DECISION: PURCHASE IS PREFERRED SINCE IT HAS THE HIGHEST AW.
PROBLEM 5.23
LIGHT BAR
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
10.00%
EOY BAR REVENUE NET CF (P|F i%,n) PW OF CF
0 -$6,000.00 -$6,000.00 1.00000 -$6,000.00
1 $2,000.00 $2,000.00 0.90909 $1,818.18
2 $2,000.00 $2,000.00 0.82645 $1,652.89
3 $2,000.00 $2,000.00 0.75131 $1,502.63
4 $2,000.00 $2,000.00 0.68301 $1,366.03
5 $2,000.00 $2,000.00 0.62092 $1,241.84
6 $2,000.00 $2,000.00 0.56447 $1,128.95
$2,710.52 <- PW
0.22961 <- (A|P i%,n)
$622.36 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $622.36 =2000+PMT(10%,6,6000)
SOLUTION USING FACTOR TABLES
AW = $2,000.00 – $6,000(A|P 10%,6)
AW = $2,000.00 – $6,000(0.22961)
AW = $622.34
SLIDING SPOTS
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY SPOTS REVENUE NET CF (P|F i%,n) PW OF CF
0 -$14,000.00 -$14,000.00 1.00000 -$14,000.00
1 $3,500.00 $3,500.00 0.90909 $3,181.82
2 $3,500.00 $3,500.00 0.82645 $2,892.56
3 $3,500.00 $3,500.00 0.75131 $2,629.60
4 $3,500.00 $3,500.00 0.68301 $2,390.55
5 $3,500.00 $3,500.00 0.62092 $2,173.22
6 $3,500.00 $3,500.00 0.56447 $1,975.66
$1,243.41 <- PW
0.22961 <- (A|P i%,n)
$285.50 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $285.50
=3500+PMT(10%,6,14000)
SOLUTION USING FACTOR TABLES
AW = $3,500.00 – $14,000(A|P 10%,6)
AW = $3,500.00 – $14,000(0.22961)
AW = $285.46
REFLECTED BEAM
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY BEAM REVENUE NET CF (P|F i%,n) PW OF CF
0 -$20,000.00 -$20,000.00 1.00000 -$20,000.00
1 $0.00 $0.00 0.90909 $0.00
2 $2,300.00 $2,300.00 0.82645 $1,900.83
3 $4,600.00 $4,600.00 0.75131 $3,456.05
4 $6,900.00 $6,900.00 0.68301 $4,712.79
5 $9,200.00 $9,200.00 0.62092 $5,712.48
6 $11,500.00 $11,500.00 0.56447 $6,491.45
$2,273.59 <- PW
0.22961 <- (A|P i%,n)
$522.03 <- AW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S PMT FUNCTION
IS NOT USED TO COMPUTE AW DIRECTLY.
SOLUTION USING EXCEL’S NPV AND PMT FUNCTIONS
AW = $522.03 =-PMT(10%,6,NPV(10%,E56:E61)+E55)
SOLUTION USING FACTOR TABLES
AW = $2,300.00(A|G 10%,6) – $20,000(A|P 10%,6)
AW = $2,300.00(2.22356) – $20,000(0.22961)
AW = $521.99
DECISION: LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST AW
PROBLEM 5.24
SPRINKLER SYSTEM
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
15.00%
EOY SPRINKLERS LOAN O&M SAVINGS NET CF (P|F i%,n) PW OF CF
0 -$30,000.00 $30,000.00 $0.00 1.00000 $0.00
1 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.86957 -$3,371.33
2 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.75614 -$2,931.59
3 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.65752 -$2,549.21
4 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.57175 -$2,216.71
5 -$9,000.00 $15,000.00 $6,000.00 0.49718 $2,983.06
6 -$9,000.00 $15,000.00 $6,000.00 0.43233 $2,593.97
7 -$9,000.00 $15,000.00 $6,000.00 0.37594 $2,255.62
8 -$9,000.00 $15,000.00 $6,000.00 0.32690 $1,961.41
9 $2,000.00 -$9,000.00 $15,000.00 $8,000.00 0.28426 $2,274.10
$999.31 <- PW
0.20957 <- (A|P i%,n)
$209.43 <- AW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S PMT FUNCTION
IS NOT USED TO COMPUTE A
=30000+PMT(10%,6,70000,-2000)
SOLUTION USING EXCEL’S NPV AND PMT FUNCTIONS
AW = $209.43 =-PMT(15%,9,NPV(15%,G8:G16))
SOLUTION USING FACTOR TABLES
AW = -$3,877.03(P|A 15%,4)(A|P 15%,9)+($6,000(F|A 15%,5)+$2,000)(A|F 15%,9)
AW = -$3,877.03(2.85498)(0.20957)+($6,000(6.74238)+$2,000)(0.05957)
AW = $209.30
SPRINKLER SYSTEM IS ECONOMICALLY ATTRACTIVE SINCE THE AW IS POSITIVE.
