1. Chapter 7 Homework: 2 (a, b, c, e), 4, 6, 10 (a, b), 20 (a, b), 25, 33, 36, 41 (a, b, c)

2. # 2 2 4 = 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 A15 1011yyyn1011yyyn 1100ynyy1100ynyy 1101ynyn1101ynyn 1110ynyn1110ynyn 1111ynyn1111ynyn 1612 8

3. # 2--continued (a) No Dependencies (b) 1 & 2 are M.E. (c) 4 contingent on 3 (e) 2, 3, & 4 are M.E.

4. # 4 P1 0 0 0A0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 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

5. # 4--c Cash Flow: YR0 YR1-5 YR 5 0 0 0 -7000 4200 1500 -4000 3000 1000 A0 A2 A4

6. # 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%:

7. # 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) 104,120-100,000 i = 6% + 104,120-100,000 104,120-98,749 =6.76% = IRR

8. # 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) -500 + 260 ( 6.7101 ) = $1245 = PW b) +260 - 500 (.1490 ) = $185 = AE Inc Inv of option A is desirable P/A, 8%, 10 A/P, 8%, 10

9. # 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)

10. # 20--b A: -1M + 406,180 ( 6.8109 ) = 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 ( ) = 2.1108M F: -1.9M + 562,476 ( ) = 1.931M Dischosen (Largest Total PW)

11. # 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

12. # 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!)

13. # 33 Devise M.E. Alternatives: 2 4 = 16 Alts But, due to A1  A2; B1  B2: (2+1)(2+1)=9 A1A2B1B2 A0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111  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 “ “ “

14. # 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:

15. # 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 = 8000 + 15,000 (.2943 ) A/P, 15%, 5 AEC A = $12,475 AEC B = 6500 + 25,000 (.2229 ) A/P, 15%, 8 AEC B = $12,072

16. # 36--continued Choose B at 15% MARR a) b) For what i* are A+B Equivalent? (also the incremental ROR of B over A) 8000 + 15,000 ( ) = 6500 + 25,000 ( ) Try:20% A/P, i, 5A/P, i, 8.3344.2606  13,016 = 13,015 i* = 20% ROR B-A = 20%

17. Using n*= 6; AEC AEC C1 (20%) = 76,000-200,000 (.3007 ) (A/P, 20%, 6) Using n* = 9; FW for n = 6, (C1, C3, X1) FW(C1) = [-200,000 ( 2.986 ) + 76,000 ( 9.930 )] F/P, 20%, 6F/A, 20%, 6  F/P, 20%, 3 # 41 For n = 9

18. #41--continued ( 1.728 ) 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 ( 5.160 ) + 80K ( 20.799) F/P, 20%F/A, 20%   

19. # 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