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A B
PROBLEM 2.4
FOUR DCF RULES:
1. MONEY HAS A TIME VALUE
2. MONEY CANNOT BE ADDED OR SUBTRACTED UNLESS IT OCCURS AT THE SAME
POINT(S) IN TIME
3. TO MOVE MONEY FORWARD ONE TIME UNIT, MULTIPLY TIMES ONE PLUS THE
DISCOUNT OR INTEREST RATE
4. TO MOVE MONEY BACKWARD ONE TIME UNIT, DIVIDE BY ONE PLUS THE
DISCOUNT OR INTEREST RATE
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A B C D E F G
PROBLEM 2.5
CFD FROM BANK’S PERSPECTIVE
NOT NECESSARILY TO SCALE
(+) $X $X $X $X
0 1 2 3 4
(-)
$2,000
PROBLEM 2.6
LASER CUTTING MACHINE CFD
NOT NECESSARILY TO SCALE
$14,000 $14,000 $14,000 $14,000 $14,000 $14,000
(+)
0 1 2 3 4 5 6
$2,000
(-) $3,000 $4,000
$5,000
$23,000
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A B C D E F G H I J K
PROBLEM 2.7
USA DENIM (TWO MACHINES)
NOT NECESSARILY TO SCALE
0 1 2 3 4 5 6 7 8
(-)
$12,000
$14,000
$16,000
$18,000
$20,000
$22,000
$30,000
$38,000
$30,000+24,000
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A B C D E F G H I J K L M N O
PROBLEM 2.8
CFD OF APARTMENT RENT
NOT NECESSARILY TO SCALE $450
(+)
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(-) $150
$550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150
$550+450
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A B C D E F G H I J K L M N
PROBLEM 2.9
FROM KAELYN’S GRANDFATHER’S PERSPECTIVE
$X+6000
NOT NECESSARILY TO SCALE $X+4500
$X+3000
$X+1500
(+) $X
$2,000
0 1 2 3 4 5 6 7 8 9 10 11
(-)
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A B C D E F G H I J K L
PROBLEM 2.10
CFD FROM DAVID’S PERSPECTIVE
NOT NECESSARILY TO SCALE
########
(+)
0 1 2 3 4 5 6 7 8 9
(-) ####### #######
$X
$X+8000
$X+16,000
$X+24,000
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A B C D E F G H I J K L M
PROBLEM 2.11
CFD OF SYNTHETIC RUBBER BLENDING MACHINE
NOT NECESSARILY TO SCALE
$24,000-4000+8000-1600
$24,000-4000 $24,000-4000 $24,000-4000
$18,000-1600 $24,000-4000 $24,000-4000 $24,000-4000
$12,000-1200
$10,000-800
(+)
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(-)
$62,000+8000
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A B C D E F G H I J K L M N O P
PROBLEM 2.12
CFD FROM YOUR PERSPECTIVE
NOT NECESSARILY TO SCALE
$10,000
(+)
012345678910 11 12 13
(-)
$4,000
$2,880
$2,880
$2,880
$2,880
$2,880
$2,880
$2,880
$2,880
$2,880
$2,880
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A B C D E F G
PROBLEM 2.13
i= 8.50%
n= 10-4= 6
P= $5,000.00
FINDING FW AT END OF YEAR 10 OF DEPOSIT AT END OF YEAR 4
F= $8,157.34 USING ELECTRONIC INTEREST TABLES THIS IS
=$5,000*(F|P 8.5%,6)
F= $8,157.34 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*(1+0.085)^6
F= $8,157.34 USING EXCEL’S FV FUNCTION THIS IS
=FV(8.5%,6,,-5000)
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A B C D E F G
PROBLEM 2.14
i= 7.00%
n= 10
P= $25,000.00
F= $49,178.78 USING COMPOUND INTEREST FORMULAS THIS IS
=25000*(1+0.07)^10
F= $49,178.75 USING INTEREST TABLES THIS IS
=$25,000*(F|P 7%,10)
F= $49,178.78 USING EXCEL’S FV FUNCTION THIS IS
=FV(7%,10,,-25000)
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A B C D E F G H I J K L M