PROBLEM 5.25
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
12.00%
EOY CF (F|P i%,n-t) FW OF CF
0 -$30,000.00 1.57352 -$47,205.58
1 $6,000.00 1.40493 $8,429.57
2 $13,500.00 1.25440 $16,934.40
3 $0.00 1.12000 $0.00
4 $13,500.00 1.00000 $13,500.00
-$8,341.61 <- FW WITHOUT YEAR 3 RETURN
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S FV FUNCTION
IS NOT USED TO COMPUTE FW DIRECTLY.
SOLUTION USING EXCEL’S NPV AND FV FUNCTIONS
FW = -$8,341.61 =FV(12%,5,,-NPV(12%,C6:C10))
THE FUTURE WORTH WITHOUT THE YEAR 3 RETURN IS -$8,341.61.
TO BE MINIMALLY ATTRACTIVE, THE FUTURE WORTH OF THE YEAR 3
RETURN MUST BRING THE TOTAL FUTURE WORTH TO ZERO.
LET X EQUAL THE YEAR 3 CASH FLOW, THEN
(F|P 12%,1)(X) = $8,341.61
(1.12000)(X) = 8341.61
X = $7,447.87
EXCEL’S SOLVER CAN BE USED TO SOLVE FOR X. LET THE TARGET CELL BE
E12 AND SET IT EQUAL TO A VALUE OF ZERO. DESIGNATE C9 AS THE CHANGE CELL.
PROBLEM 5.26
a A = $2,000,000(A|F 10.4%,40) = 2000000(0.00203) = $4,060
USING EXCEL’S PMT FUNCTION
A = $4,052.10 =PMT(10.4%,40,,-2000000)
b A = $2,000,000(P|F 10.4%,1)(A|F 10.4%,40) = 2000000(0.90580)(0.00203) = $3,677.55
USING EXCEL FUNCTIONS
A = NPV(10.4%,PMT(10.4%,40,,-2000000))
A = $3,670.38
= NPV(10.4%,PMT(10.4%,40,,-2000000))
OR
A=PV(10.4%,1,PMT(10.4%,40,,2000000))
A = $3,670.38 =PV(10.4%,1,PMT(10.4%,40,,2000000))
c (i) $2,000,000 = (A + 200(A|G 10.4%,40))(F|A 10.4%,40)
$2,000,000 = (A + 200(8.83614))(493.57183)
A = FIRST DEPOSIT = $2,284.87
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S
FUNCTIONS ARE NOT USED TO COMPUTE DEPOSITS.
(ii) LAST DEPOSIT = $2,284.87 + 39(200) = $10,084.87
d (i) $2,000,000 = A(F|A1 10.4%, 5%, 40)
$2,000,000 = A(838.73114)
A = FIRST DEPOSIT = $2,384.55
(ii) LAST DEPOSIT = $2,284.87(1.05)^39 = $15,319.48
PROBLEM 5.27
a A = $2,000,000(A|F 10.4%/12,40*12) = 2000000(A|F 0.8667%,480) = 2000000(0.00014) = $280
USING EXCEL’S PMT FUNCTION
A = $279.87 =PMT(10.4%/12,40*12,,-2000000)
b THIS QUESTION PRESUMES THE STARTING DEPOSIT IS $280 PER MONTH AS CALCULATED
BALANCE; A TOTAL OF $2,965,261.
