Excel Avanzado

Adolfo Aparicio

www.excelavanzado.com

www.excelavanzado.com

Excel Avanzado

Adolfo Aparicio

www.excelavanzado.com

document.xlsx Página 3

VanTir.xls

VALOR ACTUAL NETO

Año Flujo Caja Tasa Dto. VAN0 -4,000 € 0.0% 1,000 €1 1,400 € 0.5% 941 €2 1,300 € 1.0% 882 €3 1,200 € 1.5% 825 €4 1,100 € 2.0% 769 €

2.5% 714 €3.0% 660 €3.5% 607 €4.0% 555 €4.5% 504 €5.0% 454 €5.5% 405 €6.0% 357 €6.5% 309 €7.0% 263 €7.5% 217 €8.0% 172 €8.5% 128 €9.0% 84 €9.5% 42 € TASA INTERNA DE RENTABILIDAD

10.0% 0 €10.5% -41 € TIR 10% efectivo anual11.0% -82 €11.5% -121 €12.0% -160 €12.5% -199 €13.0% -237 €13.5% -274 €14.0% -310 €14.5% -346 €15.0% -382 €

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

(€3,000)

(€2,500)

(€2,000)

(€1,500)

(€1,000)

(€500)

€0

€500

€1,000

€1,500

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

Si alguno de los flujos de caja intermedios no existe se debe poner cero, no se dabe dejar vacia la celda.

La TIR se puede definir como el tipo de interés que hace el VAN = 0

En la fórmula de la TIR no se indica en este caso la estimación, ya que no estamos en un caso de TIR múltiple.Cuando se omite la estimación, Excel la supone del 10%.

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document.xlsx Página 4

Si alguno de los flujos de caja intermedios no existe se debe poner cero, no se dabe dejar vacia la celda.C9:

=VNA(E6;$C$7:$C$10)+$C$6F6:

La TIR se puede definir como el tipo de interés que hace el VAN = 0F26:

En la fórmula de la TIR no se indica en este caso la estimación, ya que no estamos en un caso de TIR múltiple.Cuando se omite la estimación, Excel la supone del 10%.

K27:

VAN y TIR no periódicos

Dias Fecha Flujo Caja VAN

0 0 14-Oct-03 -4,000 € 0.0% 200.00 €105 105 27-Jan-04 1,200 € 0.5% 187.35 €138 33 29-Feb-04 1,100 € 1.0% 174.82 €259 121 29-Jun-04 1,000 € 1.5% 162.39 €434 175 21-Dec-04 900 € 2.0% 150.08 €

2.5% 137.88 €3.0% 125.78 €3.5% 113.78 €4.0% 101.89 €4.5% 90.10 €

Dia Flujo Caja 5.0% 78.41 €0 -4,000 € 5.5% 66.83 €1 0 6.0% 55.34 €2 0 6.5% 43.94 €3 0 7.0% 32.64 €4 0 7.5% 21.44 €5 0 8.0% 10.33 €6 0 8.5% -0.69 €7 0 9.0% -11.62 €8 0 9.5% -22.46 €

9 0 10.0% -33.21 € TIR NO PERIÓDICA10 0 10.5% -43.87 €11 0 11.0% -54.45 € TIR 8.4686%12 0 11.5% -64.95 €13 0 12.0% -75.36 € TIR Diaria 0.02227%14 0 12.5% -85.68 €15 0 13.0% -95.93 € TIR Anual 8.4686%16 0 13.5% -106.10 €17 0 14.0% -116.18 €18 0 14.5% -126.19 €19 0 15.0% -136.12 €20 0 15.5% -145.97 €21 0 16.0% -155.75 €22 0 16.5% -165.45 €23 0 17.0% -175.08 €24 0 17.5% -184.64 €25 0 18.0% -194.12 €26 0 18.5% -203.53 €27 0 19.0% -212.87 €28 0 19.5% -222.15 €29 0 20.0% -231.35 €30 0 20.5% -240.49 €31 0 21.0% -249.56 €32 0 21.5% -258.56 €33 0 22.0% -267.50 €34 0 22.5% -276.37 €35 0 23.0% -285.18 €36 0 23.5% -293.92 €

Dias Acum.

Tasa Dto.

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

(€1,400.00)

(€1,200.00)

(€1,000.00)

(€800.00)

(€600.00)

(€400.00)

(€200.00)

€0.00

€200.00

€400.00 VAN

La fórmula TIR.NO.PER siempre da la TIR anual.

Es necesario poner una estimación muy pequeña pq sino da error.

La fórmula TIR dará una TIR mensual si los periodos son meses, dará una TIR diaria si lo periodos son días, o dará una TIR anual si los periodos son años.

37 0 24.0% -302.61 €38 0 24.5% -311.23 €39 0 25.0% -319.79 €40 0 25.5% -328.29 €41 0 26.0% -336.73 €42 0 26.5% -345.11 €43 0 27.0% -353.43 €44 0 27.5% -361.69 €45 0 28.0% -369.90 €46 0 28.5% -378.05 €47 0 29.0% -386.15 €48 0 29.5% -394.19 €49 0 30.0% -402.17 €50 0 30.5% -410.10 €51 0 31.0% -417.98 €52 0 31.5% -425.81 €53 0 32.0% -433.58 €54 0 32.5% -441.30 €55 0 33.0% -448.97 €56 0 33.5% -456.59 €57 0 34.0% -464.16 €58 0 34.5% -471.68 €59 0 35.0% -479.15 €60 0 35.5% -486.57 €61 0 36.0% -493.94 €62 0 36.5% -501.27 €63 0 37.0% -508.55 €64 0 37.5% -515.78 €65 0 38.0% -522.97 €66 0 38.5% -530.11 €67 0 39.0% -537.20 €68 0 39.5% -544.26 €69 0 40.0% -551.26 €70 0 40.5% -558.22 €71 0 41.0% -565.14 €72 0 41.5% -572.02 €73 0 42.0% -578.85 €74 0 42.5% -585.65 €75 0 43.0% -592.40 €76 0 43.5% -599.11 €77 0 44.0% -605.77 €78 0 44.5% -612.40 €79 0 45.0% -618.99 €80 0 45.5% -625.54 €81 0 46.0% -632.05 €82 0 46.5% -638.52 €83 0 47.0% -644.95 €84 0 47.5% -651.34 €85 0 48.0% -657.70 €86 0 48.5% -664.02 €87 0 49.0% -670.30 €88 0 49.5% -676.54 €89 0 50.0% -682.75 €90 0 50.5% -688.92 €

91 0 51.0% -695.06 €92 0 51.5% -701.16 €93 0 52.0% -707.22 €94 0 52.5% -713.25 €95 0 53.0% -719.25 €96 0 53.5% -725.21 €97 0 54.0% -731.14 €98 0 54.5% -737.04 €99 0 55.0% -742.90 €

