10 -$57,444 $57,444 $0 -$57,444
11 $2,556 $0 $2,556 $0
12 $40,556 $0 $40,556 $0
6-18. EOY CF[D] CF[B] CF[B-D] B-D(-) B-D(+) B-D
(cont’d) 0 -$50,000 -$75,000 -$25,000 $25,000 $0 -$25,000
1 $17,879 $16,212 -$1,667 $1,667 $0 -$1,667
2 $17,879 $16,212 -$1,667 $1,667 $0 -$1,667
3 $17,879 $16,212 -$1,667 $1,667 $0 -$1,667
4 -$20,121 $16,212 $36,333 $0 $36,333 $0
5 $17,879 $16,212 -$1,667 $1,667 $0 -$1,667
60
14 $17,879 $22,675 $4,796 $0 $4,796 $0
15 $17,879 $22,675 $4,796 $0 $4,796 $0
16 -$20,121 $22,675 $42,796 $0 $42,796 $0
6-19. MARR = 10%
(a) Internal rate of return analysis
EOY CF(A) CF(B) CF(B-A) B-A(-) B-A(+) B-A
0 -$100,000 -$100,000 $0 $0 $0 $0
1 $20,000 $0 -$20,000 $20,000 $0 -$20,000
12 -$50,000 $40,000 $90,000 $0 $90,000 $0
13 $20,000 $50,000 $30,000 $0 $30,000 $0
14 $20,000 -$40,000 -$60,000 $60,000 $0 -$60,000
15 $20,000 $0 -$20,000 $20,000 $0 -$20,000
16 $20,000 $10,000 -$10,000 $10,000 $0 -$10,000
27 $20,000 $50,000 $30,000 $0 $30,000 $0
28 $20,000 -$40,000 -$60,000 $60,000 $0 -$60,000
29 $20,000 $0 -$20,000 $20,000 $0 -$20,000
30 -$50,000 $10,000 $60,000 $0 $60,000 $0
61
(b) External rate of return analysis
EOY CF(A)
0 -$100,000
1 $20,000
6-20. EOY CF(A) CF(B) CF(B-A) MARR = 10%
0 -$780,000 -$1,840,000 -$1,060,000
1 $138,060 $311,000 $172,940
2 $138,060 $311,000 $172,940
3 $138,060 $311,000 $172,940
6-21. EOY CF[A] CF[C] CF[B] MARR = 15%
0 -$30,000 -$40,000 -$60,000
1 $12,000 $13,000 $23,500
62
5 $22,000 $13,000 $33,500
6 $23,000
IRR = 33.05% 26.00% 29.94%
Since IRR(A) > MARR, A is acceptable. Therefore, compute IRR(C-A) over a common multiple of lives
or a 30-year period.
EOY CF[A] CF[C] CF[C-A]
0 -$30,000 -$40,000 -$10,000
1 $12,000 $13,000 $1,000
2 $12,000 $13,000 $1,000
16 $12,000 $13,000 $1,000
17 $12,000 $13,000 $1,000
18 $12,000 -$17,000 -$29,000
19 $12,000 $13,000 $1,000
20 -$8,000 $13,000 $21,000
21 $12,000 $13,000 $1,000
63
6-22. EOY CF(F) CF(D) CF(E) MARR = 15%
0 -$17,000 -$22,000 -$26,200
1 $6,200 $7,000 $7,500
2 $6,200 $7,000 $7,500
Since IRR(F) > MARR, F is acceptable. Determine IRR(D-F) over a 20-year period.
EOY CF(F) CF(D) CF(D-F)
0 -$17,000 -$22,000 -$5,000
1 $6,200 $7,000 $800
2 $6,200 $7,000 $800
3 $6,200 $7,000 $800
4 $6,200 -$11,000 -$17,200
5 -$7,300 $7,000 $14,300
Since the sum of the (D-F) cash flows equals -$20,000, there is no positive-valued IRR for the incremental
cash flows. Therefore, D is unacceptable. Determine IRR(E-F) over a 10-year period.
