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Ms. Cristiana Piccini is valuing an investment that pays her $27,000 per year for the first ten years, $35,000 per year for the next ten years, and $48,000 per year the following ten years (all payments are at the end of each year). If the appropriate annual discount rate is 9 percent, what is the value of the investment to Ms. Cristiana Piccini today?

Question

Ms. Cristiana Piccini is valuing an investment that pays her $27,000 per year for the first ten years, $35,000 per year for the next ten years, and $48,000 per year the following ten years (all payments are at the end of each year). If the appropriate annual discount rate is 9 percent, what is the value of the investment to Ms. Cristiana Piccini today?

check_circleAnswer
Step 1

Calculation of Value of Investment:

 

Excel Spreadsheet:

A
B
1Years Cash Flows FVIF @ 9% PV of Cash Flows
$27,000
$27,000
$27,000
$27,000
5
1.0900
$24,770.64
$22,725.36
3
2
1.1881
3
1.2950
$20,848.95
$19,127.48
4
5
4
1.4116
$27,000
$27,000
$27,000
6
1.5386
$17,548.15
7
6
1.6771
$16,099.22
7
1.8280
$14,769.92
$27,000
1.9926
$13,550.39
$27,000
$27,000
2.1719
$12,431.55
$11,405.09
10
11
10
2.3674
12
11
$35,000
2.5804
$13,563.65
2,8127
13
12
$35,000
$12,443.72
$11,416.25
$10,473.63
$9,608.83
3.0658
14
13
$35,000
$35,000
$35,000
$35,000
15
14
3.3417
16
15
3.6425
17
16
3.9703
$8,815.44
$35,000
$35,000
$35,000
$35,000
$48,000
$48,000
$48,000
18
17
4.3276
$8,087.56
$7,419.78
$6,807.14
19
18
4.7171
20
19
5.1417
21
20
$6,245.08
5.6044
$7,857.51
22
21
6.1088
23
22
6.6586
$7,208.72
$6,613.5
$6,067.44
$5,566.46
$5,106.84
24
23
7.2579
25
$48,000
$48,000
$48,000
$48,000
7.9111
24
26
25
8.6231
9.3992
27
26
28
27
10.2451
$4,685.17
$4,298.33
$3,943.42
29
28
$48,000
$48,000
11.1671
30
29
12.1722
31
30
$48,000
13.2677
$3,617.81
help_outline

Image Transcriptionclose

A B 1Years Cash Flows FVIF @ 9% PV of Cash Flows $27,000 $27,000 $27,000 $27,000 5 1.0900 $24,770.64 $22,725.36 3 2 1.1881 3 1.2950 $20,848.95 $19,127.48 4 5 4 1.4116 $27,000 $27,000 $27,000 6 1.5386 $17,548.15 7 6 1.6771 $16,099.22 7 1.8280 $14,769.92 $27,000 1.9926 $13,550.39 $27,000 $27,000 2.1719 $12,431.55 $11,405.09 10 11 10 2.3674 12 11 $35,000 2.5804 $13,563.65 2,8127 13 12 $35,000 $12,443.72 $11,416.25 $10,473.63 $9,608.83 3.0658 14 13 $35,000 $35,000 $35,000 $35,000 15 14 3.3417 16 15 3.6425 17 16 3.9703 $8,815.44 $35,000 $35,000 $35,000 $35,000 $48,000 $48,000 $48,000 18 17 4.3276 $8,087.56 $7,419.78 $6,807.14 19 18 4.7171 20 19 5.1417 21 20 $6,245.08 5.6044 $7,857.51 22 21 6.1088 23 22 6.6586 $7,208.72 $6,613.5 $6,067.44 $5,566.46 $5,106.84 24 23 7.2579 25 $48,000 $48,000 $48,000 $48,000 7.9111 24 26 25 8.6231 9.3992 27 26 28 27 10.2451 $4,685.17 $4,298.33 $3,943.42 29 28 $48,000 $48,000 11.1671 30 29 12.1722 31 30 $48,000 13.2677 $3,617.81

