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Excel Avanzado

www.excelavanzado.comAdolfo Aparicio

o.com

A B 1 VanTir.xls 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

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D

E

F

G

H

I

J

K

L

M

N

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VALOR ACTUAL NETOAo Flujo Caja 1 -8500 2 1500 3 3,670 4 8,794 4 8,194 5 -8,194 Si alguno de los flujos de caja intermedios no existe se debe poner cero, no se dabe dejar vacia la celda.

=VNA(E6;$C$7:$C$10)+$C$6

VANTasa Dto. 0.0% 0.5% 1.0% 1.5% 2.0% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% VAN 5,464 5,329 5,196 5,064 4,933 4,675 4,548 4,423 4,298 4,175 4,053 3,932 3,813 3,695 3,578 3,462 3,348 3,235 3,123 3,012 2,903 2,795 2,688 2,582 2,478 2,374 2,272 2,171 2,071 1,973

8,000

6,000 4,000 2,000 0 0.0% -2,000 -4,000 -6,000 -8,000 La TIR se puede definir como el tipo de inters que hace el VAN = 0

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

TASA INTERNA DE RENTABILIDAD TIR 26% efectivo anual

En la frmula de la TIR no se indica en este caso la estimacin, ya que no estamos en un caso de TIR mltiple. Cuando se omite la estimacin, Excel la supone del 10%.

98390900.xls.ms_office

Pgina 3

VAN y TIR no peridicosDias Dias Acum. 0 0 105 105 138 33 259 121 434 175 Fecha 14-Oct-03 27-Jan-04 29-Feb-04 29-Jun-04 21-Dec-04 Flujo Caja -4,000 1,200 1,100 1,000 900 Tasa Dto. 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.5% 16.0% 16.5% 17.0% 17.5% 18.0% 18.5% 19.0% 19.5% 20.0% 20.5% 21.0% 21.5% 22.0% 22.5% 23.0% 23.5% 24.0% VAN 200.00 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?250.00 200.00

150.00 100.00 50.00 0.00 0.0% -50.00

Dia Flujo Caja 0 -4,000 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10.0%

20.0%

30.0%

TIR NO PERIDICATIR TIR Diaria TIR Anual #NAME? 0.02227% 8.4686%

38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

24.5% 25.0% 25.5% 26.0% 26.5% 27.0% 27.5% 28.0% 28.5% 29.0% 29.5% 30.0% 30.5% 31.0% 31.5% 32.0% 32.5% 33.0% 33.5% 34.0% 34.5% 35.0% 35.5% 36.0% 36.5% 37.0% 37.5% 38.0% 38.5% 39.0% 39.5% 40.0% 40.5% 41.0% 41.5% 42.0% 42.5% 43.0% 43.5% 44.0% 44.5% 45.0% 45.5% 46.0% 46.5% 47.0% 47.5% 48.0% 48.5% 49.0% 49.5% 50.0% 50.5% 51.0% 51.5% 52.0%

#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149

0 0 0 0 0 0 0 0 0 0 0 1200 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1100 0 0 0 0 0 0 0 0 0 0 0

52.5% 53.0% 53.5% 54.0% 54.5% 55.0% 55.5% 56.0% 56.5% 57.0% 57.5% 58.0% 58.5% 59.0% 59.5% 60.0% 60.5% 61.0% 61.5% 62.0% 62.5% 63.0% 63.5% 64.0% 64.5% 65.0% 65.5% 66.0% 66.5% 67.0% 67.5% 68.0% 68.5% 69.0% 69.5% 70.0% 70.5% 71.0% 71.5% 72.0% 72.5% 73.0% 73.5% 74.0% 74.5% 75.0% 75.5% 76.0% 76.5% 77.0% 77.5% 78.0% 78.5% 79.0% 79.5% 80.0%

#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

80.5% 81.0% 81.5% 82.0% 82.5% 83.0% 83.5% 84.0% 84.5% 85.0% 85.5% 86.0% 86.5% 87.0% 87.5% 88.0% 88.5% 89.0% 89.5% 90.0% 90.5% 91.0% 91.5% 92.0% 92.5% 93.0% 93.5% 94.0% 94.5% 95.0% 95.5% 96.0% 96.5% 97.0% 97.5% 98.0% 98.5% 99.0% 99.5% #####

#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000 0 0

262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

430 431 432 433 434

0 0 0 0 900

VAN

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0% 100.0%

TIR NO PERIDICAefectivo anual

efectivo anual

TIRmultiple.xls

TIR MULTIPLETIR 1 TIR 2 TIR 3 1.537% 16.788% 26.000%

Ao 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Flujo Caja -365 200 200 200 200 200 -200 -200 -200 -200 -200 0 0 0 0 0 0 0 0 0 400

Tasa 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.5% 16.0% 16.5% 17.0% 17.5% 18.0% 18.5% 19.0% 19.5% 20.0% 20.5% 21.0% 21.5% 22.0%

VAN 35.00 21.29 9.93 0.61 -6.94 -12.97 -17.69 -21.27 -23.90 -25.70 -26.80 -27.32 -27.35 -26.98 -26.27 -25.30 -24.11 -22.77 -21.30 -19.75 -18.14 -16.51 -14.87 -13.25 -11.67 -10.13 -8.64 -7.23 -5.89 -4.63 -3.45 -2.37 -1.37 -0.47 0.33 1.04 1.65 2.17 2.60 2.94 3.18 3.34 3.42 3.41 3.32

50.00

0.00 0.0% -50.00

20.0%

40.0%

-100.00

-150.00

-200.00

22.5% 23.0% 23.5% 24.0% 24.5% 25.0% 25.5% 26.0% 26.5% 27.0% 27.5% 28.0% 28.5% 29.0% 29.5% 30.0% 30.5% 31.0% 31.5% 32.0% 32.5% 33.0% 33.5% 34.0% 34.5% 35.0% 35.5% 36.0% 36.5% 37.0% 37.5% 38.0% 38.5% 39.0% 39.5% 40.0% 40.5% 41.0% 41.5% 42.0% 42.5% 43.0% 43.5% 44.0% 44.5% 45.0% 45.5% 46.0% 46.5% 47.0% 47.5% 48.0%

