6-1. MARR = 12%
EOY A B C D E
0 -$8,000 -$10,000 -$12,000 -$15,000 -$16,000
1 $2,000 $3,000 $3,200 $3,800 $4,400
2 $2,000 $3,000 $3,200 $3,800 $4,400
6-2. MARR = 12%
EOY A B C-B D-B E-B
0 -$8,000 -$10,000 -$2,000 -$5,000 -$6,000
1 $2,000 $3,000 $200 $800 $1,400
2 $2,000 $3,000 $200 $800 $1,400
6-3. MARR = 10%
EOY A B C D E F
0 -$5,000 -$5,000 -$8,000 -$12,000 $0 -$15,000
1 -$5,000 $800 $1,000 $1,500 $0 $1,000
2 $1,000 $1,200 $1,000 $1,500 $0 $1,500
3 $1,000 $1,600 $1,000 $1,500 -$6,000 $2,000
4 $2,000 $2,000 $1,000 $1,500 $2,000 $2,500
Chapter 6
Inde
p
endent Investment O
pp
ortunit
y
Mutuall
y
Exclusive Investment Alternative
Inde
p
endent Non-re
p
eatin
g
Investment O
pp
ortunit
y
49
ERR = 9.39% 14.33%
6-3. EOY C C(-) C(+) CDEF
(cont’d) 0 -$8,000 $8,000 -$8,000 -$12,000 $0 -$15,000
1 $1,000 $0 $1,000 $0 $1,500 $0 $1,000
ERR = 4.92% 7.79% 13.74% 11.77%
The ERR for B, E, and F > MARR. Therefore, they are acceptable investments.
6-4. MARR = 10%
EOY E B A C D F
0 $0 -$5,000 -$5,000 -$8,000 -$12,000 -$15,000
1 $0 $800 -$5,000 $1,000 $1,500 $1,000
2 $0 $1,200 $1,000 $1,000 $1,500 $1,500
3 -$6,000 $1,600 $1,000 $1,000 $1,500 $2,000
4 $2,000 $2,000 $2,000 $1,000 $1,500 $2,500
Mutuall
y
Exclusive Investment Alternative
50
ERR = 12.16%
6-4. EOY A-B A-B(-) A-B(+) A-B
(cont’d) 0$0$0$0$0
1 -$5,800 $5,800 $0 -$5,800
FWA-B
(
+
)
= $13,526
ERR = 2.32%
EOY C-B C-B(-) C-B(+) C-B
0 -$3,000 $3,000 $0 -$3,000
1 $200 $0 $200 $0
2 -$200 $200 $0 -$200
3 -$600 $600 $0 -$600
4 -$1,000 $1,000 $0 -$1,000
5 -$1,400 $1,400 $0 -$1,400
6 -$1,800 $1,800 $0 -$1,800
7 $1,000 $0 $1,000 $0
51
EOY F-B F-B(-) F-B(+) F-B
0 -$10,000 $10,000 $0 -$10,000
1 $200 $0 $200 $0
2 $300 $0 $300 $0
3 $400 $0 $400 $0
6-5. MARR = 10%
EOY B E C A D F
0 -$5,000 -$6,000 -$8,000 -$10,000 -$12,000 -$15,000
Inde
p
endent Investment O
pp
ortunit
y
52
6-6. MARR = 10%
EOY B E C A D F
0 -$5,000 -$6,000 -$8,000 -$10,000 -$12,000 -$15,000
EOY E-B C-E C-E(-) C-E(+) C-E
0 -$1,000 -$2,000 $2,000 $0 -$2,000
1 $0 $2,000 $0 $2,000 $0
EOY A-E D-E D-E(-) D-E(+) D-E
0 -$4,000 -$6,000 $6,000 $0 -$6,000
1 $1,000 $4,000 $0 $4,000 $0
6-7. MARR = 8%
EOY CF(A) CF(B) CF( C)
0 -$12,500 -$12,500 -$12,500
1 $1,000 $5,000 $3,000
Mutuall
y
Exclusive Investment Alternative
Investment O
pp
ortunities
53
ERR = 5.96% 8.16% 7.08% Favor B
6-8. MARR = 5%
EOY CF(A) CF(B-A) B-A(-) B-A(+) B-A
0 -$12,500 $0 $0 $0 $0
ERR = 58.86%
EOY CF(C-B) C-B(-) C-B(+) C-B