0.87%
MONTH CF (F|P i%,480-t) FW OF CF
1$280.00 62.39265 $17,469.94
2 $280.00 61.85656 $17,319.84
3 $280.00 61.32508 $17,171.02
4 $280.00 60.79816 $17,023.48
5 $280.00 60.27577 $16,877.22
6 $280.00 59.75787 $16,732.20
7 $280.00 59.24442 $16,588.44
8 $280.00 58.73538 $16,445.91
9 $280.00 58.23071 $16,304.60
10 $280.00 57.73038 $16,164.51
11 $280.00 57.23435 $16,025.62
12 $280.00 56.74258 $15,887.92
13 $291.20 56.25504 $16,381.47
14 $291.20 55.77168 $16,240.71
15 $291.20 55.29248 $16,101.17
16 $291.20 54.81740 $15,962.83
17 $291.20 54.34639 $15,825.67
18 $291.20 53.87944 $15,689.69
19 $291.20 53.41650 $15,554.88
20 $291.20 52.95753 $15,421.23
21 $291.20 52.50251 $15,288.73
22 $291.20 52.05140 $15,157.37
23 $291.20 51.60416 $15,027.13
24 $291.20 51.16077 $14,898.02
25 $302.85 50.72118 $15,360.81
26 $302.85 50.28538 $15,228.83
27 $302.85 49.85332 $15,097.98
28 $302.85 49.42497 $14,968.25
29 $302.85 49.00030 $14,839.64
30 $302.85 48.57928 $14,712.14
31 $302.85
48.16187 $14,585.73
32 $302.85
47.74806 $14,460.40
33 $302.85
47.33780 $14,336.16
34 $302.85
46.93106 $14,212.98
35 $302.85
46.52782 $14,090.86
36 $302.85
46.12804 $13,969.79
37 $314.96
45.73170 $14,403.74
38 $314.96
45.33876 $14,279.98
39 $314.96
44.94920 $14,157.29
40 $314.96
44.56299 $14,035.65
41 $314.96
44.18010 $13,915.05
42 $314.96
43.80049 $13,795.49
43 $314.96
43.42415 $13,676.95
44 $314.96
43.05104 $13,559.44
45 $314.96
42.68114 $13,442.93
46 $314.96
42.31441 $13,327.43
47 $314.96
41.95084 $13,212.92
48 $314.96
41.59039 $13,099.39
49 $327.56
41.23304 $13,506.31
50 $327.56
40.87875 $13,390.26
51 $327.56
40.52752 $13,275.21
52 $327.56
40.17930 $13,161.15
53 $327.56
39.83407 $13,048.06
54 $327.56
39.49180 $12,935.95
55 $327.56
39.15248 $12,824.80
56 $327.56
38.81608 $12,714.61
57 $327.56
38.48256 $12,605.36
58 $327.56
38.15191 $12,497.06
59 $327.56
37.82410 $12,389.68
60 $327.56
37.49911 $12,283.22
61 $340.66
37.17691 $12,664.79
62 $340.66
36.85748 $12,555.97
63 $340.66
36.54079 $12,448.09
64 $340.66
36.22683 $12,341.13
65 $340.66
35.91556 $12,235.10
66 $340.66
35.60696 $12,129.97
67 $340.66
35.30102 $12,025.75
68 $340.66
34.99771 $11,922.42
69 $340.66
34.69700 $11,819.98
70 $340.66
34.39888 $11,718.42
71 $340.66
34.10332 $11,617.73
72 $340.66
33.81029 $11,517.91
73 $354.29
33.51979 $11,875.70
74 $354.29
33.23178 $11,773.66
75 $354.29
32.94625 $11,672.50
76 $354.29
32.66316 $11,572.21
77 $354.29
32.38252 $11,472.78
78 $354.29
32.10428 $11,374.20
79 $354.29
31.82843 $11,276.47
80 $354.29