3.15 2.90 2.59 2.20 1.74 1.22 0.64 -0.00 -0.70 -1.45 -2.26 -3.11 -4.01 -4.96 -5.95 -6.98 -8.04 -9.14 -10.28 -11.45 -12.65 -13.88 -15.13 -16.41 -17.71 -19.03 -20.38 -21.74 -23.12 -24.52 -25.93 -27.36 -28.79 -30.24 -31.70 -33.17 -34.65 -36.13 -37.62 -39.12 -40.62 -42.13 -43.64 -45.15 -46.66 -48.18 -49.70 -51.21 -52.73 -54.24 -55.76 -57.27

48.5% 49.0% 49.5% 50.0% 50.5% 51.0% 51.5% 52.0% 52.5% 53.0% 53.5% 54.0% 54.5% 55.0% 55.5% 56.0% 56.5% 57.0% 57.5% 58.0% 58.5% 59.0% 59.5% 60.0% 60.5% 61.0% 61.5% 62.0% 62.5% 63.0% 63.5% 64.0% 64.5% 65.0% 65.5% 66.0% 66.5% 67.0% 67.5% 68.0% 68.5% 69.0% 69.5% 70.0% 70.5% 71.0% 71.5% 72.0% 72.5% 73.0% 73.5% 74.0%

-58.78 -60.29 -61.79 -63.29 -64.79 -66.28 -67.77 -69.26 -70.74 -72.21 -73.68 -75.14 -76.60 -78.05 -79.49 -80.93 -82.36 -83.79 -85.20 -86.61 -88.02 -89.41 -90.80 -92.18 -93.55 -94.92 -96.28 -97.62 -98.97 -100.30 -101.62 -102.94 -104.25 -105.55 -106.84 -108.13 -109.40 -110.67 -111.93 -113.18 -114.43 -115.66 -116.89 -118.10 -119.31 -120.52 -121.71 -122.89 -124.07 -125.24 -126.40 -127.55

74.5% 75.0% 75.5% 76.0% 76.5% 77.0% 77.5% 78.0% 78.5% 79.0% 79.5% 80.0% 80.5% 81.0% 81.5% 82.0% 82.5% 83.0% 83.5% 84.0% 84.5% 85.0% 85.5% 86.0% 86.5% 87.0% 87.5% 88.0% 88.5% 89.0% 89.5% 90.0% 90.5% 91.0% 91.5% 92.0% 92.5% 93.0% 93.5% 94.0% 94.5% 95.0% 95.5% 96.0% 96.5% 97.0% 97.5% 98.0% 98.5% 99.0% 99.5% 100.0%

-128.70 -129.83 -130.96 -132.08 -133.19 -134.30 -135.39 -136.48 -137.56 -138.64 -139.70 -140.76 -141.81 -142.85 -143.88 -144.91 -145.93 -146.94 -147.95 -148.95 -149.94 -150.92 -151.90 -152.86 -153.83 -154.78 -155.73 -156.67 -157.60 -158.53 -159.45 -160.36 -161.27 -162.17 -163.06 -163.95 -164.83 -165.71 -166.58 -167.44 -168.29 -169.14 -169.98 -170.82 -171.65 -172.48 -173.30 -174.11 -174.92 -175.72 -176.51 -177.30

VAN

40.0%

60.0%

80.0%

100.0%

TIR Multiple (caso de dos tir)Ao Flujo Caja 0 -1,600 1 10,000 2 -10,000 Tasa Dto. 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00% 31.00% 32.00% 33.00% 34.00% 35.00% 36.00% 37.00% 38.00% 39.00% 40.00% 41.00% 42.00% 43.00% 44.00% 45.00% 46.00% 47.00% 48.00% VAN -1,600.00 -1,501.97 -1,407.77 -1,317.22 -1,230.18 -1,146.49 -1,066.00 -988.59 -914.13 -842.49 -773.55 -707.22 -643.37 -581.91 -522.75 -465.78 -410.94 -358.13 -307.27 -258.29 -211.11 -165.67 -121.90 -79.74 -39.13 0.00 37.69 74.00 108.98 142.68 175.15 206.42 236.55 265.57 293.52 320.44 346.37 371.34 395.38 418.53 440.82 462.27 482.92 502.79 521.91 540.31 558.00 575.02 591.38

1,500.00 1,000.00

500.00 0.00 0.00% -500.00 -1,000.00 -1,500.00 -2,000.00

200.00%

400.00%

TIR 1 25% TIR 2 400%

49.00% 50.00% 51.00% 52.00% 53.00% 54.00% 55.00% 56.00% 57.00% 58.00% 59.00% 60.00% 61.00% 62.00% 63.00% 64.00% 65.00% 66.00% 67.00% 68.00% 69.00% 70.00% 71.00% 72.00% 73.00% 74.00% 75.00% 76.00% 77.00% 78.00% 79.00% 80.00% 81.00% 82.00% 83.00% 84.00% 85.00% 86.00% 87.00% 88.00% 89.00% 90.00% 91.00% 92.00% 93.00% 94.00% 95.00% 96.00% 97.00% 98.00% 99.00% 100.00% 101.00% 102.00% 103.00% 104.00%

607.11 622.22 636.74 650.69 664.09 676.94 689.28 701.12 712.47 723.35 733.77 743.75 753.30 762.44 771.18 779.54 787.51 795.12 802.38 809.30 815.88 822.15 828.10 833.75 839.11 844.18 848.98 853.51 857.79 861.81 865.59 869.14 872.45 875.55 878.43 881.10 883.56 885.84 887.92 889.81 891.53 893.07 894.45 895.66 896.71 897.61 898.36 898.96 899.42 899.74 899.94 900.00 899.94 899.75 899.45 899.04

105.00% 106.00% 107.00% 108.00% 109.00% 110.00% 111.00% 112.00% 113.00% 114.00% 115.00% 116.00% 117.00% 118.00% 119.00% 120.00% 121.00% 122.00% 123.00% 124.00% 125.00% 126.00% 127.00% 128.00% 129.00% 130.00% 131.00% 132.00% 133.00% 134.00% 135.00% 136.00% 137.00% 138.00% 139.00% 140.00% 141.00% 142.00% 143.00% 144.00% 145.00% 146.00% 147.00% 148.00% 149.00% 150.00% 151.00% 152.00% 153.00% 154.00% 155.00% 156.00% 157.00% 158.00% 159.00% 160.00%