100 0 55.5% -748.73 €101 0 56.0% -754.53 €102 0 56.5% -760.29 €103 0 57.0% -766.02 €104 0 57.5% -771.72 €105 1200 58.0% -777.39 €106 0 58.5% -783.03 €107 0 59.0% -788.64 €108 0 59.5% -794.22 €109 0 60.0% -799.76 €110 0 60.5% -805.28 €111 0 61.0% -810.76 €112 0 61.5% -816.22 €113 0 62.0% -821.65 €114 0 62.5% -827.05 €115 0 63.0% -832.42 €116 0 63.5% -837.76 €117 0 64.0% -843.07 €118 0 64.5% -848.36 €119 0 65.0% -853.62 €120 0 65.5% -858.85 €121 0 66.0% -864.05 €122 0 66.5% -869.22 €123 0 67.0% -874.37 €124 0 67.5% -879.49 €125 0 68.0% -884.59 €126 0 68.5% -889.66 €127 0 69.0% -894.70 €128 0 69.5% -899.72 €129 0 70.0% -904.71 €130 0 70.5% -909.68 €131 0 71.0% -914.62 €132 0 71.5% -919.54 €133 0 72.0% -924.43 €134 0 72.5% -929.30 €135 0 73.0% -934.14 €136 0 73.5% -938.96 €137 0 74.0% -943.75 €138 1100 74.5% -948.53 €139 0 75.0% -953.27 €140 0 75.5% -958.00 €141 0 76.0% -962.70 €142 0 76.5% -967.38 €143 0 77.0% -972.03 €144 0 77.5% -976.67 €

145 0 78.0% -981.28 €146 0 78.5% -985.86 €147 0 79.0% -990.43 €148 0 79.5% -994.97 €149 0 80.0% -999.50 €150 0 80.5% -1,004.00 €151 0 81.0% -1,008.48 €152 0 81.5% -1,012.93 €153 0 82.0% -1,017.37 €154 0 82.5% -1,021.79 €155 0 83.0% -1,026.18 €156 0 83.5% -1,030.56 €157 0 84.0% -1,034.91 €158 0 84.5% -1,039.24 €159 0 85.0% -1,043.56 €160 0 85.5% -1,047.85 €161 0 86.0% -1,052.13 €162 0 86.5% -1,056.38 €163 0 87.0% -1,060.61 €164 0 87.5% -1,064.83 €165 0 88.0% -1,069.02 €166 0 88.5% -1,073.20 €167 0 89.0% -1,077.36 €168 0 89.5% -1,081.50 €169 0 90.0% -1,085.62 €170 0 90.5% -1,089.72 €171 0 91.0% -1,093.80 €172 0 91.5% -1,097.87 €173 0 92.0% -1,101.91 €174 0 92.5% -1,105.94 €175 0 93.0% -1,109.95 €176 0 93.5% -1,113.95 €177 0 94.0% -1,117.92 €178 0 94.5% -1,121.88 €179 0 95.0% -1,125.82 €180 0 95.5% -1,129.74 €181 0 96.0% -1,133.65 €182 0 96.5% -1,137.54 €183 0 97.0% -1,141.41 €184 0 97.5% -1,145.27 €185 0 98.0% -1,149.11 €186 0 98.5% -1,152.93 €187 0 99.0% -1,156.73 €188 0 99.5% -1,160.52 €189 0 100.0% -1,164.30 €190 0191 0192 0193 0194 0195 0196 0197 0198 0

199 0200 0201 0202 0203 0204 0205 0206 0207 0208 0209 0210 0211 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 0223 0224 0225 0226 0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 0238 0239 0240 0241 0242 0243 0244 0245 0246 0247 0248 0249 0250 0251 0252 0

253 0254 0255 0256 0257 0258 0259 1000260 0261 0262 0263 0264 0265 0266 0267 0268 0269 0270 0271 0272 0273 0274 0275 0276 0277 0278 0279 0280 0281 0282 0283 0284 0285 0286 0287 0288 0289 0290 0291 0292 0293 0294 0295 0296 0297 0298 0299 0300 0301 0302 0303 0304 0305 0306 0

307 0308 0309 0310 0311 0312 0313 0314 0315 0316 0317 0318 0319 0320 0321 0322 0323 0324 0325 0326 0327 0328 0329 0330 0331 0332 0333 0334 0335 0336 0337 0338 0339 0340 0341 0342 0343 0344 0345 0346 0347 0348 0349 0350 0351 0352 0353 0354 0355 0356 0357 0358 0359 0360 0

361 0362 0363 0364 0365 0366 0367 0368 0369 0370 0371 0372 0373 0374 0375 0376 0377 0378 0379 0380 0381 0382 0383 0384 0385 0386 0387 0388 0389 0390 0391 0392 0393 0394 0395 0396 0397 0398 0399 0400 0401 0402 0403 0404 0405 0406 0407 0408 0409 0410 0411 0412 0413 0414 0

415 0416 0417 0418 0419 0420 0421 0422 0423 0424 0425 0426 0427 0428 0429 0430 0431 0432 0433 0434 900

TIR NO PERIÓDICA

efectivo anual

efectivo anual

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

(€1,400.00)

(€1,200.00)

(€1,000.00)

(€800.00)

(€600.00)

(€400.00)

(€200.00)

€0.00

€200.00

€400.00 VAN

La fórmula TIR.NO.PER siempre da la TIR anual.

Es necesario poner una estimación muy pequeña pq sino da error.

La fórmula TIR dará una TIR mensual si los periodos son meses, dará una TIR diaria si lo periodos son días, o dará una TIR anual si los periodos son años.

TIRmultiple.xls

TIR MULTIPLETIR 1 1.537%TIR 2 16.788%

Año Flujo Caja Tasa VAN TIR 3 26.000%0 -365 0.0% 35.00 €1 200 0.5% 21.29 €2 200 1.0% 9.93 €3 200 1.5% 0.61 €4 200 2.0% -6.94 €5 200 2.5% -12.97 €6 -200 3.0% -17.69 €7 -200 3.5% -21.27 €8 -200 4.0% -23.90 €9 -200 4.5% -25.70 €

10 -200 5.0% -26.80 €11 0 5.5% -27.32 €12 0 6.0% -27.35 €13 0 6.5% -26.98 €14 0 7.0% -26.27 €15 0 7.5% -25.30 €16 0 8.0% -24.11 €17 0 8.5% -22.77 €18 0 9.0% -21.30 €19 0 9.5% -19.75 €20 400 10.0% -18.14 €

10.5% -16.51 €11.0% -14.87 €11.5% -13.25 €12.0% -11.67 €12.5% -10.13 €13.0% -8.64 €13.5% -7.23 €14.0% -5.89 €14.5% -4.63 €15.0% -3.45 €15.5% -2.37 €16.0% -1.37 €16.5% -0.47 €17.0% 0.33 €17.5% 1.04 €18.0% 1.65 €18.5% 2.17 €19.0% 2.60 €19.5% 2.94 €20.0% 3.18 €20.5% 3.34 €21.0% 3.42 €21.5% 3.41 €22.0% 3.32 €22.5% 3.15 €23.0% 2.90 €

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

(€200.00)

(€150.00)

(€100.00)

(€50.00)

