Chapter 7 Homework: 2 (a, b, c, e), 4, 6, 10 (a, b), 20 (a, b), 25, 33, 36, 41 (a, b, c)
# = 16 Alternatives 1234abce1234abce 0000yyyy0000yyyy 0001yyny0001yyny 0010yyyy0010yyyy 0011yyyn0011yyyn 0100yyyy0100yyyy 0101yynn0101yynn 0110yyyn0110yyyn 0111yyyn0111yyyn 1000yyyy1000yyyy 1001yyny1001yyny 1010yyyy1010yyyy A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A yyyn1011yyyn 1100ynyy1100ynyy 1101ynyn1101ynyn 1110ynyn1110ynyn 1111ynyn1111ynyn
# 2--continued (a) No Dependencies (b) 1 & 2 are M.E. (c) 4 contingent on 3 (e) 2, 3, & 4 are M.E.
# 4 P A A1 A2 A3 A4 A5 A6 A7 2 3 = 8 Alternatives ok R2 ok Budget ok (B), (R2) (B), (R1) R1 1 & 2 are M.E. R2 3 is contingent on 2 B = $10,000 P2P3P1
# 4--c Cash Flow: YR0 YR1-5 YR A0 A2 A4
# 6--a $400 $102 = $40,800/yr. =A 0 or P = -100,000 A = 5,500 + $400 $31 = $17,900 = A 1 F = 25,000 Incremental Benefit=40,800-17,900 =$22,900 F = 25,000 22,900 = A -100,000 = P 100,000 = 22,900 ( ) + 25,000 ( ) n = 10, i = ? 100,000 = 100,000 (4.1925)(.1615) P/A, i, 10P/F, i, 10 IRR- 20%:
# 6--b V = 250: A 0 = 250 102 = 25,500 A 1 = 250 31 = 13,250 12,250Increment: 100,000 = 12,250 ( ) + 25,000 ( ) P/A, i, 10P/F, i, 10 6%: 104,120 = 7%: 98,749 = (7.3601) (7.0236) (.5584) (.5084) 104, ,000 i = 6% + 104, , ,120-98,749 =6.76% = IRR
# 10 i = 8%, n = 10 Option B: P = 2500 A = 2860(= 5200 .55) Option A: P = 3000 A = 3120(= 5200 .6) Opt. (A-B): P = 500 A = 260 a) ( ) = $1245 = PW b) (.1490 ) = $185 = AE Inc Inv of option A is desirable P/A, 8%, 10 A/P, 8%, 10
# 20--a Inc Inv A- : -1M + 407,180 (6.8109) = $1.7 m B-A: -120K + 37,614 ( ) = 136,185 C-B: -140K + 37,583 ( ) = 115,974 D-C: -160K + 36,042 ( ) = 85,478 E-D: -200K + 29,352 ( ) = -86 F-D: -480K + 44,057 ( ) = -179,932 Reject E Reject F Dischosen (Last Inc PW > 0)
# 20--b A: -1M + 406,180 ( ) = 1.7M B: -1.12M + 444,794 ( ) = 1.9M C: -1.26M + 482,377 ( ) = 2.025M D: -1.42M + 518,419 ( ) = 2.111M E: -1.62M + 547,771 ( ) = M F: -1.9M + 562,476 ( ) = 1.931M Dischosen (Largest Total PW)
# 20--c Total ROR A = 40.46% ROR B = 39.44% ROR C = 38%if accept all ROR>MARR, do all ROR D = 36% ROR E = 33% ROR F = 29% if MAX ROR, choose A NEITHER is correct
# 25 1) Consider: E1, E2, E3 (in this order) 2) ALL have total ROR>12% (none can be excluded) 3) E2-E1 25%, accept E2 4) E3-E2 10%, reject E3 <MARR = 12% Accept E2, (Here all methods lead to E2!)
# 33 Devise M.E. Alternatives: 2 4 = 16 Alts But, due to A1 A2; B1 B2: (2+1)(2+1)=9 A1A2B1B2 A Not do nothing TC = $10K TC = $8K Not B1+B2 TC = $12K TC = 22K>20K TC = $20K Not B1+B2 TC = 9K TC = 19K TC = 17K Not B1+B2 Not A1+A2 Not “ “ “
# 33--continued Budget = $20,000 (Not Alt 5) 7 Left: Sort by increasing Inc Inv: 2, 8, 1, 4, 10, 9, 6 B1 in A1 in (40%) B2 in (30%) Rej A2 (8%) Rej (A1+B1) (9%) (A1+B2) in (17%) Rej (A2+B1) MARR = 15%: Cur best: Choose A1 + B2 B1 A1 B2 (A1+B2) Alt’s:
# 36 for n= 40, Can solve for each project life individually! (or for salvage = 0) Basically; implied salvage = 0 when salvage = 0, or when study period = even multiple of live of projects (least common multiple) 40 years of lcm of 5+8, and SV = 0 AEC A = ,000 (.2943 ) A/P, 15%, 5 AEC A = $12,475 AEC B = ,000 (.2229 ) A/P, 15%, 8 AEC B = $12,072
# 36--continued Choose B at 15% MARR a) b) For what i* are A+B Equivalent? (also the incremental ROR of B over A) ,000 ( ) = ,000 ( ) Try:20% A/P, i, 5A/P, i, 13,016 = 13,015 i* = 20% ROR B-A = 20%
Using n*= 6; AEC AEC C1 (20%) = 76, ,000 (.3007 ) (A/P, 20%, 6) Using n* = 9; FW for n = 6, (C1, C3, X1) FW(C1) = [-200,000 ( ) + 76,000 ( )] F/P, 20%, 6F/A, 20%, 6 F/P, 20%, 3 # 41 For n = 9
#41--continued ( ) a) Opt AEC(C1) = $15,860 (C2) = 15,494 (C3) = 15,804 (X1) = 19,930 (X2) = 17,823 b) FW(C1) = 272,140 (C2) = 322,320 (C3) = 271,158 (X1) = 341,970 (X2) = 370,740 *for n=9, (C2,X2) FW (C2) = -260,000 ( ) + 80K ( ) F/P, 20%F/A, 20%
# 41--continued ! for n* = 6, choose (C1,X1); for n* = 9, (C2,X2) Why? All Inv return >20%, but for n* = 9, assume C1, C3, X1 get “only” 20% for last 3 years. c) (a) (C1,X1) meets B (Same Sol’n) AE = $35,790 (b) (C2,X1) meets B FW = $664,290