898.51 897.88 897.14 896.30 895.36 894.33 893.21 891.99 890.69 889.30 887.83 886.28 884.66 882.96 881.18 879.34 877.43 875.45 873.41 871.30 869.14 866.91 864.63 862.30 859.91 857.47 854.98 852.44 849.85 847.22 844.55 841.83 839.07 836.27 833.43 830.56 827.64 824.70 821.72 818.70 815.66 812.59 809.48 806.35 803.19 800.00 796.79 793.55 790.29 787.00 783.70 780.37 777.02 773.66 770.27 766.86

161.00% 162.00% 163.00% 164.00% 165.00% 166.00% 167.00% 168.00% 169.00% 170.00% 171.00% 172.00% 173.00% 174.00% 175.00% 176.00% 177.00% 178.00% 179.00% 180.00% 181.00% 182.00% 183.00% 184.00% 185.00% 186.00% 187.00% 188.00% 189.00% 190.00% 191.00% 192.00% 193.00% 194.00% 195.00% 196.00% 197.00% 198.00% 199.00% 200.00% 201.00% 202.00% 203.00% 204.00% 205.00% 206.00% 207.00% 208.00% 209.00% 210.00% 211.00% 212.00% 213.00% 214.00% 215.00% 216.00%

763.44 760.00 756.55 753.08 749.59 746.09 742.58 739.05 735.51 731.96 728.40 724.83 721.24 717.65 714.05 710.44 706.82 703.19 699.56 695.92 692.27 688.62 684.96 681.29 677.62 673.95 670.27 666.59 662.90 659.22 655.52 651.83 648.13 644.44 640.74 637.03 633.33 629.63 625.93 622.22 618.52 614.82 611.11 607.41 603.71 600.01 596.31 592.61 588.92 585.22 581.53 577.84 574.16 570.47 566.79 563.11

217.00% 218.00% 219.00% 220.00% 221.00% 222.00% 223.00% 224.00% 225.00% 226.00% 227.00% 228.00% 229.00% 230.00% 231.00% 232.00% 233.00% 234.00% 235.00% 236.00% 237.00% 238.00% 239.00% 240.00% 241.00% 242.00% 243.00% 244.00% 245.00% 246.00% 247.00% 248.00% 249.00% 250.00% 251.00% 252.00% 253.00% 254.00% 255.00% 256.00% 257.00% 258.00% 259.00% 260.00% 261.00% 262.00% 263.00% 264.00% 265.00% 266.00% 267.00% 268.00% 269.00% 270.00% 271.00% 272.00%

559.44 555.77 552.10 548.44 544.78 541.12 537.47 533.82 530.18 526.54 522.90 519.27 515.65 512.03 508.41 504.80 501.20 497.60 494.01 490.42 486.84 483.26 479.69 476.12 472.57 469.01 465.47 461.93 458.39 454.86 451.34 447.83 444.32 440.82 437.32 433.83 430.35 426.88 423.41 419.95 416.49 413.05 409.61 406.17 402.75 399.33 395.92 392.51 389.12 385.73 382.34 378.97 375.60 372.24 368.89 365.55

273.00% 274.00% 275.00% 276.00% 277.00% 278.00% 279.00% 280.00% 281.00% 282.00% 283.00% 284.00% 285.00% 286.00% 287.00% 288.00% 289.00% 290.00% 291.00% 292.00% 293.00% 294.00% 295.00% 296.00% 297.00% 298.00% 299.00% 300.00% 301.00% 302.00% 303.00% 304.00% 305.00% 306.00% 307.00% 308.00% 309.00% 310.00% 311.00% 312.00% 313.00% 314.00% 315.00% 316.00% 317.00% 318.00% 319.00% 320.00% 321.00% 322.00% 323.00% 324.00% 325.00% 326.00% 327.00% 328.00%

362.21 358.88 355.56 352.24 348.93 345.63 342.34 339.06 335.78 332.51 329.25 326.00 322.75 319.51 316.28 313.06 309.85 306.64 303.44 300.25 297.07 293.89 290.72 287.56 284.41 281.27 278.13 275.00 271.88 268.77 265.66 262.56 259.47 256.39 253.32 250.25 247.19 244.14 241.10 238.06 235.03 232.01 229.00 226.00 223.00 220.01 217.03 214.06 211.09 208.14 205.19 202.24 199.31 196.38 193.46 190.55

329.00% 330.00% 331.00% 332.00% 333.00% 334.00% 335.00% 336.00% 337.00% 338.00% 339.00% 340.00% 341.00% 342.00% 343.00% 344.00% 345.00% 346.00% 347.00% 348.00% 349.00% 350.00% 351.00% 352.00% 353.00% 354.00% 355.00% 356.00% 357.00% 358.00% 359.00% 360.00% 361.00% 362.00% 363.00% 364.00% 365.00% 366.00% 367.00% 368.00% 369.00% 370.00% 371.00% 372.00% 373.00% 374.00% 375.00% 376.00% 377.00% 378.00% 379.00% 380.00% 381.00% 382.00% 383.00% 384.00%

187.65 184.75 181.86 178.98 176.10 173.24 170.38 167.53 164.68 161.85 159.02 156.20 153.38 150.58 147.78 144.99 142.20 139.43 136.66 133.90 131.14 128.40 125.66 122.92 120.20 117.48 114.77 112.07 109.37 106.68 104.00 101.32 98.66 96.00 93.34 90.70 88.06 85.42 82.80 80.18 77.57 74.97 72.37 69.78 67.20 64.62 62.05 59.49 56.93 54.38 51.84 49.31 46.78 44.26 41.74 39.23

385.00% 386.00% 387.00% 388.00% 389.00% 390.00% 391.00% 392.00% 393.00% 394.00% 395.00% 396.00% 397.00% 398.00% 399.00% 400.00% 401.00% 402.00% 403.00% 404.00% 405.00% 406.00% 407.00% 408.00% 409.00% 410.00% 411.00% 412.00% 413.00% 414.00% 415.00% 416.00% 417.00% 418.00% 419.00% 420.00% 421.00% 422.00% 423.00% 424.00% 425.00% 426.00% 427.00% 428.00% 429.00% 430.00% 431.00% 432.00% 433.00% 434.00% 435.00% 436.00% 437.00% 438.00% 439.00% 440.00%