€0.00

€50.00 VAN

23.5% 2.59 €24.0% 2.20 €24.5% 1.74 €25.0% 1.22 €25.5% 0.64 €26.0% -0.00 €26.5% -0.70 €27.0% -1.45 €27.5% -2.26 €28.0% -3.11 €28.5% -4.01 €29.0% -4.96 €29.5% -5.95 €30.0% -6.98 €30.5% -8.04 €31.0% -9.14 €31.5% -10.28 €32.0% -11.45 €32.5% -12.65 €33.0% -13.88 €33.5% -15.13 €34.0% -16.41 €34.5% -17.71 €35.0% -19.03 €35.5% -20.38 €36.0% -21.74 €36.5% -23.12 €37.0% -24.52 €37.5% -25.93 €38.0% -27.36 €38.5% -28.79 €39.0% -30.24 €39.5% -31.70 €40.0% -33.17 €40.5% -34.65 €41.0% -36.13 €41.5% -37.62 €42.0% -39.12 €42.5% -40.62 €43.0% -42.13 €43.5% -43.64 €44.0% -45.15 €44.5% -46.66 €45.0% -48.18 €45.5% -49.70 €46.0% -51.21 €46.5% -52.73 €47.0% -54.24 €47.5% -55.76 €48.0% -57.27 €48.5% -58.78 €49.0% -60.29 €49.5% -61.79 €50.0% -63.29 €

50.5% -64.79 €51.0% -66.28 €51.5% -67.77 €52.0% -69.26 €52.5% -70.74 €53.0% -72.21 €53.5% -73.68 €54.0% -75.14 €54.5% -76.60 €55.0% -78.05 €55.5% -79.49 €56.0% -80.93 €56.5% -82.36 €57.0% -83.79 €57.5% -85.20 €58.0% -86.61 €58.5% -88.02 €59.0% -89.41 €59.5% -90.80 €60.0% -92.18 €60.5% -93.55 €61.0% -94.92 €61.5% -96.28 €62.0% -97.62 €62.5% -98.97 €63.0% -100.30 €63.5% -101.62 €64.0% -102.94 €64.5% -104.25 €65.0% -105.55 €65.5% -106.84 €66.0% -108.13 €66.5% -109.40 €67.0% -110.67 €67.5% -111.93 €68.0% -113.18 €68.5% -114.43 €69.0% -115.66 €69.5% -116.89 €70.0% -118.10 €70.5% -119.31 €71.0% -120.52 €71.5% -121.71 €72.0% -122.89 €72.5% -124.07 €73.0% -125.24 €73.5% -126.40 €74.0% -127.55 €74.5% -128.70 €75.0% -129.83 €75.5% -130.96 €76.0% -132.08 €76.5% -133.19 €77.0% -134.30 €

77.5% -135.39 €78.0% -136.48 €78.5% -137.56 €79.0% -138.64 €79.5% -139.70 €80.0% -140.76 €80.5% -141.81 €81.0% -142.85 €81.5% -143.88 €82.0% -144.91 €82.5% -145.93 €83.0% -146.94 €83.5% -147.95 €84.0% -148.95 €84.5% -149.94 €85.0% -150.92 €85.5% -151.90 €86.0% -152.86 €86.5% -153.83 €87.0% -154.78 €87.5% -155.73 €88.0% -156.67 €88.5% -157.60 €89.0% -158.53 €89.5% -159.45 €90.0% -160.36 €90.5% -161.27 €91.0% -162.17 €91.5% -163.06 €92.0% -163.95 €92.5% -164.83 €93.0% -165.71 €93.5% -166.58 €94.0% -167.44 €94.5% -168.29 €95.0% -169.14 €95.5% -169.98 €96.0% -170.82 €96.5% -171.65 €97.0% -172.48 €97.5% -173.30 €98.0% -174.11 €98.5% -174.92 €99.0% -175.72 €99.5% -176.51 €

100.0% -177.30 €

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

(€200.00)

(€150.00)

(€100.00)

(€50.00)

€0.00

€50.00 VAN

TIR Multiple (caso de dos tir)Año Flujo Caja Tasa Dto. VAN

0 -1,600 0.00% -1,600.00 €1 10,000 1.00% -1,501.97 €2 -10,000 2.00% -1,407.77 €

3.00% -1,317.22 €4.00% -1,230.18 €5.00% -1,146.49 €6.00% -1,066.00 €7.00% -988.59 €8.00% -914.13 €9.00% -842.49 €

10.00% -773.55 €11.00% -707.22 €12.00% -643.37 €13.00% -581.91 €14.00% -522.75 €15.00% -465.78 €16.00% -410.94 €17.00% -358.13 €18.00% -307.27 €19.00% -258.29 € TIR 1 25%20.00% -211.11 € TIR 2 400%21.00% -165.67 €22.00% -121.90 €23.00% -79.74 €24.00% -39.13 €25.00% 0.00 €26.00% 37.69 €27.00% 74.00 €28.00% 108.98 €29.00% 142.68 €30.00% 175.15 €31.00% 206.42 €32.00% 236.55 €33.00% 265.57 €34.00% 293.52 €35.00% 320.44 €36.00% 346.37 €37.00% 371.34 €38.00% 395.38 €39.00% 418.53 €40.00% 440.82 €41.00% 462.27 €42.00% 482.92 €43.00% 502.79 €44.00% 521.91 €45.00% 540.31 €46.00% 558.00 €47.00% 575.02 €

0.00% 200.00% 400.00% 600.00% 800.00% 1000.00%

(€2,000.00)

(€1,500.00)

(€1,000.00)

(€500.00)

€0.00

€500.00

€1,000.00

€1,500.00

48.00% 591.38 €49.00% 607.11 €50.00% 622.22 €51.00% 636.74 €52.00% 650.69 €53.00% 664.09 €54.00% 676.94 €55.00% 689.28 €56.00% 701.12 €57.00% 712.47 €58.00% 723.35 €59.00% 733.77 €60.00% 743.75 €61.00% 753.30 €62.00% 762.44 €63.00% 771.18 €64.00% 779.54 €65.00% 787.51 €66.00% 795.12 €67.00% 802.38 €68.00% 809.30 €69.00% 815.88 €70.00% 822.15 €71.00% 828.10 €72.00% 833.75 €73.00% 839.11 €74.00% 844.18 €75.00% 848.98 €76.00% 853.51 €77.00% 857.79 €78.00% 861.81 €79.00% 865.59 €80.00% 869.14 €81.00% 872.45 €82.00% 875.55 €83.00% 878.43 €84.00% 881.10 €85.00% 883.56 €86.00% 885.84 €87.00% 887.92 €88.00% 889.81 €89.00% 891.53 €90.00% 893.07 €91.00% 894.45 €92.00% 895.66 €93.00% 896.71 €94.00% 897.61 €95.00% 898.36 €96.00% 898.96 €97.00% 899.42 €98.00% 899.74 €99.00% 899.94 €

100.00% 900.00 €101.00% 899.94 €

102.00% 899.75 €103.00% 899.45 €104.00% 899.04 €105.00% 898.51 €106.00% 897.88 €107.00% 897.14 €108.00% 896.30 €109.00% 895.36 €110.00% 894.33 €111.00% 893.21 €112.00% 891.99 €113.00% 890.69 €114.00% 889.30 €115.00% 887.83 €116.00% 886.28 €117.00% 884.66 €118.00% 882.96 €119.00% 881.18 €120.00% 879.34 €121.00% 877.43 €122.00% 875.45 €123.00% 873.41 €124.00% 871.30 €125.00% 869.14 €126.00% 866.91 €127.00% 864.63 €128.00% 862.30 €129.00% 859.91 €130.00% 857.47 €131.00% 854.98 €132.00% 852.44 €133.00% 849.85 €134.00% 847.22 €135.00% 844.55 €136.00% 841.83 €137.00% 839.07 €138.00% 836.27 €139.00% 833.43 €140.00% 830.56 €141.00% 827.64 €142.00% 824.70 €143.00% 821.72 €144.00% 818.70 €145.00% 815.66 €146.00% 812.59 €147.00% 809.48 €148.00% 806.35 €149.00% 803.19 €150.00% 800.00 €151.00% 796.79 €152.00% 793.55 €153.00% 790.29 €154.00% 787.00 €155.00% 783.70 €