31.55496 $11,179.58
31.28383 $11,083.53
31.01503 $10,988.30
30.74855 $10,893.88
30.48435 $10,800.28
30.22242 $11,135.78
29.96274 $11,040.10
29.70530 $10,945.24
29.45006 $10,851.20
29.19702 $10,757.96
28.94616 $10,665.53
28.69744 $10,573.89
28.45087 $10,483.03
28.20641 $10,392.96
27.96406 $10,303.66
27.72379 $10,215.13
27.48558 $10,127.36
27.24942 $10,441.96
27.01528 $10,352.24
26.78316 $10,263.29
26.55304 $10,175.11
26.32489 $10,087.68
26.09870 $10,001.00
119 $398.53
22.53764 $8,981.87
120 $398.53
22.34400 $8,904.69
121 $414.47
22.15201 $9,181.31
122 $414.47
21.96168 $9,102.42
123 $414.47
21.77298 $9,024.21
124 $414.47
21.58590 $8,946.67
21.40043 $8,869.80
126 $414.47
21.21655 $8,793.59
127 $414.47
21.03426 $8,718.03
128 $414.47
20.85352 $8,643.13
129 $414.47
20.67435 $8,568.86
130 $414.47
20.49671 $8,495.24
131 $414.47
20.32060 $8,422.25
132 $414.47
20.14600 $8,349.88
133 $431.05
19.97290 $8,609.26
134 $431.05
19.80129 $8,535.29
135 $431.05
19.63115 $8,461.95
136 $431.05
19.46248 $8,389.25
137 $431.05
19.29525 $8,317.16
138 $431.05
19.12946 $8,245.70
139 $431.05
18.96510 $8,174.85
140 $431.05
18.80215 $8,104.61
141 $431.05
18.64060 $8,034.98
142 $431.05
18.48043 $7,965.94
143 $431.05
18.32164 $7,897.49
144 $431.05
18.16422 $7,829.64
145 $448.29
18.00815 $8,072.86
146 $448.29
17.85342 $8,003.49
147 $448.29
17.70002 $7,934.72
17.54794 $7,866.55
149 $448.29
17.39716 $7,798.96
150 $448.29
17.24768 $7,731.95
151 $448.29
17.09949 $7,665.51
152 $448.29
16.95257 $7,599.65
153 $448.29
16.80691 $7,534.35
154 $448.29
16.66250 $7,469.61
155 $448.29
16.51933 $7,405.43
156 $448.29
16.37739 $7,341.81
157 $466.22
16.23667 $7,569.87
158 $466.22
16.09717 $7,504.83
159 $466.22
15.95886 $7,440.35
160 $466.22
15.82173 $7,376.42
161 $466.22
15.68579 $7,313.04
162 $466.22
15.55101 $7,250.20
163 $466.22
15.41740 $7,187.91
164 $466.22
15.28493 $7,126.15
165 $466.22
15.15360 $7,064.92
166 $466.22
15.02339 $7,004.22
167 $466.22
14.89431 $6,944.03
168 $466.22
14.76634 $6,884.37
14.63946 $7,098.23
170 $484.87
14.51367 $7,037.24
171 $484.87
14.38897 $6,976.77
172 $484.87
14.26534 $6,916.83
173 $484.87
14.14277 $6,857.39
174 $484.87
14.02125 $6,798.47
175 $484.87
13.90078 $6,740.06
176 $484.87
13.78134 $6,682.15
177 $484.87
13.66293 $6,624.73
178 $484.87
13.54553 $6,567.81
179 $484.87
13.42914 $6,511.38
180 $484.87
13.31376 $6,455.43
181 $504.26
13.19936 $6,655.97
182 $504.26
13.08595 $6,598.78
183 $504.26
12.97352 $6,542.08
184 $504.26
12.86204 $6,485.87
185 $504.26