EOY CF(F) CF(E) CF(E-F)
0 -$17,000 -$26,200 -$9,200
1 $6,200 $7,500 $1,300
2 $6,200 $7,500 $1,300
64
6-23. EOY CF(K) CF(M) CF(L) CF(M-K) CF(L-M) MARR = 10%
0 -$170,000 -$300,000 -$330,000 -$130,000 -$30,000
1 $44,000 $66,000 $68,000 $22,000 $2,000
2 $44,000 $66,000 $68,000 $22,000 $2,000
3 $44,000 $66,000 $68,000 $22,000 $2,000
IRR(K) & ERR(K) > MARR → K’s acceptable; IRR(M-K) & ERR(M-K) > MARR → M’s acceptable;
IRR
(
L-M
)
& ERR
(
L-M
)
< MARR → L’s unacce
p
table; select M.
6-24. EOY CF(B) CF(A) CF(A-B) MARR = 10%
0 $0 -$80,000 -$80,000
1 $0 $21,750 $21,750
2 -$80,000 $21,750 $101,750
6-25. EOY CF(A) CF(B) CF(B-A) B-A(-) B-A(+) B-A
0 $0 -$10,000 -$10,000 $10,000 $0 -$10,000
1 -$20,000 $5,000 $25,000 $0 $25,000 $0
6-26. EOY CF(A) CF(B) CF(B-A) MARR = 10%
0 -$20,000 -$35,000 -$15,000
1 $12,000 $17,000 $5,000
65
6-27. EOY CF(A) CF(B) CF(B-A) B-A(+) B-A(-) B-A = CF
(
B-A
)
0 -$15,000 -$20,000 -$5,000 $0 -$5,000 -$5,000
1 $0$0 $0 $0$0 $0
ERR = 15.44% 10.67% 10.44% ERR(A) & ERR(B) < MARR → reject both
6-28. EOY CF[A] CF[B] CF[C] CF[D] CF[E] MARR = 10%
0 -$3,000 -$3,800 -$4,500 -$5,000 -$6,000
1-10 -$1,800 -$1,770 -$1,470 -$1,320 -$1,000
EOY CF[B-A] CF[C-A] CF[D-C] CF[E-D]
0 -$800 -$1,500 -$500 -$1,000
1 $30 $330 $150 $320
6-29. EOY CF[A] CF[B] CF[D] CF[C] MARR = 10%
0 $0 -$100,000 -$125,000 -$180,000
1 $0 -$100,000 -$75,000 -$20,000
2 $0 $0 $60,000 $100,000
3 $0 $25,000 $60,000 $75,000
6-30. EOY CF[A] CF[B] CF[C] MARR = 12%
0 -$1,150 -$1,250 -$2,000
1-10 -$425 -$400 -$875
10 $750 $750 $875
EOY CF[B-A] CF[C-B] CF[C-A]
0 -$100 -$750 -$850
1 $25 $475 $450
2 $25 $475 $450
6-31. MARR = 25%
AD E BF C
Investment -$30,000 -$50,000 -$55,000 -$60,000 -$70,000 -$75,000
Ann. Return $10,000 $14,000 $16,000 $18,000 $20,500 $21,500
6-32. MARR = 8%
In this problem, all three B/C methods reduce to the same calculations.
EOY CF[A] CF[B] CF[C-B] CumPW[B]
0 -$12,500 -$12,500 $0 -$12,500.00
67
6-33. MARR = 15% The incremental investments are considered in increasing order of initial investment.
EOY CF[A] CF[B-A] CF[D-B] CF[C-B] CF[C] CumPW[C]
0 -$50,000 -$50,000 -$125,000 -$150,000 -$250,000 -$250,000.00
1 -$100,000 $0 $25,000 $175,000 $75,000 -$184,782.61
6-34. MARR = 12% (Cash flows in $000’s)
EOY CF[A] CF[D-A] CF[B-D] CF[C-D] CF[D] CumPW[D]
0 -$50 -$50 -$25 -$100 -$100 -$100.00
1 -$100 -$50 $75 $200 -$150 -$233.93
2 $50 $25 -$5 -$25 $75 -$174.14
6-35. MARR = 10%
EOY CF[K] CF[M] CF[L]
0 -$170,000 -$300,000 -$330,000
1 $44,000 $66,000 $68,000
2 $44,000 $66,000 $68,000
68
EOY CF[K] CF[M-K] CF[L-M] CF[M] CumPW[M]
0 -$170,000 -$130,000 -$30,000 -$300,000 -$300,000.00
1 $44,000 $22,000 $2,000 $66,000 -$240,000.00
2 $44,000 $22,000 $2,000 $66,000 -$185,454.55
3 $44,000 $22,000 $2,000 $66,000 -$135,867.77
69