36.73 34.24 31.75 29.27 26.79 24.32 21.86 19.41 16.96 14.52 12.08 9.65 7.23 4.81 2.40 0.00 -2.40 -4.79 -7.17 -9.55 -11.92 -14.29 -16.64 -19.00 -21.34 -23.68 -26.02 -28.34 -30.67 -32.98 -35.29 -37.59 -39.89 -42.18 -44.47 -46.75 -49.02 -51.29 -53.55 -55.80 -58.05 -60.29 -62.53 -64.76 -66.99 -69.21 -71.42 -73.63 -75.83 -78.03 -80.22 -82.40 -84.58 -86.75 -88.92 -91.08

441.00% 442.00% 443.00% 444.00% 445.00% 446.00% 447.00% 448.00% 449.00% 450.00% 451.00% 452.00% 453.00% 454.00% 455.00% 456.00% 457.00% 458.00% 459.00% 460.00% 461.00% 462.00% 463.00% 464.00% 465.00% 466.00% 467.00% 468.00% 469.00% 470.00% 471.00% 472.00% 473.00% 474.00% 475.00% 476.00% 477.00% 478.00% 479.00% 480.00% 481.00% 482.00% 483.00% 484.00% 485.00% 486.00% 487.00% 488.00% 489.00% 490.00% 491.00% 492.00% 493.00% 494.00% 495.00% 496.00%

-93.24 -95.39 -97.54 -99.68 -101.81 -103.94 -106.06 -108.18 -110.29 -112.40 -114.50 -116.59 -118.68 -120.77 -122.85 -124.92 -126.99 -129.05 -131.11 -133.16 -135.21 -137.25 -139.29 -141.32 -143.35 -145.37 -147.38 -149.39 -151.40 -153.40 -155.40 -157.39 -159.37 -161.35 -163.33 -165.30 -167.26 -169.22 -171.18 -173.13 -175.07 -177.01 -178.95 -180.88 -182.80 -184.72 -186.64 -188.55 -190.46 -192.36 -194.26 -196.15 -198.03 -199.92 -201.79 -203.67

497.00% 498.00% 499.00% 500.00% 501.00% 502.00% 503.00% 504.00% 505.00% 506.00% 507.00% 508.00% 509.00% 510.00% 511.00% 512.00% 513.00% 514.00% 515.00% 516.00% 517.00% 518.00% 519.00% 520.00% 521.00% 522.00% 523.00% 524.00% 525.00% 526.00% 527.00% 528.00% 529.00% 530.00% 531.00% 532.00% 533.00% 534.00% 535.00% 536.00% 537.00% 538.00% 539.00% 540.00% 541.00% 542.00% 543.00% 544.00% 545.00% 546.00% 547.00% 548.00% 549.00% 550.00% 551.00% 552.00%

-205.53 -207.40 -209.26 -211.11 -212.96 -214.81 -216.65 -218.48 -220.31 -222.14 -223.96 -225.78 -227.59 -229.40 -231.20 -233.00 -234.80 -236.59 -238.38 -240.16 -241.94 -243.71 -245.48 -247.24 -249.00 -250.76 -252.51 -254.26 -256.00 -257.74 -259.47 -261.20 -262.93 -264.65 -266.37 -268.08 -269.79 -271.50 -273.20 -274.89 -276.59 -278.28 -279.96 -281.64 -283.32 -284.99 -286.66 -288.32 -289.98 -291.64 -293.29 -294.94 -296.58 -298.22 -299.86 -301.49

553.00% 554.00% 555.00% 556.00% 557.00% 558.00% 559.00% 560.00% 561.00% 562.00% 563.00% 564.00% 565.00% 566.00% 567.00% 568.00% 569.00% 570.00% 571.00% 572.00% 573.00% 574.00% 575.00% 576.00% 577.00% 578.00% 579.00% 580.00% 581.00% 582.00% 583.00% 584.00% 585.00% 586.00% 587.00% 588.00% 589.00% 590.00% 591.00% 592.00% 593.00% 594.00% 595.00% 596.00% 597.00% 598.00% 599.00% 600.00% 601.00% 602.00% 603.00% 604.00% 605.00% 606.00% 607.00% 608.00%

-303.12 -304.75 -306.37 -307.99 -309.60 -311.21 -312.81 -314.42 -316.02 -317.61 -319.20 -320.79 -322.37 -323.95 -325.52 -327.10 -328.66 -330.23 -331.79 -333.35 -334.90 -336.45 -338.00 -339.54 -341.08 -342.61 -344.15 -345.67 -347.20 -348.72 -350.24 -351.75 -353.26 -354.77 -356.27 -357.77 -359.27 -360.76 -362.25 -363.74 -365.22 -366.70 -368.18 -369.65 -371.12 -372.59 -374.05 -375.51 -376.97 -378.42 -379.87 -381.31 -382.76 -384.20 -385.63 -387.07

609.00% 610.00% 611.00% 612.00% 613.00% 614.00% 615.00% 616.00% 617.00% 618.00% 619.00% 620.00% 621.00% 622.00% 623.00% 624.00% 625.00% 626.00% 627.00% 628.00% 629.00% 630.00% 631.00% 632.00% 633.00% 634.00% 635.00% 636.00% 637.00% 638.00% 639.00% 640.00% 641.00% 642.00% 643.00% 644.00% 645.00% 646.00% 647.00% 648.00% 649.00% 650.00% 651.00% 652.00% 653.00% 654.00% 655.00% 656.00% 657.00% 658.00% 659.00% 660.00% 661.00% 662.00% 663.00% 664.00%

-388.50 -389.92 -391.35 -392.77 -394.18 -395.60 -397.01 -398.41 -399.82 -401.22 -402.62 -404.01 -405.40 -406.79 -408.18 -409.56 -410.94 -412.32 -413.69 -415.06 -416.43 -417.79 -419.15 -420.51 -421.86 -423.21 -424.56 -425.91 -427.25 -428.59 -429.93 -431.26 -432.59 -433.92 -435.25 -436.57 -437.89 -439.21 -440.52 -441.83 -443.14 -444.44 -445.75 -447.05 -448.34 -449.64 -450.93 -452.22 -453.50 -454.78 -456.06 -457.34 -458.62 -459.89 -461.16 -462.42