12.75153 $6,430.14
186 $504.26
12.64197 $6,374.89
187 $504.26
12.53335 $6,320.12
188 $504.26
12.42566 $6,265.81
189 $504.26
12.31889 $6,211.98
190 $504.26
12.21305 $6,158.60
191 $504.26
12.10811 $6,105.69
12.00407 $6,053.22
193 $524.43
11.90093 $6,241.26
194 $524.43
11.79868 $6,187.64
195 $524.43
11.69730 $6,134.47
196 $524.43
11.59680 $6,081.76
197 $524.43
11.49715 $6,029.51
198 $524.43
11.39837 $5,977.70
199 $524.43
11.30043 $5,926.34
200 $524.43
11.20333 $5,875.42
201 $524.43
11.10707 $5,824.94
202 $524.43
11.01164 $5,774.89
203 $524.43
10.91702 $5,725.27
204 $524.43
10.82322 $5,676.07
205 $545.41
10.73023 $5,852.40
206 $545.41
10.63803 $5,802.11
207 $545.41
10.54663 $5,752.26
208 $545.41
10.45601 $5,702.83
209 $545.41
10.36617 $5,653.83
210 $545.41
10.27710 $5,605.26
211 $545.41
10.18880 $5,557.09
212 $545.41
10.10125 $5,509.35
10.01446 $5,462.01
214 $545.41
9.92842 $5,415.08
215 $545.41
9.84311 $5,368.55
216 $545.41
9.75853 $5,322.42
217 $567.23
9.67469 $5,487.76
218 $567.23
9.59156 $5,440.61
219 $567.23
9.50915 $5,393.86
220 $567.23
9.42744 $5,347.52
221 $567.23
9.34644 $5,301.57
222 $567.23
9.26613 $5,256.02
223 $567.23
9.18652 $5,210.86
224 $567.23
9.10759 $5,166.08
225 $567.23
9.02933 $5,121.70
226 $567.23
8.95175 $5,077.69
227 $567.23
8.87483 $5,034.06
228 $567.23
8.79858 $4,990.81
229 $589.92
8.72298 $5,145.84
230 $589.92
8.64803 $5,101.63
231 $589.92
8.57373 $5,057.79
232 $589.92
8.50006 $5,014.34
233 $589.92
8.42702 $4,971.25
234 $589.92
8.35462 $4,928.54
235 $589.92
8.28283 $4,886.19
236 $589.92
8.21167 $4,844.21
237 $589.92
8.14111 $4,802.58
238 $589.92
8.07116 $4,761.32
239 $589.92
8.00181 $4,720.41
240 $589.92
7.93306 $4,679.85
241 $613.51
7.86489 $4,825.23
242 $613.51
7.79732 $4,783.77
243 $613.51
7.73032 $4,742.66
244 $613.51
7.66390 $4,701.91
245 $613.51
7.59805 $4,661.51
246 $613.51
7.53277 $4,621.46
247 $613.51
7.46804 $4,581.75
248 $613.51
7.40388 $4,542.39
249 $613.51
7.34026 $4,503.36
250 $613.51
7.27719 $4,464.66
251 $613.51
7.21467 $4,426.30
252 $613.51
7.15268 $4,388.27
253 $638.06
7.09122 $4,524.59
254 $638.06
7.03029 $4,485.71
255 $638.06
6.96988 $4,447.17
256 $638.06
6.91000 $4,408.96
257 $638.06
6.85062 $4,371.08
258 $638.06
6.79176 $4,333.52
259 $638.06
6.73341 $4,296.28
260 $638.06
6.67555 $4,259.37
261 $638.06
6.61819 $4,222.77
262 $638.06
6.56133 $4,186.49
263 $638.06
6.50495 $4,150.52
264 $638.06
6.44906 $4,114.86
265 $663.58
6.39365 $4,242.68
266 $663.58
6.33871 $4,206.23
267 $663.58
6.28425 $4,170.09
268 $663.58
