chapter 3-combining factors and spread sheet functions_0

8/12/2019 Chapter 3-Combining Factors and Spread Sheet Functions_0

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C 3CF

F

L

E E

7

L B

A 1


2/22

L :

. :

1. D , F, A

2. C , F, A .

3.

M .

4. D M

.

5. D

.

2


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C

I C 2, , , I ,

. F ,

1, /A ,

0, . F ,

. , , F .

, F, A .

3


4/22

LEA NING C ME

4


5/22

A

2, 1

5

Remember: / / ,

/ / ,


6/22

E /A F :

6

The present worth of the cash flow shown below at i = 10% is:

(a) $25,304 (b) $29,562 (c) $34,462 (d) $37,908

P0 = ?

A = $10,000

0 1 2 3 4 5 6

i = 10%

Solution: (1) Use P/A factor with n = 5 (for 5 arrows) to get P1 in year 1(2) Use P/F factor with n = 1 to move P1 back for P0 in year 0

0 1 2 3 4 5

P1 = ?

Actual year

Series year

0 1( / ,10%,1) ( / ,10%,5)( / ,10%,1) 10,000(3.7 08) (0. 0 1) $34,462

( )


7/22

E F/A F :

How much money would be available in year 10 if $8000 is depositedeach year in years 3 through 10 at an interest rate of 10% per year?

7

0 1 2 3 4 5 6 7 8 9 10

FA = ?

A = $8000

i = 10%

: Re-number diagram to determine n = 8 (number of arrows)

0 1 2 3 4 5 6 7 8

Cash flow diagram is:

FA= 8000(F/A,10%,8)= 8000(11.4359)= $91,487

Actual year Series year


8/22

A

F :

8


9/22

E : A

F 0 10% .

9

0 1 2 3 4 5 6 7 8 9 10

PT = ?

A = $5000

i = 10%

First, re-number cash flow diagram to get n for uniform series:n = 8

$2000

0 1 2 3 4 5 6 7 8 9 10

PT = ?

A = $5000

i = 10%

$2000

0 1 2 3 4 5 6 7 8

Solution:

Actual year Series year


10/22

E : A

/A A 2: A = 5000( /A,10%,8) = 5000(5.3349) = $26,675M A 0 /F: 0 = 26,675( /F,10%,2) = 26,675(0.8264) = $22,044

M $2000 0: 2000 = 2000( /F,10%,8) = 2000(0.4665)

= $933

N , 0 2000 : = 22,044 + 933 = $22,977

10

A = $5000

i = 10%

0 1 2 3 4 5 6 7 8

Actual year 0 1 2 3 4 5 6 7 8 9 10

$2000

PT = ?

PA


11/22

E D

( F/A /A )

:

F/A FA 10: FA = 5000(F/A,10%,8) = 5000(11.4359) = $57,180

M FA 0 /F: 0 = 57,180( /F,10%,10) = 57,180(0.3855) = $22,043

M $2000 0: 2000 = 2000( /F,10%,8) = 2000(0.4665) = $933

N , : = 22,043 + 933 = $22,976 .. A ,

11

0 1 2 3 4 5 6 7 8 9 10

PT = ?

A = $5000

i = 10%

0 1 2 3 4 5 6 7 8

FA = ?


12/22


13/22

A G

1 21

G 2 2

M 03

A , 0 (A/ , , )4

13


14/22

E : A G J D $5

4 . I 1 3 $60, 10 12% .

2 $5 ($60 ) 2 2 = 60( /A,12%,8) + 5( /G,12%,8) = $370.41

N , 2 0 0 = 2( /F,12%,2) = $295.29

N , A $60 1 2 A = 60( /A,12%,2) = $101.41

F , 0 A 0 = 0 + A = $396.70

14

0 1 2 3 104 5

60 60 6065

70

95

PT = ?i = 12%

G = 5

0 1 2 3 8 Gradient years

Actual years


15/22

G G

15

1 2

( 1

( ) 1 1 (1+ )/(1+ ) /( )

( ) 1 1 (1+ )/(1+ ) /( )


16/22

E : G G 5

$7000 . , 12%

8 . I $3 0

= 15% .

16


17/22

E : G G

G 5 6; 1 2.

= 7000 1 (1+0.12)/(1+0.15) 9/(0.15 0.12) = $49,401

M 0

= 35,000 + 7000( /A,15%,4) + 49,401( /F,15%,4) = $83,232 17


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N G F , G +

G :

F ,

1 1 (1 )/(1+ ) /( + )

A

18

Changed from + to -

Changed from + to-

Changed from - to +


19/22

E : N A G F ,

= 10%

: G G 2

1 2

G 0 ( 1);

$700 1 6 G = 700( /A,10%,6) 50( /G,10%,6) = 700(4.3553) 50(9.6842) = $2565

F = G(F/ ,10%,6) = 2565(1.7716) = $4544 19

F = ?

G = $-50

0 1 2 3 4 5 6 7

700 650

500 450550600

0 1 2 3 4 5 6

Actual years

Gradient years

i = 10%PG = ?


20/22


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A

21


22/22

A

22

chapter 3-combining factors and spread sheet functions_0

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