665.00% 666.00% 667.00% 668.00% 669.00% 670.00% 671.00% 672.00% 673.00% 674.00% 675.00% 676.00% 677.00% 678.00% 679.00% 680.00% 681.00% 682.00% 683.00% 684.00% 685.00% 686.00% 687.00% 688.00% 689.00% 690.00% 691.00% 692.00% 693.00% 694.00% 695.00% 696.00% 697.00% 698.00% 699.00% 700.00% 701.00% 702.00% 703.00% 704.00% 705.00% 706.00% 707.00% 708.00% 709.00% 710.00% 711.00% 712.00% 713.00% 714.00% 715.00% 716.00% 717.00% 718.00% 719.00% 720.00%

-463.68 -464.95 -466.20 -467.46 -468.71 -469.96 -471.21 -472.45 -473.69 -474.93 -476.17 -477.40 -478.64 -479.86 -481.09 -482.31 -483.54 -484.75 -485.97 -487.18 -488.39 -489.60 -490.81 -492.01 -493.21 -494.41 -495.60 -496.80 -497.99 -499.17 -500.36 -501.54 -502.72 -503.90 -505.08 -506.25 -507.42 -508.59 -509.75 -510.92 -512.08 -513.24 -514.39 -515.55 -516.70 -517.85 -518.99 -520.14 -521.28 -522.42 -523.56 -524.69 -525.82 -526.96 -528.08 -529.21

721.00% 722.00% 723.00% 724.00% 725.00% 726.00% 727.00% 728.00% 729.00% 730.00% 731.00% 732.00% 733.00% 734.00% 735.00% 736.00% 737.00% 738.00% 739.00% 740.00% 741.00% 742.00% 743.00% 744.00% 745.00% 746.00% 747.00% 748.00% 749.00% 750.00% 751.00% 752.00% 753.00% 754.00% 755.00% 756.00% 757.00% 758.00% 759.00% 760.00% 761.00% 762.00% 763.00% 764.00% 765.00% 766.00% 767.00% 768.00% 769.00% 770.00% 771.00% 772.00% 773.00% 774.00% 775.00% 776.00%

-530.33 -531.45 -532.57 -533.69 -534.80 -535.91 -537.02 -538.13 -539.24 -540.34 -541.44 -542.54 -543.64 -544.73 -545.82 -546.91 -548.00 -549.08 -550.17 -551.25 -552.33 -553.40 -554.48 -555.55 -556.62 -557.69 -558.75 -559.82 -560.88 -561.94 -563.00 -564.05 -565.10 -566.15 -567.20 -568.25 -569.30 -570.34 -571.38 -572.42 -573.45 -574.49 -575.52 -576.55 -577.58 -578.61 -579.63 -580.65 -581.67 -582.69 -583.71 -584.72 -585.74 -586.75 -587.76 -588.76

777.00% 778.00% 779.00% 780.00% 781.00% 782.00% 783.00% 784.00% 785.00% 786.00% 787.00% 788.00% 789.00% 790.00% 791.00% 792.00% 793.00% 794.00% 795.00% 796.00% 797.00% 798.00% 799.00% 800.00% 801.00% 802.00% 803.00% 804.00% 805.00% 806.00% 807.00% 808.00% 809.00% 810.00% 811.00% 812.00% 813.00% 814.00% 815.00% 816.00% 817.00% 818.00% 819.00% 820.00% 821.00% 822.00% 823.00% 824.00% 825.00% 826.00% 827.00% 828.00% 829.00% 830.00% 831.00% 832.00%

-589.77 -590.77 -591.77 -592.77 -593.77 -594.76 -595.75 -596.74 -597.73 -598.72 -599.71 -600.69 -601.67 -602.65 -603.63 -604.60 -605.58 -606.55 -607.52 -608.49 -609.46 -610.42 -611.38 -612.35 -613.30 -614.26 -615.22 -616.17 -617.12 -618.07 -619.02 -619.97 -620.91 -621.86 -622.80 -623.74 -624.68 -625.61 -626.55 -627.48 -628.41 -629.34 -630.27 -631.19 -632.11 -633.04 -633.96 -634.88 -635.79 -636.71 -637.62 -638.53 -639.44 -640.35 -641.26 -642.16

833.00% 834.00% 835.00% 836.00% 837.00% 838.00% 839.00% 840.00% 841.00% 842.00% 843.00% 844.00% 845.00% 846.00% 847.00% 848.00% 849.00% 850.00% 851.00% 852.00% 853.00% 854.00% 855.00% 856.00% 857.00% 858.00% 859.00% 860.00% 861.00% 862.00% 863.00% 864.00% 865.00% 866.00% 867.00% 868.00% 869.00% 870.00% 871.00% 872.00% 873.00% 874.00% 875.00% 876.00% 877.00% 878.00% 879.00% 880.00% 881.00% 882.00% 883.00% 884.00% 885.00% 886.00% 887.00% 888.00%

-643.07 -643.97 -644.87 -645.77 -646.66 -647.56 -648.45 -649.34 -650.23 -651.12 -652.01 -652.89 -653.78 -654.66 -655.54 -656.42 -657.30 -658.17 -659.05 -659.92 -660.79 -661.66 -662.53 -663.39 -664.26 -665.12 -665.98 -666.84 -667.70 -668.56 -669.41 -670.26 -671.12 -671.97 -672.82 -673.66 -674.51 -675.35 -676.20 -677.04 -677.88 -678.72 -679.55 -680.39 -681.22 -682.05 -682.89 -683.72 -684.54 -685.37 -686.19 -687.02 -687.84 -688.66 -689.48 -690.30

889.00% 890.00% 891.00% 892.00% 893.00% 894.00% 895.00% 896.00% 897.00% 898.00% 899.00% 900.00% 901.00% 902.00% 903.00% 904.00% 905.00% 906.00% 907.00% 908.00% 909.00% 910.00% 911.00% 912.00% 913.00% 914.00% 915.00% 916.00% 917.00% 918.00% 919.00% 920.00% 921.00% 922.00% 923.00% 924.00% 925.00% 926.00% 927.00% 928.00% 929.00% 930.00% 931.00% 932.00% 933.00% 934.00% 935.00% 936.00% 937.00% 938.00% 939.00% 940.00% 941.00% 942.00% 943.00% 944.00%