156.00% 780.37 €157.00% 777.02 €158.00% 773.66 €159.00% 770.27 €160.00% 766.86 €161.00% 763.44 €162.00% 760.00 €163.00% 756.55 €164.00% 753.08 €165.00% 749.59 €166.00% 746.09 €167.00% 742.58 €168.00% 739.05 €169.00% 735.51 €170.00% 731.96 €171.00% 728.40 €172.00% 724.83 €173.00% 721.24 €174.00% 717.65 €175.00% 714.05 €176.00% 710.44 €177.00% 706.82 €178.00% 703.19 €179.00% 699.56 €180.00% 695.92 €181.00% 692.27 €182.00% 688.62 €183.00% 684.96 €184.00% 681.29 €185.00% 677.62 €186.00% 673.95 €187.00% 670.27 €188.00% 666.59 €189.00% 662.90 €190.00% 659.22 €191.00% 655.52 €192.00% 651.83 €193.00% 648.13 €194.00% 644.44 €195.00% 640.74 €196.00% 637.03 €197.00% 633.33 €198.00% 629.63 €199.00% 625.93 €200.00% 622.22 €201.00% 618.52 €202.00% 614.82 €203.00% 611.11 €204.00% 607.41 €205.00% 603.71 €206.00% 600.01 €207.00% 596.31 €208.00% 592.61 €209.00% 588.92 €

210.00% 585.22 €211.00% 581.53 €212.00% 577.84 €213.00% 574.16 €214.00% 570.47 €215.00% 566.79 €216.00% 563.11 €217.00% 559.44 €218.00% 555.77 €219.00% 552.10 €220.00% 548.44 €221.00% 544.78 €222.00% 541.12 €223.00% 537.47 €224.00% 533.82 €225.00% 530.18 €226.00% 526.54 €227.00% 522.90 €228.00% 519.27 €229.00% 515.65 €230.00% 512.03 €231.00% 508.41 €232.00% 504.80 €233.00% 501.20 €234.00% 497.60 €235.00% 494.01 €236.00% 490.42 €237.00% 486.84 €238.00% 483.26 €239.00% 479.69 €240.00% 476.12 €241.00% 472.57 €242.00% 469.01 €243.00% 465.47 €244.00% 461.93 €245.00% 458.39 €246.00% 454.86 €247.00% 451.34 €248.00% 447.83 €249.00% 444.32 €250.00% 440.82 €251.00% 437.32 €252.00% 433.83 €253.00% 430.35 €254.00% 426.88 €255.00% 423.41 €256.00% 419.95 €257.00% 416.49 €258.00% 413.05 €259.00% 409.61 €260.00% 406.17 €261.00% 402.75 €262.00% 399.33 €263.00% 395.92 €

264.00% 392.51 €265.00% 389.12 €266.00% 385.73 €267.00% 382.34 €268.00% 378.97 €269.00% 375.60 €270.00% 372.24 €271.00% 368.89 €272.00% 365.55 €273.00% 362.21 €274.00% 358.88 €275.00% 355.56 €276.00% 352.24 €277.00% 348.93 €278.00% 345.63 €279.00% 342.34 €280.00% 339.06 €281.00% 335.78 €282.00% 332.51 €283.00% 329.25 €284.00% 326.00 €285.00% 322.75 €286.00% 319.51 €287.00% 316.28 €288.00% 313.06 €289.00% 309.85 €290.00% 306.64 €291.00% 303.44 €292.00% 300.25 €293.00% 297.07 €294.00% 293.89 €295.00% 290.72 €296.00% 287.56 €297.00% 284.41 €298.00% 281.27 €299.00% 278.13 €300.00% 275.00 €301.00% 271.88 €302.00% 268.77 €303.00% 265.66 €304.00% 262.56 €305.00% 259.47 €306.00% 256.39 €307.00% 253.32 €308.00% 250.25 €309.00% 247.19 €310.00% 244.14 €311.00% 241.10 €312.00% 238.06 €313.00% 235.03 €314.00% 232.01 €315.00% 229.00 €316.00% 226.00 €317.00% 223.00 €

318.00% 220.01 €319.00% 217.03 €320.00% 214.06 €321.00% 211.09 €322.00% 208.14 €323.00% 205.19 €324.00% 202.24 €325.00% 199.31 €326.00% 196.38 €327.00% 193.46 €328.00% 190.55 €329.00% 187.65 €330.00% 184.75 €331.00% 181.86 €332.00% 178.98 €333.00% 176.10 €334.00% 173.24 €335.00% 170.38 €336.00% 167.53 €337.00% 164.68 €338.00% 161.85 €339.00% 159.02 €340.00% 156.20 €341.00% 153.38 €342.00% 150.58 €343.00% 147.78 €344.00% 144.99 €345.00% 142.20 €346.00% 139.43 €347.00% 136.66 €348.00% 133.90 €349.00% 131.14 €350.00% 128.40 €351.00% 125.66 €352.00% 122.92 €353.00% 120.20 €354.00% 117.48 €355.00% 114.77 €356.00% 112.07 €357.00% 109.37 €358.00% 106.68 €359.00% 104.00 €360.00% 101.32 €361.00% 98.66 €362.00% 96.00 €363.00% 93.34 €364.00% 90.70 €365.00% 88.06 €366.00% 85.42 €367.00% 82.80 €368.00% 80.18 €369.00% 77.57 €370.00% 74.97 €371.00% 72.37 €

372.00% 69.78 €373.00% 67.20 €374.00% 64.62 €375.00% 62.05 €376.00% 59.49 €377.00% 56.93 €378.00% 54.38 €379.00% 51.84 €380.00% 49.31 €381.00% 46.78 €382.00% 44.26 €383.00% 41.74 €384.00% 39.23 €385.00% 36.73 €386.00% 34.24 €387.00% 31.75 €388.00% 29.27 €389.00% 26.79 €390.00% 24.32 €391.00% 21.86 €392.00% 19.41 €393.00% 16.96 €394.00% 14.52 €395.00% 12.08 €396.00% 9.65 €397.00% 7.23 €398.00% 4.81 €399.00% 2.40 €400.00% 0.00 €401.00% -2.40 €402.00% -4.79 €403.00% -7.17 €404.00% -9.55 €405.00% -11.92 €406.00% -14.29 €407.00% -16.64 €408.00% -19.00 €409.00% -21.34 €410.00% -23.68 €411.00% -26.02 €412.00% -28.34 €413.00% -30.67 €414.00% -32.98 €415.00% -35.29 €416.00% -37.59 €417.00% -39.89 €418.00% -42.18 €419.00% -44.47 €420.00% -46.75 €421.00% -49.02 €422.00% -51.29 €423.00% -53.55 €424.00% -55.80 €425.00% -58.05 €