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Step 2

Excel Workings:

...
A
Years Cash Flows
FVIF a9%
1
PV of Cash Flows
|=(1+9%) A2 |B2/C2
|(1+9 % ) A3 -B3/ C3
- ( 1+9% ) A4-B4/C4
(1+9% ) A5 - B5/ C5
(1+9 % ) A6 -B6/C6
(1+9% ) A7 B7/C7
- ( 1+9% ) A8 B8/ C8
27000
1
27000
2
27000
27000
5
4
5
27000
7 6
27000
8 7
27000
|=(1+9% ) A9 -B9/ C9
(1+9% ) A10B10/C10
(1+9% ) A11
=(1+9% ) A12 -B12/C12
=(1+9% ) A13 B13/C13
( 1+9 % ) A1 4 -B14/C14.
27000
10 9
27000
11 10
27000
Bl1/C11
12 11
35000
35000
35000
13 12
14 13
(1+9%) A15
=(1+9% ) A16 -B16/C16
-(1+9 % ) A17 -B17/ C17
|(1+9% ) A18
(1+9% ) A19 -B19/C19
=(1+9% ) A20 -B20/C20
1+9% ) A21 B21/C21
(1+9% ) A22
-(1+9% ) A23 -B23/ C23
(1+9 % ) ' A24 -B24/C24
(1+9% ) A25 B25/C25
-(1+9% ) A26 B26/C26
(1+9% ) A27 -B27/ C27
(1+9% ) A28 B28/C28
(1+9% ) A29B29/C29
(1+9%) A30 -B30/C30
(1+9% ) A31 -B31/C31
15 14
35000
B15/C15
16 15
35000
17 16
35000
35000
18 17
B18/C18
19 18
35000
20 19
35000
21 20
35000
48000
22 21
B22/C22
23 22
48000
48000
24 23
48000
25 24
26 25
48000
48000
27 26
28 27
48000
0008t
48000
29 28
30 29
31 30
48000
help_outline

Image Transcriptionclose

A Years Cash Flows FVIF a9% 1 PV of Cash Flows |=(1+9%) A2 |B2/C2 |(1+9 % ) A3 -B3/ C3 - ( 1+9% ) A4-B4/C4 (1+9% ) A5 - B5/ C5 (1+9 % ) A6 -B6/C6 (1+9% ) A7 B7/C7 - ( 1+9% ) A8 B8/ C8 27000 1 27000 2 27000 27000 5 4 5 27000 7 6 27000 8 7 27000 |=(1+9% ) A9 -B9/ C9 (1+9% ) A10B10/C10 (1+9% ) A11 =(1+9% ) A12 -B12/C12 =(1+9% ) A13 B13/C13 ( 1+9 % ) A1 4 -B14/C14. 27000 10 9 27000 11 10 27000 Bl1/C11 12 11 35000 35000 35000 13 12 14 13 (1+9%) A15 =(1+9% ) A16 -B16/C16 -(1+9 % ) A17 -B17/ C17 |(1+9% ) A18 (1+9% ) A19 -B19/C19 =(1+9% ) A20 -B20/C20 1+9% ) A21 B21/C21 (1+9% ) A22 -(1+9% ) A23 -B23/ C23 (1+9 % ) ' A24 -B24/C24 (1+9% ) A25 B25/C25 -(1+9% ) A26 B26/C26 (1+9% ) A27 -B27/ C27 (1+9% ) A28 B28/C28 (1+9% ) A29B29/C29 (1+9%) A30 -B30/C30 (1+9% ) A31 -B31/C31 15 14 35000 B15/C15 16 15 35000 17 16 35000 35000 18 17 B18/C18 19 18 35000 20 19 35000 21 20 35000 48000 22 21 B22/C22 23 22 48000 48000 24 23 48000 25 24 26 25 48000 48000 27 26 28 27 48000 0008t 48000 29 28 30 29 31 30 48000

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