6.23025 $4,134.26
269 $663.58
6.17672 $4,098.73
270 $663.58
6.12365 $4,063.52
271 $663.58
6.07104 $4,028.60
272 $663.58
6.01887 $3,993.99
273 $663.58
5.96716 $3,959.67
274 $663.58
5.91589 $3,925.65
275 $663.58
5.86506 $3,891.92
276 $663.58
5.81466 $3,858.48
277 $690.12
5.76470 $3,978.34
278 $690.12
5.71517 $3,944.15
279 $690.12
5.66606 $3,910.27
280 $690.12
5.61738 $3,876.67
281 $690.12
5.56911 $3,843.36
282 $690.12
5.52126 $3,810.34
283 $690.12
5.47382 $3,777.60
284 $690.12
5.42679 $3,745.14
285 $690.12
5.38016 $3,712.96
286 $690.12
5.33394 $3,681.06
287 $690.12
5.28811 $3,649.43
288 $690.12
5.24267 $3,618.07
289 $717.73
5.19762 $3,730.46
290 $717.73
5.15296 $3,698.41
291 $717.73
5.10869 $3,666.63
292 $717.73
5.06479 $3,635.13
293 $717.73
5.02128 $3,603.90
294 $717.73
4.97813 $3,572.93
295 $717.73
4.93536 $3,542.23
296 $717.73
4.89295 $3,511.80
297 $717.73
4.85091 $3,481.62
298 $717.73
4.80923 $3,451.71
299 $717.73
4.76791 $3,422.05
300 $717.73
4.72694 $3,392.65
301 $746.43
4.68633 $3,498.04
302 $746.43
4.64606 $3,467.98
303 $746.43
4.60614 $3,438.18
304 $746.43
4.56657 $3,408.64
305 $746.43
4.52733 $3,379.35
306 $746.43
4.48843 $3,350.32
307 $746.43
4.44986 $3,321.53
308 $746.43
4.41163 $3,292.99
309 $746.43
4.37372 $3,264.70
310 $746.43
4.33614 $3,236.65
311 $746.43
4.29889 $3,208.84
312 $746.43
4.26195 $3,181.27
313 $776.29
4.22533 $3,280.09
314 $776.29
4.18903 $3,251.91
315 $776.29
4.15303 $3,223.96
316 $776.29
4.11735 $3,196.26
317 $776.29
4.08197 $3,168.80
318 $776.29
4.04690 $3,141.57
319 $776.29
4.01213 $3,114.58
320 $776.29
3.97765 $3,087.82
321 $776.29
3.94348 $3,061.29
322 $776.29
3.90959 $3,034.99
323 $776.29
3.87600 $3,008.91
324 $776.29
3.84270 $2,983.05
325 $807.34
3.80968 $3,075.72
326 $807.34
3.77695 $3,049.29
327 $807.34
3.74450 $3,023.09
328 $807.34
3.71232 $2,997.12
329 $807.34
3.68043 $2,971.37
330 $807.34
3.64880 $2,945.84
331 $807.34
3.61745 $2,920.52
332 $807.34
3.58637 $2,895.43
333 $807.34
3.55555 $2,870.55
334 $807.34
3.52500 $2,845.89
335 $807.34
3.49472 $2,821.44
336 $807.34
3.46469 $2,797.19
337 $839.64
3.43492 $2,884.09
338 $839.64
3.40541 $2,859.31
339 $839.64
3.37615 $2,834.74
340 $839.64
3.34714 $2,810.38
341 $839.64
3.31838 $2,786.23
342 $839.64
3.28987 $2,762.29
343 $839.64
3.26160 $2,738.56
344 $839.64
3.23358 $2,715.03
345 $839.64
3.20579 $2,691.70
346 $839.64
3.17825 $2,668.57
347 $839.64
3.15094 $2,645.64
348 $839.64
3.12387 $2,622.91
349 $873.22
3.09702 $2,704.39
350 $873.22
3.07041 $2,681.15
351 $873.22