PROBLEM 2.15
ai= 5.00%
APPR 1 APPR 2 APPR 3
14.40000 F|P 5%,14 1.97993 14.20670
=72/(100*0.05) F|P 5%,15 2.07893 =LOG(2)/LOG(1+0.05)
INTERPOLATING
14.20273
=14+(2-1.97993)/(2.07893-1.97993)
APPR 4 APPR 5
14.20670 n= 14.20670 <–SOLVER CHANGED CELL
=NPER(5%,,-1,2) F= $2.00 <–SOLVER TARGET CELL
=FV(5%,n,,-1)
APPR 6
n= 14.20658 <–GOAL SEEK CHANGED CELL
F= $2.00 <–GOAL SEEK SET CELL
=FV(5%,n,,-1)
bi= 7.00%
APPR 1 APPR 2 APPR 3
10.28571 F|P 7%,10 1.96715 10.24477
=72/(100*0.07) F|P 7%,11 2.10485 =LOG(2)/LOG(1+0.07)
INTERPOLATING
10.23856
=10+(2-1.96715)/(2.10485-1.96715)
APPR 4 APPR 5
10.24477 n= 10.24477 <–SOLVER CHANGED CELL
=NPER(7%,,-1,2) F= $2.00 <–SOLVER TARGET CELL
=FV(7%,n,,-1)
APPR 6
n= 10.24499 <–GOAL SEEK CHANGED CELL
F= $2.00 <–GOAL SEEK SET CELL
=FV(5%,n,,-1)
ci= 10.00%
APPR 1 APPR 2 APPR 3
7.20000 F|P 10%,7 1.94872 7.27254
=72/(100*0.10) F|P 10%,8 2.14359 =LOG(2)/LOG(1+0.10)
INTERPOLATING
7.26315
=7+(2-1.94872)/(2.14359-1.94872)
APPR 4 APPR 5
7.27254 n= 7.27254 <–SOLVER CHANGED CELL
=NPER(10%,,-1,2) F= $2.00 <–SOLVER TARGET CELL
=FV(10%,n,,-1)
APPR 6
n= 7.27432 <–GOAL SEEK CHANGED CELL
F= $2.00 <–GOAL SEEK SET CELL
=FV(5%,n,,-1)
di= 15.00%
APPR 1 APPR 2 APPR 3
4.80000 F|P 15%,4 1.74901 4.95948
=72/(100*0.15) F|P 15%,5 2.01136 =LOG(2)/LOG(1+0.15)
INTERPOLATING
4.95670
=4+(2-1.74901)/(2.01136-1.74901)
APPR 4 APPR 5
4.95948 n= 4.95948 <–SOLVER CHANGED CELL
=NPER(15%,,-1,2) F= $2.00 <–SOLVER TARGET CELL
=FV(15%,n,,-1)
APPR 6
n= 4.96242 <–GOAL SEEK CHANGED CELL
F= $2.00 <–GOAL SEEK SET CELL
=FV(5%,n,,-1)
ei= 20.00%
APPR 1 APPR 2 APPR 3
3.60000 F|P 20%,3 1.72800 3.80178
=72/(100*0.20) F|P 20%,4 2.07360 =LOG(2)/LOG(1+0.20)
INTERPOLATING
3.78704
=3+(2-1.728)/(2.0736-1.728)
APPR 4 APPR 5
3.80178 n= 3.80178 <–SOLVER CHANGED CELL
=NPER(20%,,-1,2) F= $2.00 <–SOLVER TARGET CELL
=FV(20%,n,,-1)
APPR 6
n= 3.80304 <–GOAL SEEK CHANGED CELL
F= $2.00 <–GOAL SEEK SET CELL
=FV(5%,n,,-1)
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A B C D E F G H I J K L M N O P
PROBLEM 2.16
P= $0.04
n= 49
F= $0.41
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 4.8641% =(0.41/0.04)^(1/49)-1
OR, CAN USE RATE FUNCTION
P= $0.04
n= 49
F= $0.41
i= 4.8641% =RATE(49,,-0.04,0.41)
OR, CAN USE SOLVER
P= $0.04
n= 49
i= 4.8641% <–SOLVER CHANGED CELL
F= $0.41 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$0.04*(1+i)^49
F= $0.41 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL‘S FV FUNCTION THIS IS
=FV(i%,49,,-0.04)
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A B C D E F G H I J K L M N O
PROBLEM 2.17
P= $1.00
n= 10
F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 11.6123% =(3/1)^(1/10)-1
USE 12%
OR, CAN USE RATE FUNCTION
P= $1.00
n= 10
F= $3.00
i= 11.6123% =RATE(10,,-1,3)
USE 12%
OR, CAN USE SOLVER
P= $1.00
n= 10
i= 11.6123% <–SOLVER CHANGED CELL
USE 12%
F= $3.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$1.00*(1+i)^10
F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL‘S FV FUNCTION THIS IS
=FV(i%,10,,-1)
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A B C D E F G H I J K L M N O
PROBLEM 2.18
P= $176,000.00