-691.11 -691.93 -692.74 -693.55 -694.37 -695.17 -695.98 -696.79 -697.59 -698.40 -699.20 -700.00 -700.80 -701.60 -702.39 -703.19 -703.98 -704.77 -705.57 -706.36 -707.14 -707.93 -708.72 -709.50 -710.28 -711.06 -711.84 -712.62 -713.40 -714.18 -714.95 -715.72 -716.50 -717.27 -718.04 -718.80 -719.57 -720.34 -721.10 -721.86 -722.63 -723.39 -724.14 -724.90 -725.66 -726.41 -727.17 -727.92 -728.67 -729.42 -730.17 -730.92 -731.66 -732.41 -733.15 -733.89

945.00% 946.00% 947.00% 948.00% 949.00% 950.00% 951.00% 952.00% 953.00% 954.00% 955.00% 956.00% 957.00% 958.00% 959.00% 960.00% 961.00% 962.00% 963.00% 964.00% 965.00% 966.00% 967.00% 968.00% 969.00% 970.00% 971.00% 972.00% 973.00% 974.00% 975.00% 976.00% 977.00% 978.00% 979.00% 980.00% 981.00% 982.00% 983.00% 984.00% 985.00% 986.00% 987.00% 988.00% 989.00% 990.00% 991.00% 992.00% 993.00% 994.00% 995.00% 996.00% 997.00% 998.00% 999.00% 1000.00%

-734.64 -735.38 -736.11 -736.85 -737.59 -738.32 -739.06 -739.79 -740.52 -741.25 -741.98 -742.71 -743.43 -744.16 -744.88 -745.60 -746.32 -747.05 -747.76 -748.48 -749.20 -749.91 -750.63 -751.34 -752.05 -752.76 -753.47 -754.18 -754.89 -755.60 -756.30 -757.00 -757.71 -758.41 -759.11 -759.81 -760.51 -761.20 -761.90 -762.59 -763.29 -763.98 -764.67 -765.36 -766.05 -766.74 -767.42 -768.11 -768.79 -769.48 -770.16 -770.84 -771.52 -772.20 -772.88 -773.55

400.00%

600.00%

800.00%

1000.00%

Otro Caso de TIR Mltiple

Ao 0 1 2 3 4

Flujo Caja -17 20 20 15 -40

TIR 1 TIR 2

4.35% 69.45%

TIR MODIFICADA

TIR 1 TIR 2 TIR 3 VAN 1,489.00 967.74 544.55 206.06 -59.46 -262.31 -411.53 -515.02 -579.73 -611.72 -616.30 -598.10 -561.15 -508.97 -444.61 -370.72 -289.60 -203.22 -113.28 -21.24 71.65 164.33 255.91 345.63 432.88 517.12 597.95 675.02 748.07 816.89 881.34 941.32 996.76 1,047.65 1,093.97 1,135.77 1,173.08 1,205.99 1,234.56 1,258.90 1,279.10 1,295.28 1,307.55 1,316.05 1,320.88 Ao 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Q+ 0 10,229 9,609 15,004 3,774 0 0 4,217 18,298 0 0 0 0 0 0 13,570 377 0 16,642 1,609 10,859

1.88% 9.61% 40.13% Q-15,000 0 0 0 0 -9,709 -18,097 0 0 -12,041 -10 -7,500 -11,855 -12,070 -6,349 0 0 -10,068 0 0 0

Tasa Descuento Gastos Tasa Capitalizacin Ingresos TIR Modificada

Ao Flujo Caja 0 -15,000 1 10,229 2 9,609 3 15,004 4 3,774 5 -9,709 6 -18,097 7 4,217 8 18,298 9 -12,041 10 -10 11 -7,500 12 -11,855 13 -12,070 14 -6,349 15 13,570 16 377 17 -10,068 18 16,642 19 1,609 20 10,859

Tasa 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.5% 16.0% 16.5% 17.0% 17.5% 18.0% 18.5% 19.0% 19.5% 20.0% 20.5% 21.0% 21.5% 22.0%

Valor Actual Gastos Valor Final Ingresos TIR Modificada

4,000

2,000

0 0.0% -2,000 20.0% 40.0%

-4,000

-6,000

-8,000

-10,000

-12,000

22.5% 23.0% 23.5% 24.0% 24.5% 25.0% 25.5% 26.0% 26.5% 27.0% 27.5% 28.0% 28.5% 29.0% 29.5% 30.0% 30.5% 31.0% 31.5% 32.0% 32.5% 33.0% 33.5% 34.0% 34.5% 35.0% 35.5% 36.0% 36.5% 37.0% 37.5% 38.0% 38.5% 39.0% 39.5% 40.0% 40.5% 41.0% 41.5% 42.0% 42.5% 43.0% 43.5% 44.0% 44.5% 45.0% 45.5% 46.0% 46.5% 47.0% 47.5% 48.0%

1,322.19 1,320.10 1,314.73 1,306.22 1,294.69 1,280.28 1,263.10 1,243.27 1,220.92 1,196.16 1,169.11 1,139.88 1,108.57 1,075.28 1,040.13 1,003.20 964.60 924.40 882.71 839.60 795.15 749.45 702.57 654.57 605.54 555.53 504.60 452.83 400.27 346.96 292.97 238.35 183.15 127.40 71.17 14.48 -42.62 -100.10 -157.91 -216.02 -274.41 -333.02 -391.85 -450.85 -510.01 -569.28 -628.66 -688.12 -747.63 -807.17 -866.73 -926.28

48.5% 49.0% 49.5% 50.0% 50.5% 51.0% 51.5% 52.0% 52.5% 53.0% 53.5% 54.0% 54.5% 55.0% 55.5% 56.0% 56.5% 57.0% 57.5% 58.0% 58.5% 59.0% 59.5% 60.0% 60.5% 61.0% 61.5% 62.0% 62.5% 63.0% 63.5% 64.0% 64.5% 65.0% 65.5% 66.0% 66.5% 67.0% 67.5% 68.0% 68.5% 69.0% 69.5% 70.0% 70.5% 71.0% 71.5% 72.0% 72.5% 73.0% 73.5% 74.0%