3.04403 $2,658.12
352 $873.22
3.01788 $2,635.28
353 $873.22
2.99195 $2,612.64
354 $873.22
2.96624 $2,590.19
355 $873.22
2.94075 $2,567.93
356 $873.22
2.91549 $2,545.87
357 $873.22
2.89044 $2,523.99
358 $873.22
2.86560 $2,502.31
359 $873.22
2.84098 $2,480.81
360 $873.22
2.81657 $2,459.49
361 $908.15
2.79237 $2,535.89
362 $908.15
2.76838 $2,514.10
363 $908.15
2.74459 $2,492.50
364 $908.15
2.72101 $2,471.09
365 $908.15
2.69763 $2,449.85
366 $908.15
2.67445 $2,428.80
367 $908.15
2.65147 $2,407.94
368 $908.15
2.62869 $2,387.25
369 $908.15
2.60610 $2,366.73
370 $908.15
2.58371 $2,346.40
371 $908.15
2.56151 $2,326.24
372 $908.15
2.53950 $2,306.25
373 $944.48
2.51768 $2,377.89
374 $944.48
2.49605 $2,357.46
375 $944.48
2.47460 $2,337.20
376 $944.48
2.45334 $2,317.12
377 $944.48
2.43226 $2,297.21
378 $944.48
2.41136 $2,277.48
379 $944.48
2.39064 $2,257.91
380 $944.48
2.37010 $2,238.51
381 $944.48
2.34974 $2,219.27
382 $944.48
2.32955 $2,200.20
383 $944.48
2.30953 $2,181.30
384 $944.48
2.28969 $2,162.56
385 $982.26
2.27001 $2,229.74
386 $982.26
2.25051 $2,210.58
387 $982.26
2.23117 $2,191.58
388 $982.26
2.21200 $2,172.75
389 $982.26
2.19300 $2,154.08
390 $982.26
2.17415 $2,135.58
391 $982.26
2.15547 $2,117.23
392 $982.26
2.13695 $2,099.04
393 $982.26
2.11859 $2,081.00
394 $982.26
2.10039 $2,063.12
395 $982.26
2.08234 $2,045.39
396 $982.26
2.06445 $2,027.82
397 $1,021.55
2.04671 $2,090.81
398 $1,021.55
2.02913 $2,072.85
399 $1,021.55
2.01169 $2,055.04
400 $1,021.55
1.99441 $2,037.38
401 $1,021.55
1.97727 $2,019.87
402 $1,021.55
1.96028 $2,002.52
403 $1,021.55
1.94344 $1,985.31
404 $1,021.55
1.92674 $1,968.25
405 $1,021.55
1.91018 $1,951.34
406 $1,021.55
1.89377 $1,934.58
407 $1,021.55
1.87750 $1,917.95
408 $1,021.55
1.86137 $1,901.47
409 $1,062.41
1.84537 $1,960.54
410 $1,062.41
1.82952 $1,943.70
411 $1,062.41
1.81380 $1,927.00
412 $1,062.41
1.79821 $1,910.44
413 $1,062.41
1.78276 $1,894.02
414 $1,062.41
1.76745 $1,877.75
415 $1,062.41
1.75226 $1,861.62
416 $1,062.41
1.73720 $1,845.62
417 $1,062.41
1.72228 $1,829.76
418 $1,062.41
1.70748 $1,814.04
419 $1,062.41
1.69281 $1,798.45
420 $1,062.41
1.67826 $1,783.00
421 $1,104.90
1.66384 $1,838.39
422 $1,104.90
1.64955 $1,822.59
423 $1,104.90
1.63537 $1,806.93
424 $1,104.90
1.62132 $1,791.41
425 $1,104.90
1.60739 $1,776.02
426 $1,104.90
1.59358 $1,760.76
427 $1,104.90
1.57989 $1,745.63
428 $1,104.90
1.56631 $1,730.63
429 $1,104.90
1.55286 $1,715.76
430 $1,104.90
1.53951 $1,701.02
431 $1,104.90
1.52629 $1,686.40
