2% (Excel) 7.11 (a) 0 = -(220,000 + 15,000 + 76,000)(A/P,i%,36) + 12,000(2.00 - 1.05) + 2000 + 100,000(A/F,i%,36) 0 = -(311,000)(A/P,i%,36) + 13,400 + 100,000(A/F,i%,36) Solve by trial and error or Excel i= 3.3% per month (Excel) (b) Nominal per year = 3.3(12) = 39.6% per year Effective per year = (1 + 0.396/12)!? — 1 = 47.6% per year 7.26 (a) There are two sign changes, indicating that there may be two real-number rate of return values. (b) 0 = -30,000 + 20,000(P/F,i%,1) + 15,000(P/F,i%,2) - 2000(P/F,i%,3) Solve by trial and error or Excel i= 7.43% per year (Excel) 7.33, Apply net reinvestment procedure. Fo = 3000 Fo > 0; use c F, = 3000(1 + 0.14) - 2000 = 1420 F, > 0; use c F, = 1420(1 + 0.14) + 1000 = 2618.80 F, > 0; usec F3 = 2618.80(1 + 0.14) ~ 6000 = -3014.57 F3 < 0; use i’ Fy = -3014.57(1 +i’) + 3800 Set F, = 0 and solve for i’. 0 =-3014.57(1 +i’) + 3800 i? = 26.1% ENMG400 Assigned Problems Eng. & Arch. Library Fall 05-06 Chapters 1 > 9 7.37 (a) i=5,000,000(0.06)/4 = $75,000 per quarter After brokerage fees, the City got $4,500,000. However, before brokerage fees, the ROR equation from the City’s standpoint is: 0 = 4,600,000 — 75,000(P/A,i%, 120) - 5,000,000(P/F,i%, 120) Solve for i by trial and error or Excel i= 1.65% per quarter (Excel) (b) Nominal i per year = 1.65(4) = 6.6% per year Effective i per year = (1 + 0.066/4)' —1 = 6.77% per year 8.16 0=-10,000 + 1200(P/A,i,4) + 12,000(P/F,i,2) + 1000(P/F,i,4) Solve for i by trial and error or Excel i=30.3% (Excel) Select machine B. 8.22 Find ROR for incremental cash flow over LCM of 4 years 0 = -50,000(A/P,i,4) + 5000 + (40,000 — 5000)(P/E, i,2)(A/P, i,4) + 2000(A/F,i,4) Solve for i by trial and error or Excel i=6.1% (Excel) i< MARR; select semiautomatic machine 8.28 (a) Avs DN: 0=-30,000(A/P,i,8) + 4000 + 1000(A/F,i,8) Solve for i by trial and error or Excel i=2.1% (Excel) Method A is not acceptable B vs DN: 0 =- 36,000(A/P,i,8) + 5000 + 2000(A/F,i,8) Solve for i by trial and error or Excel i=3.4% (Excel) Method B is not acceptable C vs DN: 0 = - 41,000(A/P,i,8) + 8000 + S00(A/F,i,8) Solve for i by trial and error or Excel Eng. & Arch, Library ENMG400 Assigned Problems “ — Fall 05-06 Chapters 1 > 9 i=11.3% (Excel) Method C is acceptable D vs DN: 0 = - 53,000(A/P,i,8) + 10,500 - 2000(A/F.i,8) Solve for i by trial and error or Excel i=11.1% (Excel) Method D is acceptable (b) A vs DN: 0 = -30,000(A/P.i,8) + 4000 + 1000(A/F,i,8) Solve for i by trial and error or Excel i=2.1% (Excel) Eliminate A B vs DN: 0 = - 36,000(A/P.i,8) + 5000 + 2000(A/F,i,8) Solve for i by trial and error or Excel i=3.4% (Excel) Eliminate B C vs DN: 0 = - 41,000(A/P,i,8) + 8000 + 500(A/F.i,8) Solve for i by trial and error or Excel i=11.3% (Excel) Eliminate DN CvsD: 0=- 12,000(A/P,i,8) + 2,500 - 2500(A/F,i,8) Solve for i by trial and error or Excel i=10.4% (Excel) Eliminate D Select method C 9.16 Convert all estimates to PW values. PW disbenefits = 45,000(P/A,6%,15) = 45,000(9.7122) = $437,049 PW M&O Cost = 300,000(P/A,6%, 15) = 300,000(9.7122) = $2,913,660 B/C = 3,800,000 — 437.049 2,200,000 + 2,913,660 = 3,362,951/5,113,660 = 0.66 9.22 Alternative B has a larger total annual cost; it must be incrementally justified. Use PW values. Benefit is the difference in damage costs. For B incrementally over A: ENMG400 Assigned Problems Eng, & Arch, Library Fall 05-06 Chapters 1 > 9 Incr cost = (800,000 — 600,000) + (70,000 — 50,000)(P/A,8%,20) = $200,000 + 20,000(9.8181) = $396,362 Incr benefit = (950,000 ~ 250,000)(P/F,8%.6) = 700,000(0.6302) = 441,140 Incr B/C = 441,140/396,362 =1.11 Select alternative B. 9.33 Compare A to DN since it is not necessary to select one of the sites. Avs DN AW of Cost = 50(A/P,10%,5) + 3 = §0(0.26380) + 3 = 16.19 AW of Benefits = 20 - 0.5 =19.5 B/C = 19.5 16.19 =1.20>1.0 Eliminate DN. BysA AC = (90 — 50)(A/P,10%,5) + (4-3) = 40(0.26380) + 1 = $11.552 AB = (29 - 20) — (1.5 ~ 0.5) = 8 AB/C = 8/11.552 = 0.69 < 1.0 Eliminate B. CvsA AC = (200 — 50)(A/P,10%,5) + (6 - 3) = 150(0.26380) + 3 = 42,57 AB = (61 — 20) - (2.1 — 0.5) = 39.4 AB/C = 39.4/42.57 = 0,93 < 1.0 Eliminate C Select site A