n= 9
F= $525,000.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 12.9116% =(525000/176000)^(1/9)-1
OR, CAN USE RATE FUNCTION
P= $176,000.00
n= 9
F= $525,000.00
i= 12.9116% =RATE(9,,-176000,525000)
OR, CAN USE SOLVER
P= $176,000.00
n= 9
i= 12.9116% <–SOLVER CHANGED CELL
F= $525,000.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$176000.00*(1+i)^9
F= $525,000.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(i%,9,,-176000)
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A B C D E F G H I J K L M N
PROBLEM 2.19
P= $1.00
i= 9.00%
F= $2.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR n
n=ln(F/P)/ln(1+i)
n= 8.04 =LN(2/1)/LN(1+0.09)
USE 9 YEARS
OR, CAN USE NPER EXCEL FUNCTION
P= $1.00
i= 9.00%
F= $2.00
n= 8.04 =NPER(5%,,-2500,4430)
USE 9 YEARS
OR, CAN USE SOLVER
P= $1.00
i= 9.00%
n= 8.04 <–SOLVER CHANGED CELL
USE 9 YEARS
F= $2.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$2,500*(1+0.05)^n
F= $2.00
COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(5%,n,,-2500)
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A B C D E F
PROBLEM 2.20
aP= $1.00
n= 10
F= $2.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
i= 7.1773% =RATE(10,,-1.00,2.00)
bP= $1.00
n= 10
P= $1.00
n= 10
F= $3.00
i= 11.6123% =RATE(10,,-1.00,3.00)
i= 14.8698% =(4/1)^(1/10)-1
OR, CAN USE RATE FUNCTION
P= $1.00
n= 10
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A B C D E F G H
PROBLEM 2.21
ai= 8.00% COMPOUNDED ANNUALLY
n= 10
P= $1,000.00
F= $2,158.92 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*(1+0.08)^10
F= $2,158.92 USING INTEREST TABLES THIS IS
$1,000*(F|P 8%,10)
F= $2,158.92 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,10,,-1000)
bi= 11.00%
n= 4
P= $5,000.00
F= $7,590.35 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*(1+0.11)^4
F= $7,590.35 USING INTEREST TABLES THIS IS
F= $23,764.52 USING INTEREST TABLES THIS IS
$13,000*(F|P 9%,7)
F= $23,764.51 USING EXCEL’S FV FUNCTION THIS IS
=FV(9%,7,,-13000)
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A B C D E F G H I J K L M N O
PROBLEM 2.22
P= $1,500.00
n= 3
F= $2,500.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 18.5631% =(2500/1500)^(1/3)-1
OR, CAN USE RATE FUNCTION
P= $1,500.00
n= 3
F= $2,500.00
i= 18.5631% =RATE(3,,-1500,2500)
OR, CAN USE SOLVER
P= $1,500.00
n= 3
i= 18.5631% <–SOLVER CHANGED CELL
F= $2,500.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$1,500*(1+i)^3
F= $2,500.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(i%,3,,-1500)
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A B C D E F G H I
PROBLEM 2.23
ai= 14.00% COMPOUNDED ANNUALLY
n= 7
P= $3,000.00
F= $7,506.81 USING COMPOUND INTEREST FORMULAS THIS IS
=3000*(1+0.14)^7
F= $7,506.81 USING ELECTRONIC INTEREST TABLES THIS IS
F= $10,985.66 USING INTEREST TABLES THIS IS
=$1,600*(F|P 12%,17)
F= $10,985.67 USING EXCEL’S FV FUNCTION THIS IS
=FV(12%,17,,-1600)
di= 8.00% COMPOUNDED ANNUALLY
n= 71
P= $3,500.00
F= $202,448.93 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*(1+0.115)^34
F= $202,448.95 USING ELECTRONIC INTEREST TABLES THIS IS
=$5,000*(F|P 11.5%,34)