-985.80 -1,045.29 -1,104.71 -1,164.07 -1,223.34 -1,282.50 -1,341.55 -1,400.48 -1,459.27 -1,517.91 -1,576.38 -1,634.69 -1,692.82 -1,750.77 -1,808.52 -1,866.06 -1,923.40 -1,980.52 -2,037.41 -2,094.08 -2,150.51 -2,206.70 -2,262.64 -2,318.34 -2,373.78 -2,428.97 -2,483.89 -2,538.55 -2,592.94 -2,647.07 -2,700.92 -2,754.49 -2,807.79 -2,860.81 -2,913.54 -2,966.00 -3,018.17 -3,070.06 -3,121.66 -3,172.97 -3,224.00 -3,274.74 -3,325.19 -3,375.35 -3,425.22 -3,474.81 -3,524.10 -3,573.10 -3,621.82 -3,670.25 -3,718.39 -3,766.24

74.5% 75.0% 75.5% 76.0% 76.5% 77.0% 77.5% 78.0% 78.5% 79.0% 79.5% 80.0% 80.5% 81.0% 81.5% 82.0% 82.5% 83.0% 83.5% 84.0% 84.5% 85.0% 85.5% 86.0% 86.5% 87.0% 87.5% 88.0% 88.5% 89.0% 89.5% 90.0% 90.5% 91.0% 91.5% 92.0% 92.5% 93.0% 93.5% 94.0% 94.5% 95.0% 95.5% 96.0% 96.5% 97.0% 97.5% 98.0% 98.5% 99.0% 99.5% 100.0%

-3,813.80 -3,861.08 -3,908.07 -3,954.78 -4,001.20 -4,047.34 -4,093.19 -4,138.77 -4,184.06 -4,229.07 -4,273.81 -4,318.26 -4,362.45 -4,406.35 -4,449.99 -4,493.35 -4,536.43 -4,579.25 -4,621.80 -4,664.09 -4,706.11 -4,747.86 -4,789.35 -4,830.58 -4,871.55 -4,912.26 -4,952.72 -4,992.92 -5,032.86 -5,072.55 -5,112.00 -5,151.19 -5,190.13 -5,228.83 -5,267.29 -5,305.50 -5,343.47 -5,381.20 -5,418.70 -5,455.95 -5,492.97 -5,529.76 -5,566.32 -5,602.64 -5,638.74 -5,674.61 -5,710.25 -5,745.68 -5,780.87 -5,815.85 -5,850.61 -5,885.15

100.5% 101.0% 101.5% 102.0% 102.5% 103.0% 103.5% 104.0% 104.5% 105.0% 105.5% 106.0% 106.5% 107.0% 107.5% 108.0% 108.5% 109.0% 109.5% 110.0% 110.5% 111.0% 111.5% 112.0% 112.5% 113.0% 113.5% 114.0% 114.5% 115.0% 115.5% 116.0% 116.5% 117.0% 117.5% 118.0% 118.5% 119.0% 119.5% 120.0% 120.5% 121.0% 121.5% 122.0% 122.5% 123.0% 123.5% 124.0% 124.5% 125.0% 125.5% 126.0%

-5,919.47 -5,953.58 -5,987.48 -6,021.17 -6,054.64 -6,087.91 -6,120.97 -6,153.82 -6,186.47 -6,218.92 -6,251.17 -6,283.21 -6,315.06 -6,346.72 -6,378.18 -6,409.44 -6,440.51 -6,471.39 -6,502.08 -6,532.59 -6,562.91 -6,593.04 -6,622.99 -6,652.75 -6,682.34 -6,711.74 -6,740.97 -6,770.02 -6,798.90 -6,827.60 -6,856.12 -6,884.48 -6,912.66 -6,940.68 -6,968.53 -6,996.21 -7,023.73 -7,051.08 -7,078.27 -7,105.30 -7,132.16 -7,158.87 -7,185.42 -7,211.82 -7,238.05 -7,264.14 -7,290.07 -7,315.85 -7,341.47 -7,366.95 -7,392.28 -7,417.46

126.5% 127.0% 127.5% 128.0% 128.5% 129.0% 129.5% 130.0% 130.5% 131.0% 131.5% 132.0% 132.5% 133.0% 133.5% 134.0% 134.5% 135.0% 135.5% 136.0% 136.5% 137.0% 137.5% 138.0% 138.5% 139.0% 139.5% 140.0% 140.5% 141.0% 141.5% 142.0% 142.5% 143.0% 143.5% 144.0% 144.5% 145.0% 145.5% 146.0% 146.5% 147.0% 147.5% 148.0% 148.5% 149.0% 149.5% 150.0% 150.5% 151.0% 151.5% 152.0%

-7,442.50 -7,467.39 -7,492.13 -7,516.73 -7,541.19 -7,565.51 -7,589.69 -7,613.73 -7,637.63 -7,661.40 -7,685.03 -7,708.52 -7,731.88 -7,755.11 -7,778.21 -7,801.17 -7,824.01 -7,846.72 -7,869.30 -7,891.75 -7,914.08 -7,936.28 -7,958.35 -7,980.31 -8,002.14 -8,023.85 -8,045.44 -8,066.91 -8,088.26 -8,109.49 -8,130.61 -8,151.61 -8,172.49 -8,193.26 -8,213.92 -8,234.46 -8,254.90 -8,275.22 -8,295.43 -8,315.53 -8,335.52 -8,355.41 -8,375.18 -8,394.85 -8,414.42 -8,433.88 -8,453.24 -8,472.49 -8,491.64 -8,510.69 -8,529.64 -8,548.48

152.5% 153.0% 153.5% 154.0% 154.5% 155.0% 155.5% 156.0% 156.5% 157.0% 157.5% 158.0% 158.5% 159.0% 159.5% 160.0% 160.5% 161.0% 161.5% 162.0% 162.5% 163.0% 163.5% 164.0% 164.5% 165.0% 165.5% 166.0% 166.5% 167.0% 167.5% 168.0% 168.5% 169.0% 169.5% 170.0% 170.5% 171.0% 171.5% 172.0% 172.5% 173.0% 173.5% 174.0% 174.5% 175.0% 175.5% 176.0% 176.5% 177.0% 177.5% 178.0%

-8,567.23 -8,585.88 -8,604.43 -8,622.88 -8,641.24 -8,659.50 -8,677.66 -8,695.73 -8,713.71 -8,731.59 -8,749.38 -8,767.07 -8,784.68 -8,802.19 -8,819.62 -8,836.95 -8,854.20 -8,871.36 -8,888.43 -8,905.41 -8,922.30 -8,939.11 -8,955.84 -8,972.48 -8,989.04 -9,005.51 -9,021.90 -9,038.21 -9,054.43 -9,070.58 -9,086.64 -9,102.62 -9,118.53 -9,134.35 -9,150.10 -9,165.77 -9,181.36 -9,196.87 -9,212.31 -9,227.67 -9,242.96 -9,258.17 -9,273.31 -9,288.37 -9,303.36 -9,318.28 -9,333.13 -9,347.90 -9,362.60 -9,377.23 -9,391.79 -9,406.28