426.00% -60.29 €427.00% -62.53 €428.00% -64.76 €429.00% -66.99 €430.00% -69.21 €431.00% -71.42 €432.00% -73.63 €433.00% -75.83 €434.00% -78.03 €435.00% -80.22 €436.00% -82.40 €437.00% -84.58 €438.00% -86.75 €439.00% -88.92 €440.00% -91.08 €441.00% -93.24 €442.00% -95.39 €443.00% -97.54 €444.00% -99.68 €445.00% -101.81 €446.00% -103.94 €447.00% -106.06 €448.00% -108.18 €449.00% -110.29 €450.00% -112.40 €451.00% -114.50 €452.00% -116.59 €453.00% -118.68 €454.00% -120.77 €455.00% -122.85 €456.00% -124.92 €457.00% -126.99 €458.00% -129.05 €459.00% -131.11 €460.00% -133.16 €461.00% -135.21 €462.00% -137.25 €463.00% -139.29 €464.00% -141.32 €465.00% -143.35 €466.00% -145.37 €467.00% -147.38 €468.00% -149.39 €469.00% -151.40 €470.00% -153.40 €471.00% -155.40 €472.00% -157.39 €473.00% -159.37 €474.00% -161.35 €475.00% -163.33 €476.00% -165.30 €477.00% -167.26 €478.00% -169.22 €479.00% -171.18 €

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534.00% -271.50 €535.00% -273.20 €536.00% -274.89 €537.00% -276.59 €538.00% -278.28 €539.00% -279.96 €540.00% -281.64 €541.00% -283.32 €542.00% -284.99 €543.00% -286.66 €544.00% -288.32 €545.00% -289.98 €546.00% -291.64 €547.00% -293.29 €548.00% -294.94 €549.00% -296.58 €550.00% -298.22 €551.00% -299.86 €552.00% -301.49 €553.00% -303.12 €554.00% -304.75 €555.00% -306.37 €556.00% -307.99 €557.00% -309.60 €558.00% -311.21 €559.00% -312.81 €560.00% -314.42 €561.00% -316.02 €562.00% -317.61 €563.00% -319.20 €564.00% -320.79 €565.00% -322.37 €566.00% -323.95 €567.00% -325.52 €568.00% -327.10 €569.00% -328.66 €570.00% -330.23 €571.00% -331.79 €572.00% -333.35 €573.00% -334.90 €574.00% -336.45 €575.00% -338.00 €576.00% -339.54 €577.00% -341.08 €578.00% -342.61 €579.00% -344.15 €580.00% -345.67 €581.00% -347.20 €582.00% -348.72 €583.00% -350.24 €584.00% -351.75 €585.00% -353.26 €586.00% -354.77 €587.00% -356.27 €

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696.00% -501.54 €697.00% -502.72 €698.00% -503.90 €699.00% -505.08 €700.00% -506.25 €701.00% -507.42 €702.00% -508.59 €703.00% -509.75 €704.00% -510.92 €705.00% -512.08 €706.00% -513.24 €707.00% -514.39 €708.00% -515.55 €709.00% -516.70 €710.00% -517.85 €711.00% -518.99 €712.00% -520.14 €713.00% -521.28 €714.00% -522.42 €715.00% -523.56 €716.00% -524.69 €717.00% -525.82 €718.00% -526.96 €719.00% -528.08 €720.00% -529.21 €721.00% -530.33 €722.00% -531.45 €723.00% -532.57 €724.00% -533.69 €725.00% -534.80 €726.00% -535.91 €727.00% -537.02 €728.00% -538.13 €729.00% -539.24 €730.00% -540.34 €731.00% -541.44 €732.00% -542.54 €733.00% -543.64 €734.00% -544.73 €735.00% -545.82 €736.00% -546.91 €737.00% -548.00 €738.00% -549.08 €739.00% -550.17 €740.00% -551.25 €741.00% -552.33 €742.00% -553.40 €743.00% -554.48 €744.00% -555.55 €745.00% -556.62 €746.00% -557.69 €747.00% -558.75 €748.00% -559.82 €749.00% -560.88 €

750.00% -561.94 €751.00% -563.00 €752.00% -564.05 €753.00% -565.10 €754.00% -566.15 €755.00% -567.20 €756.00% -568.25 €757.00% -569.30 €758.00% -570.34 €759.00% -571.38 €760.00% -572.42 €761.00% -573.45 €762.00% -574.49 €763.00% -575.52 €764.00% -576.55 €765.00% -577.58 €766.00% -578.61 €767.00% -579.63 €768.00% -580.65 €769.00% -581.67 €770.00% -582.69 €771.00% -583.71 €772.00% -584.72 €773.00% -585.74 €774.00% -586.75 €775.00% -587.76 €776.00% -588.76 €777.00% -589.77 €778.00% -590.77 €779.00% -591.77 €780.00% -592.77 €781.00% -593.77 €782.00% -594.76 €783.00% -595.75 €784.00% -596.74 €785.00% -597.73 €786.00% -598.72 €787.00% -599.71 €788.00% -600.69 €789.00% -601.67 €790.00% -602.65 €791.00% -603.63 €792.00% -604.60 €793.00% -605.58 €794.00% -606.55 €795.00% -607.52 €796.00% -608.49 €797.00% -609.46 €798.00% -610.42 €799.00% -611.38 €800.00% -612.35 €801.00% -613.30 €802.00% -614.26 €803.00% -615.22 €

804.00% -616.17 €805.00% -617.12 €806.00% -618.07 €807.00% -619.02 €808.00% -619.97 €809.00% -620.91 €810.00% -621.86 €811.00% -622.80 €812.00% -623.74 €813.00% -624.68 €814.00% -625.61 €815.00% -626.55 €816.00% -627.48 €817.00% -628.41 €818.00% -629.34 €819.00% -630.27 €820.00% -631.19 €821.00% -632.11 €822.00% -633.04 €823.00% -633.96 €824.00% -634.88 €825.00% -635.79 €826.00% -636.71 €827.00% -637.62 €828.00% -638.53 €829.00% -639.44 €830.00% -640.35 €831.00% -641.26 €832.00% -642.16 €833.00% -643.07 €834.00% -643.97 €835.00% -644.87 €836.00% -645.77 €837.00% -646.66 €838.00% -647.56 €839.00% -648.45 €840.00% -649.34 €841.00% -650.23 €842.00% -651.12 €843.00% -652.01 €844.00% -652.89 €845.00% -653.78 €846.00% -654.66 €847.00% -655.54 €848.00% -656.42 €849.00% -657.30 €850.00% -658.17 €851.00% -659.05 €852.00% -659.92 €853.00% -660.79 €854.00% -661.66 €855.00% -662.53 €856.00% -663.39 €857.00% -664.26 €

858.00% -665.12 €859.00% -665.98 €860.00% -666.84 €861.00% -667.70 €862.00% -668.56 €863.00% -669.41 €864.00% -670.26 €865.00% -671.12 €866.00% -671.97 €867.00% -672.82 €868.00% -673.66 €869.00% -674.51 €870.00% -675.35 €871.00% -676.20 €872.00% -677.04 €873.00% -677.88 €874.00% -678.72 €875.00% -679.55 €876.00% -680.39 €877.00% -681.22 €878.00% -682.05 €879.00% -682.89 €880.00% -683.72 €881.00% -684.54 €882.00% -685.37 €883.00% -686.19 €884.00% -687.02 €885.00% -687.84 €886.00% -688.66 €887.00% -689.48 €888.00% -690.30 €889.00% -691.11 €890.00% -691.93 €891.00% -692.74 €892.00% -693.55 €893.00% -694.37 €894.00% -695.17 €895.00% -695.98 €896.00% -696.79 €897.00% -697.59 €898.00% -698.40 €899.00% -699.20 €900.00% -700.00 €901.00% -700.80 €902.00% -701.60 €903.00% -702.39 €904.00% -703.19 €905.00% -703.98 €906.00% -704.77 €907.00% -705.57 €908.00% -706.36 €909.00% -707.14 €910.00% -707.93 €911.00% -708.72 €