432 $1,104.90
1.51317 $1,671.91
1.50017 $1,723.85
434 $1,149.10
1.48728 $1,709.04
435 $1,149.10
1.47450 $1,694.35
436 $1,149.10
1.46183 $1,679.79
437 $1,149.10
1.44927 $1,665.36
438 $1,149.10
1.43682 $1,651.05
439 $1,149.10
1.42447 $1,636.86
440 $1,149.10
1.41223 $1,622.80
441 $1,149.10
1.40010 $1,608.86
442 $1,149.10
1.38807 $1,595.03
443 $1,149.10
1.37614 $1,581.33
444 $1,149.10
1.36432 $1,567.74
445 $1,195.07
1.35260 $1,616.44
446 $1,195.07
1.34098 $1,602.55
447 $1,195.07
1.32945 $1,588.78
448 $1,195.07
1.31803 $1,575.13
449 $1,195.07
1.30671 $1,561.60
450 $1,195.07
1.29548 $1,548.18
451 $1,195.07
1.28435 $1,534.88
452 $1,195.07
1.27331 $1,521.69
453 $1,195.07
1.26237 $1,508.62
454 $1,195.07
1.25152 $1,495.65
455 $1,195.07
1.24077 $1,482.80
1.23011 $1,470.06
1.21954 $1,515.73
1.20906 $1,502.70
1.19867 $1,489.79
1.18837 $1,476.99
1.17816 $1,464.30
1.16804 $1,451.72
1.15800 $1,439.25
1.14806 $1,426.88
1.13819 $1,414.62
1.12841 $1,402.47
1.11872 $1,390.42
1.10910 $1,378.47
1.09957 $1,421.29
1.09013 $1,409.08
471 $1,292.58
1.08076 $1,396.97
472 $1,292.58
1.07147 $1,384.97
473 $1,292.58
1.06227 $1,373.07
474 $1,292.58
1.05314 $1,361.27
475 $1,292.58
1.04409 $1,349.57
476 $1,292.58
1.03512 $1,337.98
477 $1,292.58
1.02623 $1,326.48
478 $1,292.58
1.01741 $1,315.08
479 $1,292.58
1.00867 $1,303.78
480 $1,292.58
1.00000 $1,292.58
########## <- FW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S FV FUNCTION
IS NOT USED TO COMPUTE FW.
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES
ARE NOT USED TO COMPUTE FW.
PROBLEM 5.28
a SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
5.00%
EOY CF (F|P i%,n-t) FW OF CF
10 $1,000.00 1.47746 $1,477.46
11 $1,000.00 1.40710 $1,407.10
12 $2,000.00 1.34010 $2,680.19
13 $1,500.00 1.27628 $1,914.42
14 -$1,500.00 1.21551 -$1,823.26
15 $3,000.00 1.15763 $3,472.88
16 $2,500.00 1.10250 $2,756.25
17 $2,000.00 1.05000 $2,100.00
18 $2,000.00 1.00000 $2,000.00
$15,985.04 <– FW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S FV FUNCTION
IS NOT USED TO COMPUTE FW DIRECTLY.
SOLUTION USING EXCEL’S NPV AND FV FUNCTIONS
FW = $15,985.04 =FV(5%,9,,-NPV(5%,C6:C14))
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES
ARE NOT USED TO COMPUTE FW.
b A = $15,985(A|F 5%,9) = $15,985(0.09069) = $1,449.68
PROBLEM 5.29
SOLUTION USING FACTOR TABLES
A = $2,000(F|A 8%,40)(F|P 8%,2)(A|P 8%,30)
A = $2,000(259.05652)(1.16640)(0.08883)
A = $53,682.37
SOLUTION USING EXCEL’S FUNCTIONS
A = $53,680.82 =PMT(8%,30,FV(8%,2,,FV(8%,40,-2000)))