178.5% 179.0% 179.5% 180.0% 180.5% 181.0% 181.5% 182.0% 182.5% 183.0% 183.5% 184.0% 184.5% 185.0% 185.5% 186.0% 186.5% 187.0% 187.5% 188.0% 188.5% 189.0% 189.5% 190.0% 190.5% 191.0% 191.5% 192.0% 192.5% 193.0% 193.5% 194.0% 194.5% 195.0% 195.5% 196.0% 196.5% 197.0% 197.5% 198.0% 198.5% 199.0% 199.5% 200.0%

-9,420.70 -9,435.06 -9,449.34 -9,463.56 -9,477.70 -9,491.78 -9,505.80 -9,519.75 -9,533.63 -9,547.44 -9,561.19 -9,574.88 -9,588.50 -9,602.06 -9,615.56 -9,628.99 -9,642.36 -9,655.67 -9,668.91 -9,682.10 -9,695.22 -9,708.28 -9,721.29 -9,734.23 -9,747.11 -9,759.94 -9,772.71 -9,785.41 -9,798.06 -9,810.66 -9,823.19 -9,835.67 -9,848.09 -9,860.46 -9,872.77 -9,885.03 -9,897.23 -9,909.37 -9,921.46 -9,933.50 -9,945.48 -9,957.41 -9,969.29 -9,981.12

8% 10% 9.3498%

56,285.27 336,321.08 9.3498%

VAN

40.0%

60.0%

80.0%

100.0%

120.0%

140.0%

160.0%

180.0%

200.0%

TIRmodificada

TIR MODIFICADA

Ao Flujo Caja 0 -15,000 1 10,229 2 9,609 3 15,004 4 3,774 5 -9,709 6 -18,097 7 4,217 8 18,298 9 -12,041 10 -10 11 -7,500 12 -11,855 13 -12,070 14 -6,349 15 13,570 16 377 17 -10,068 18 16,642 19 1,609 20 10,859

Interseccin de FisherYear 0 1 2 3 4IRR

Project A -1000 500 400 300 10014.49%

Project B -1000 100 300 400 60011.79%

Difference 0 -400 -100 100 5007.17%

k 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 9.50% 10.00% 10.50% 11.00% 11.50% 12.00% 12.50% 13.00% 13.50% 14.00% 14.50% 15.00% 15.50% 16.00% 16.50% 17.00% 17.50% 18.00% 18.50% 19.00% 19.50% 20.00% 20.50% 21.00% 21.50% 22.00% 22.50% 23.00% 23.50% 24.00%

NPV(A) 300.00 287.11 274.44 261.99 249.74 237.71 225.87 214.22 202.77 191.51 180.42 169.52 158.79 148.23 137.84 127.62 117.55 107.64 97.89 88.28 78.82 69.50 60.33 51.29 42.39 33.62 24.98 16.47 8.08 -0.18 -8.33 -16.36 -24.27 -32.08 -39.77 -47.35 -54.83 -62.20 -69.47 -76.65 -83.72 -90.70 -97.58 -104.37 -111.07 -117.68 -124.20 -130.63 -136.98

NPV(B) 400.00 378.73 357.92 337.56 317.63 298.12 279.02 260.31 242.00 224.07 206.50 189.30 172.44 155.93 139.75 123.89 108.35 93.11 78.18 63.53 49.18 35.10 21.29 7.75 -5.53 -18.56 -31.35 -43.89 -56.20 -68.28 -80.14 -91.78 -103.21 -114.42 -125.44 -136.25 -146.87 -157.30 -167.55 -177.61 -187.50 -197.21 -206.76 -216.14 -225.35 -234.41 -243.31 -252.06 -260.67

24.50% 25.00% 25.50% 26.00% 26.50% 27.00% 27.50% 28.00% 28.50% 29.00% 29.50% 30.00% 30.50% 31.00% 31.50% 32.00% 32.50% 33.00% 33.50% 34.00% 34.50% 35.00% 35.50% 36.00% 36.50% 37.00% 37.50% 38.00% 38.50% 39.00% 39.50% 40.00% 40.50% 41.00% 41.50% 42.00% 42.50% 43.00% 43.50% 44.00% 44.50% 45.00% 45.50% 46.00% 46.50% 47.00% 47.50% 48.00% 48.50% 49.00% 49.50% 50.00%

-143.25 -149.44 -155.55 -161.58 -167.53 -173.40 -179.20 -184.93 -190.59 -196.17 -201.69 -207.14 -212.52 -217.83 -223.08 -228.27 -233.39 -238.46 -243.46 -248.40 -253.28 -258.11 -262.88 -267.60 -272.26 -276.86 -281.42 -285.92 -290.37 -294.77 -299.11 -303.42 -307.67 -311.87 -316.03 -320.14 -324.21 -328.23 -332.21 -336.15 -340.04 -343.90 -347.71 -351.48 -355.21 -358.90 -362.55 -366.16 -369.74 -373.28 -376.78 -380.25

-269.12 -277.44 -285.62 -293.66 -301.57 -309.34 -316.99 -324.52 -331.92 -339.20 -346.37 -353.42 -360.36 -367.19 -373.91 -380.52 -387.03 -393.44 -399.75 -405.96 -412.08 -418.10 -424.03 -429.87 -435.62 -441.29 -446.87 -452.37 -457.78 -463.12 -468.37 -473.55 -478.66 -483.69 -488.64 -493.53 -498.34 -503.09 -507.77 -512.38 -516.93 -521.41 -525.83 -530.19 -534.49 -538.72 -542.90 -547.03 -551.09 -555.10 -559.06 -562.96

El VAN de dos proyectos se cruza600.00 400.00 200.00 0.00 -200.00 -400.00 -600.00 -800.00 Tasa de descuentoFisher Intersection

0%

10%

20%

30%

40%

50%

NPV(A)

50%

NPV(B)

Determinar la Interseccin de Fisher Year 0 1 2 3 Project A-1200 1000 500 100

Project B-1200 100 600 1080