912.00% -709.50 €913.00% -710.28 €914.00% -711.06 €915.00% -711.84 €916.00% -712.62 €917.00% -713.40 €918.00% -714.18 €919.00% -714.95 €920.00% -715.72 €921.00% -716.50 €922.00% -717.27 €923.00% -718.04 €924.00% -718.80 €925.00% -719.57 €926.00% -720.34 €927.00% -721.10 €928.00% -721.86 €929.00% -722.63 €930.00% -723.39 €931.00% -724.14 €932.00% -724.90 €933.00% -725.66 €934.00% -726.41 €935.00% -727.17 €936.00% -727.92 €937.00% -728.67 €938.00% -729.42 €939.00% -730.17 €940.00% -730.92 €941.00% -731.66 €942.00% -732.41 €943.00% -733.15 €944.00% -733.89 €945.00% -734.64 €946.00% -735.38 €947.00% -736.11 €948.00% -736.85 €949.00% -737.59 €950.00% -738.32 €951.00% -739.06 €952.00% -739.79 €953.00% -740.52 €954.00% -741.25 €955.00% -741.98 €956.00% -742.71 €957.00% -743.43 €958.00% -744.16 €959.00% -744.88 €960.00% -745.60 €961.00% -746.32 €962.00% -747.05 €963.00% -747.76 €964.00% -748.48 €965.00% -749.20 €

966.00% -749.91 €967.00% -750.63 €968.00% -751.34 €969.00% -752.05 €970.00% -752.76 €971.00% -753.47 €972.00% -754.18 €973.00% -754.89 €974.00% -755.60 €975.00% -756.30 €976.00% -757.00 €977.00% -757.71 €978.00% -758.41 €979.00% -759.11 €980.00% -759.81 €981.00% -760.51 €982.00% -761.20 €983.00% -761.90 €984.00% -762.59 €985.00% -763.29 €986.00% -763.98 €987.00% -764.67 €988.00% -765.36 €989.00% -766.05 €990.00% -766.74 €991.00% -767.42 €992.00% -768.11 €993.00% -768.79 €994.00% -769.48 €995.00% -770.16 €996.00% -770.84 €997.00% -771.52 €998.00% -772.20 €999.00% -772.88 €

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€0.00

€500.00

€1,000.00

€1,500.00

Otro Caso de TIR Múltiple

Año Flujo Caja0 -171 202 203 154 -40

TIR 1 4.35%TIR 2 69.45%

TIR MODIFICADA TIR 1 1.88%TIR 2 9.61% Tasa Descuento GastosTIR 3 40.13% Tasa Capitalización Ingresos

Año Flujo Caja Tasa VAN Año Q+ Q - TIR Modificada0 -15,000 € 0.0% 1,489.00 € 0 0 € -15,000 €1 10,229 € 0.5% 967.74 € 1 10,229 € 0 €2 9,609 € 1.0% 544.55 € 2 9,609 € 0 € Valor Actual Gastos3 15,004 € 1.5% 206.06 € 3 15,004 € 0 € Valor Final Ingresos4 3,774 € 2.0% -59.46 € 4 3,774 € 0 €5 -9,709 € 2.5% -262.31 € 5 0 € -9,709 € TIR Modificada6 -18,097 € 3.0% -411.53 € 6 0 € -18,097 €7 4,217 € 3.5% -515.02 € 7 4,217 € 0 €8 18,298 € 4.0% -579.73 € 8 18,298 € 0 €9 -12,041 € 4.5% -611.72 € 9 0 € -12,041 €

10 -10 € 5.0% -616.30 € 10 0 € -10 €11 -7,500 € 5.5% -598.10 € 11 0 € -7,500 €12 -11,855 € 6.0% -561.15 € 12 0 € -11,855 €13 -12,070 € 6.5% -508.97 € 13 0 € -12,070 €14 -6,349 € 7.0% -444.61 € 14 0 € -6,349 €15 13,570 € 7.5% -370.72 € 15 13,570 € 0 €16 377 € 8.0% -289.60 € 16 377 € 0 €17 -10,068 € 8.5% -203.22 € 17 0 € -10,068 €18 16,642 € 9.0% -113.28 € 18 16,642 € 0 €19 1,609 € 9.5% -21.24 € 19 1,609 € 0 €20 10,859 € 10.0% 71.65 € 20 10,859 € 0 €

10.5% 164.33 €11.0% 255.91 €11.5% 345.63 €12.0% 432.88 €12.5% 517.12 €13.0% 597.95 €13.5% 675.02 €14.0% 748.07 €14.5% 816.89 €15.0% 881.34 €15.5% 941.32 €16.0% 996.76 €16.5% 1,047.65 €17.0% 1,093.97 €17.5% 1,135.77 €18.0% 1,173.08 €18.5% 1,205.99 €19.0% 1,234.56 €19.5% 1,258.90 €20.0% 1,279.10 €20.5% 1,295.28 €21.0% 1,307.55 €21.5% 1,316.05 €22.0% 1,320.88 €22.5% 1,322.19 €23.0% 1,320.10 €

0.0% 20.0% 40.0% 60.0% 80.0% 100.0% 120.0% 140.0% 160.0% 180.0% 200.0%

-12,000

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000 VAN

Lo que cambia entre las tres TIR es la estimación.

23.5% 1,314.73 €24.0% 1,306.22 €24.5% 1,294.69 €25.0% 1,280.28 €25.5% 1,263.10 €26.0% 1,243.27 €26.5% 1,220.92 €27.0% 1,196.16 €27.5% 1,169.11 €28.0% 1,139.88 €28.5% 1,108.57 €29.0% 1,075.28 €29.5% 1,040.13 €30.0% 1,003.20 €30.5% 964.60 €31.0% 924.40 €31.5% 882.71 €32.0% 839.60 €32.5% 795.15 €33.0% 749.45 €33.5% 702.57 €34.0% 654.57 €34.5% 605.54 €35.0% 555.53 €35.5% 504.60 €36.0% 452.83 €36.5% 400.27 €37.0% 346.96 €37.5% 292.97 €38.0% 238.35 €38.5% 183.15 €39.0% 127.40 €39.5% 71.17 €40.0% 14.48 €40.5% -42.62 €41.0% -100.10 €41.5% -157.91 €42.0% -216.02 €42.5% -274.41 €43.0% -333.02 €43.5% -391.85 €44.0% -450.85 €44.5% -510.01 €45.0% -569.28 €45.5% -628.66 €46.0% -688.12 €46.5% -747.63 €47.0% -807.17 €47.5% -866.73 €48.0% -926.28 €48.5% -985.80 €49.0% -1,045.29 €49.5% -1,104.71 €50.0% -1,164.07 €