0$0$0$0$0
6-9. ERR
[
a
]
< 13%;
[
b
]
< 13%;
[
c
]
= 13%;
[
d
]
> 13%
6-10. MARR = 15%
EOY CF[A] CF[B] CF[D] CF[C]
0 -$50 -$100 -$225 -$250
1 -$100 -$100 -$75 $75
2 $50 $70 $100 $75
(
)
Investment Alternatives
Investment Alternative CF
(
$000s
)
54
7 $50 $20 $30 $5
IRR = 21.39% 23.18% 13.81% 26.23%
(a) IRR(A) > MARR → A is acceptable; IRR(B-A) > MARR → B is preferred to A; IRR(D-B) < MARR →
D is rejected; IRR(C-B) > MARR → C is preferred to B; C is chosen
EOY CF(A) A(-) A(+) ACF(B-A) CF(D-B) CF(C-B)
0 -$50 $50 $0 -$50 -$50 -$125 -$150
1 -$100 $100 $0 -$100 $0 $25 $175
6-11. MARR = 12%
EOY CF[A] CF[D] CF[B] CF[C]
0 -$50 -$100 -$125 -$200
1 -$100 -$150 -$75 $50
2 $50 $75 $70 $50
3 $50 $75 $70 $50
(
)
6-12. Solve for the interest rate that makes the present worths of the two alternatives equal.
Investment Alternative Cash Flows
(
$000s
)
Investment Alternative CF
(
$000s
)
55
6-13. MARR = 12%
EOY CF
0 -$5,000
1 $2,000
6-14. MARR = 10%
EOY CF CF(-) CF(+) CF
-1 -$100,000 $100,000 $0 -$100,000
0 -$150,000 $150,000 $0 -$150,000
1 $30,000 $0 $30,000 $0
6-15. MARR = 12%
EOY CF(A) CF(B) CF[B-A]
0 $0 -$150,000 -$150,000
1 -$90,000 -$55,000 $35,000
2 -$90,000 -$55,000 $35,000
6-16. EOY CF
0 -$2,000
1 $528
56
6-17. MARR = 10%
(a) Internal rate of return analysis
EOY A B C D E
0 -$1,000 -$1,400 -$2,100 -$2,700 -$3,400
(b) External rate of return analysis
EOY A B-A C-B D-C E-D
0 -$1,000 -$400 -$700 -$600 -$700
6-18. MARR = 12%
EOY CF[D] EOY CF[D] CF[A] CF[A-D]
0 -$50,000 0 -$50,000 -$75,000 -$25,000
1 $17,879 1 $17,879 $20,435 $2,556
Mutuall
y
Exclusive Investment Alternative
57
EOY CF[D] CF[B] CF[B-D]
0 -$50,000 -$75,000 -$25,000
1 $17,879 $16,212 -$1,667
2 $17,879 $16,212 -$1,667
3 $17,879 $16,212 -$1,667
The sum of the cash flows (B-D) is negative → IRR is not defined. B is rejected.
EOY CF[D] CF[C] CF[C-D]
0 -$50,000 -$100,000 -$50,000
9 $17,879 $22,675 $4,796
10 $17,879 -$52,325 -$70,204
11 $17,879 $22,675 $4,796
12 -$20,121 $22,675 $42,796
13 $17,879 $22,675 $4,796
58
4 $29,879 $16,212
5 $16,212
6 $28,212
No positive-valued interest makes the annual worths equal. B is rejected.
EOY CF[D] CF[C]
0 -$50,000 -$100,000
1 $17,879 $22,675
2 $17,879 $22,675
MARR = 12%
EOY CF[D] EOY CF[A-D] A-D(-) A-D(+) A-D
0 -$50,000 0 -$25,000 $25,000 $0 -$25,000
1 $17,879 1 $2,556 $0 $2,556 $0
Althou
g
h not re
q
uired, the followin
g
ERR solution is
p
rovided at no additional char
g
e!
59