50.5% -1,223.34 €51.0% -1,282.50 €51.5% -1,341.55 €52.0% -1,400.48 €52.5% -1,459.27 €53.0% -1,517.91 €53.5% -1,576.38 €54.0% -1,634.69 €54.5% -1,692.82 €55.0% -1,750.77 €55.5% -1,808.52 €56.0% -1,866.06 €56.5% -1,923.40 €57.0% -1,980.52 €57.5% -2,037.41 €58.0% -2,094.08 €58.5% -2,150.51 €59.0% -2,206.70 €59.5% -2,262.64 €60.0% -2,318.34 €60.5% -2,373.78 €61.0% -2,428.97 €61.5% -2,483.89 €62.0% -2,538.55 €62.5% -2,592.94 €63.0% -2,647.07 €63.5% -2,700.92 €64.0% -2,754.49 €64.5% -2,807.79 €65.0% -2,860.81 €65.5% -2,913.54 €66.0% -2,966.00 €66.5% -3,018.17 €67.0% -3,070.06 €67.5% -3,121.66 €68.0% -3,172.97 €68.5% -3,224.00 €69.0% -3,274.74 €69.5% -3,325.19 €70.0% -3,375.35 €70.5% -3,425.22 €71.0% -3,474.81 €71.5% -3,524.10 €72.0% -3,573.10 €72.5% -3,621.82 €73.0% -3,670.25 €73.5% -3,718.39 €74.0% -3,766.24 €74.5% -3,813.80 €75.0% -3,861.08 €75.5% -3,908.07 €76.0% -3,954.78 €76.5% -4,001.20 €77.0% -4,047.34 €

77.5% -4,093.19 €78.0% -4,138.77 €78.5% -4,184.06 €79.0% -4,229.07 €79.5% -4,273.81 €80.0% -4,318.26 €80.5% -4,362.45 €81.0% -4,406.35 €81.5% -4,449.99 €82.0% -4,493.35 €82.5% -4,536.43 €83.0% -4,579.25 €83.5% -4,621.80 €84.0% -4,664.09 €84.5% -4,706.11 €85.0% -4,747.86 €85.5% -4,789.35 €86.0% -4,830.58 €86.5% -4,871.55 €87.0% -4,912.26 €87.5% -4,952.72 €88.0% -4,992.92 €88.5% -5,032.86 €89.0% -5,072.55 €89.5% -5,112.00 €90.0% -5,151.19 €90.5% -5,190.13 €91.0% -5,228.83 €91.5% -5,267.29 €92.0% -5,305.50 €92.5% -5,343.47 €93.0% -5,381.20 €93.5% -5,418.70 €94.0% -5,455.95 €94.5% -5,492.97 €95.0% -5,529.76 €95.5% -5,566.32 €96.0% -5,602.64 €96.5% -5,638.74 €97.0% -5,674.61 €97.5% -5,710.25 €98.0% -5,745.68 €98.5% -5,780.87 €99.0% -5,815.85 €99.5% -5,850.61 €

100.0% -5,885.15 €100.5% -5,919.47 €101.0% -5,953.58 €101.5% -5,987.48 €102.0% -6,021.17 €102.5% -6,054.64 €103.0% -6,087.91 €103.5% -6,120.97 €104.0% -6,153.82 €

104.5% -6,186.47 €105.0% -6,218.92 €105.5% -6,251.17 €106.0% -6,283.21 €106.5% -6,315.06 €107.0% -6,346.72 €107.5% -6,378.18 €108.0% -6,409.44 €108.5% -6,440.51 €109.0% -6,471.39 €109.5% -6,502.08 €110.0% -6,532.59 €110.5% -6,562.91 €111.0% -6,593.04 €111.5% -6,622.99 €112.0% -6,652.75 €112.5% -6,682.34 €113.0% -6,711.74 €113.5% -6,740.97 €114.0% -6,770.02 €114.5% -6,798.90 €115.0% -6,827.60 €115.5% -6,856.12 €116.0% -6,884.48 €116.5% -6,912.66 €117.0% -6,940.68 €117.5% -6,968.53 €118.0% -6,996.21 €118.5% -7,023.73 €119.0% -7,051.08 €119.5% -7,078.27 €120.0% -7,105.30 €120.5% -7,132.16 €121.0% -7,158.87 €121.5% -7,185.42 €122.0% -7,211.82 €122.5% -7,238.05 €123.0% -7,264.14 €123.5% -7,290.07 €124.0% -7,315.85 €124.5% -7,341.47 €125.0% -7,366.95 €125.5% -7,392.28 €126.0% -7,417.46 €126.5% -7,442.50 €127.0% -7,467.39 €127.5% -7,492.13 €128.0% -7,516.73 €128.5% -7,541.19 €129.0% -7,565.51 €129.5% -7,589.69 €130.0% -7,613.73 €130.5% -7,637.63 €131.0% -7,661.40 €

131.5% -7,685.03 €132.0% -7,708.52 €132.5% -7,731.88 €133.0% -7,755.11 €133.5% -7,778.21 €134.0% -7,801.17 €134.5% -7,824.01 €135.0% -7,846.72 €135.5% -7,869.30 €136.0% -7,891.75 €136.5% -7,914.08 €137.0% -7,936.28 €137.5% -7,958.35 €138.0% -7,980.31 €138.5% -8,002.14 €139.0% -8,023.85 €139.5% -8,045.44 €140.0% -8,066.91 €140.5% -8,088.26 €141.0% -8,109.49 €141.5% -8,130.61 €142.0% -8,151.61 €142.5% -8,172.49 €143.0% -8,193.26 €143.5% -8,213.92 €144.0% -8,234.46 €144.5% -8,254.90 €145.0% -8,275.22 €145.5% -8,295.43 €146.0% -8,315.53 €146.5% -8,335.52 €147.0% -8,355.41 €147.5% -8,375.18 €148.0% -8,394.85 €148.5% -8,414.42 €149.0% -8,433.88 €149.5% -8,453.24 €150.0% -8,472.49 €150.5% -8,491.64 €151.0% -8,510.69 €151.5% -8,529.64 €152.0% -8,548.48 €152.5% -8,567.23 €153.0% -8,585.88 €153.5% -8,604.43 €154.0% -8,622.88 €154.5% -8,641.24 €155.0% -8,659.50 €155.5% -8,677.66 €156.0% -8,695.73 €156.5% -8,713.71 €157.0% -8,731.59 €157.5% -8,749.38 €158.0% -8,767.07 €

158.5% -8,784.68 €159.0% -8,802.19 €159.5% -8,819.62 €160.0% -8,836.95 €160.5% -8,854.20 €161.0% -8,871.36 €161.5% -8,888.43 €162.0% -8,905.41 €162.5% -8,922.30 €163.0% -8,939.11 €163.5% -8,955.84 €164.0% -8,972.48 €164.5% -8,989.04 €165.0% -9,005.51 €165.5% -9,021.90 €166.0% -9,038.21 €166.5% -9,054.43 €167.0% -9,070.58 €167.5% -9,086.64 €168.0% -9,102.62 €168.5% -9,118.53 €169.0% -9,134.35 €169.5% -9,150.10 €170.0% -9,165.77 €170.5% -9,181.36 €171.0% -9,196.87 €171.5% -9,212.31 €172.0% -9,227.67 €172.5% -9,242.96 €173.0% -9,258.17 €173.5% -9,273.31 €174.0% -9,288.37 €174.5% -9,303.36 €175.0% -9,318.28 €175.5% -9,333.13 €176.0% -9,347.90 €176.5% -9,362.60 €177.0% -9,377.23 €177.5% -9,391.79 €178.0% -9,406.28 €178.5% -9,420.70 €179.0% -9,435.06 €179.5% -9,449.34 €180.0% -9,463.56 €180.5% -9,477.70 €181.0% -9,491.78 €181.5% -9,505.80 €182.0% -9,519.75 €182.5% -9,533.63 €183.0% -9,547.44 €183.5% -9,561.19 €184.0% -9,574.88 €184.5% -9,588.50 €185.0% -9,602.06 €

185.5% -9,615.56 €186.0% -9,628.99 €186.5% -9,642.36 €187.0% -9,655.67 €187.5% -9,668.91 €188.0% -9,682.10 €188.5% -9,695.22 €189.0% -9,708.28 €189.5% -9,721.29 €190.0% -9,734.23 €190.5% -9,747.11 €191.0% -9,759.94 €191.5% -9,772.71 €192.0% -9,785.41 €192.5% -9,798.06 €193.0% -9,810.66 €193.5% -9,823.19 €194.0% -9,835.67 €194.5% -9,848.09 €195.0% -9,860.46 €195.5% -9,872.77 €196.0% -9,885.03 €196.5% -9,897.23 €197.0% -9,909.37 €197.5% -9,921.46 €198.0% -9,933.50 €198.5% -9,945.48 €199.0% -9,957.41 €199.5% -9,969.29 €200.0% -9,981.12 €

Tasa Descuento Gastos 8%Tasa Capitalización Ingresos 10%

TIR Modificada 9.3498%

Valor Actual Gastos 56,285.27 €Valor Final Ingresos 336,321.08 €

TIR Modificada 9.3498%

0.0% 20.0% 40.0% 60.0% 80.0% 100.0% 120.0% 140.0% 160.0% 180.0% 200.0%

-12,000

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000 VAN

Lo que cambia entre las tres TIR es la estimación.

Tir Modificada calculada con TIRM

Tir Modificada calculada acudiendo al concepto

0.0% 20.0% 40.0% 60.0% 80.0% 100.0% 120.0% 140.0% 160.0% 180.0% 200.0%

-12,000

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000 VAN

TIRmodificada

TIR MODIFICADA

Año Flujo Caja0 -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 €

Intersección de FisherYear Project A Project B Difference k NPV(A) NPV(B)0 -1000 -1000 0 0.00% 300.00 € 400.00 €1 500 100 -400 0.50% 287.11 € 378.73 €2 400 300 -100 1.00% 274.44 € 357.92 €3 300 400 100 1.50% 261.99 € 337.56 €4 100 600 500 2.00% 249.74 € 317.63 €

2.50% 237.71 € 298.12 €IRR 14.49% 11.79% 7.17% 3.00% 225.87 € 279.02 €

3.50% 214.22 € 260.31 €4.00% 202.77 € 242.00 €4.50% 191.51 € 224.07 €5.00% 180.42 € 206.50 €5.50% 169.52 € 189.30 €6.00% 158.79 € 172.44 €6.50% 148.23 € 155.93 €7.00% 137.84 € 139.75 €7.50% 127.62 € 123.89 €8.00% 117.55 € 108.35 €8.50% 107.64 € 93.11 €9.00% 97.89 € 78.18 €9.50% 88.28 € 63.53 €

10.00% 78.82 € 49.18 €10.50% 69.50 € 35.10 €11.00% 60.33 € 21.29 €11.50% 51.29 € 7.75 €12.00% 42.39 € -5.53 €12.50% 33.62 € -18.56 €13.00% 24.98 € -31.35 €13.50% 16.47 € -43.89 €14.00% 8.08 € -56.20 €14.50% -0.18 € -68.28 €15.00% -8.33 € -80.14 €15.50% -16.36 € -91.78 €16.00% -24.27 € -103.21 €16.50% -32.08 € -114.42 €17.00% -39.77 € -125.44 €17.50% -47.35 € -136.25 €18.00% -54.83 € -146.87 €18.50% -62.20 € -157.30 €19.00% -69.47 € -167.55 €19.50% -76.65 € -177.61 €20.00% -83.72 € -187.50 €20.50% -90.70 € -197.21 €21.00% -97.58 € -206.76 €21.50% -104.37 € -216.14 €22.00% -111.07 € -225.35 €22.50% -117.68 € -234.41 €23.00% -124.20 € -243.31 €

23.50% -130.63 € -252.06 €24.00% -136.98 € -260.67 €24.50% -143.25 € -269.12 €25.00% -149.44 € -277.44 €25.50% -155.55 € -285.62 €26.00% -161.58 € -293.66 €26.50% -167.53 € -301.57 €27.00% -173.40 € -309.34 €27.50% -179.20 € -316.99 €28.00% -184.93 € -324.52 €28.50% -190.59 € -331.92 €29.00% -196.17 € -339.20 €29.50% -201.69 € -346.37 €30.00% -207.14 € -353.42 €30.50% -212.52 € -360.36 €31.00% -217.83 € -367.19 €31.50% -223.08 € -373.91 €32.00% -228.27 € -380.52 €32.50% -233.39 € -387.03 €33.00% -238.46 € -393.44 €33.50% -243.46 € -399.75 €34.00% -248.40 € -405.96 €34.50% -253.28 € -412.08 €35.00% -258.11 € -418.10 €35.50% -262.88 € -424.03 €36.00% -267.60 € -429.87 €36.50% -272.26 € -435.62 €37.00% -276.86 € -441.29 €37.50% -281.42 € -446.87 €38.00% -285.92 € -452.37 €38.50% -290.37 € -457.78 €39.00% -294.77 € -463.12 €39.50% -299.11 € -468.37 €40.00% -303.42 € -473.55 €40.50% -307.67 € -478.66 €41.00% -311.87 € -483.69 €41.50% -316.03 € -488.64 €42.00% -320.14 € -493.53 €42.50% -324.21 € -498.34 €43.00% -328.23 € -503.09 €43.50% -332.21 € -507.77 €44.00% -336.15 € -512.38 €44.50% -340.04 € -516.93 €45.00% -343.90 € -521.41 €45.50% -347.71 € -525.83 €46.00% -351.48 € -530.19 €46.50% -355.21 € -534.49 €47.00% -358.90 € -538.72 €47.50% -362.55 € -542.90 €48.00% -366.16 € -547.03 €48.50% -369.74 € -551.09 €49.00% -373.28 € -555.10 €49.50% -376.78 € -559.06 €50.00% -380.25 € -562.96 €

0% 10% 20% 30% 40% 50%

(€800.00)

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(€200.00)

€0.00

€200.00

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€600.00

El VAN de dos proyectos se cruza

NPV(A)

Tasa de descuento

FisherIntersec-tion

0% 10% 20% 30% 40% 50%

(€800.00)

(€600.00)

(€400.00)

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€0.00

€200.00

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El VAN de dos proyectos se cruza

NPV(A)

Tasa de descuento

FisherIntersec-tion

Determinar la Intersección de Fisher

Year Project A Project B0 -1200 -12001 1000 1002 500 6003 100 1080