El valor temporal del dinero - Universidad Complutense de Madrid

Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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o*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
Curiosidad:
En 1700 AC, cuando en el reino de Babilonia reinaba Hammurabi, se escribió en
una tableta de arcilla el que puede ser el problema más antiguo de cálculo financiero. Se
trata de calcular cuánto tiempo tarda una mina de plata, que se invierte al 20% de interés
anual, en alcanzar el valor de 64 minas. El cálculo de interés compuesto debe hacerse en
una forma extraña (20% del principal se acumula –interés simple- hasta que el interés es
igual al principal, momento en el que se añade al propio principal –interés compuesto-), la
respuesta al problema es 30 años, en lugar de 22,81 años. Su solución requiere conocer el
¡cálculo logarítmico! (y todo esto escrito en sistema cuneiforme).
*
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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33*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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3W*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
!'1%(*",*"%5%'#1)*%/*(#"%&,*(0&)"1%*/,'*.&6B#-,'*5#"5,*)H,'A*)'>*70%*'#*)5%.1)*&%5#?#&*/)*
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3R*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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3G*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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3S*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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3j*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Caso real:
El manuscrito en el que Einstein escribió su famosa teoría que relacionaba la masa y la
2
energía (E=mc ) fue adquirido en 1987 por 1,2 millones de euros. Su propietario lo puso a la venta mediante una subasta pública en 1996 pidiendo un mínimo de 4 millones, la mejor oferta sólo llegó a 3,3 millones de euros. ¿Qué rentabilidad anual hubiera obtenido de haberlo vendido por los cuatro millones de
euros? Y ¿cuál hubiera obtenido de vendérselo al mejor postor?
1er caso ! 1.200.000 x (1 + k)(1996-1987) = 4.000.000 ! k = 14,31% anual
2º caso ! 1.200.000 x (1 + k)(1996-1987) = 3.300.000 ! k = 11,90% anual
3o*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
9. Cap ital ización semestral, trimestral, etc.
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Caso real:
j;G3FA3n*Y*
En una operación de compra de una empresa –omitiré su nombre por razones de privaci-
dad- el comprador y el vendedor llegaron a un acuerdo por el que las acciones de éste último pasaban a
poder de aquél a cambio de un precio global de 130 millones de euros. Ambas partes acuerdan que el pago se realice en varias fechas:
- En el momento inicial: 70,3 millones de euros
- 6 meses después: 9,5 millones de euros
- 18 meses después: 20,4 millones de euros
3n*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
- 30 meses después: 29,8 millones de euros
Como observará si suma las cuatro cantidades el valor total es de 130 millones de euros, lo que quiere
decir que en el contrato no se tuvo en cuenta el valor temporal del dinero. Por tanto, queremos saber
cuál es el dinero realmente pagado por el comprador sabiendo que el tipo de interés utilizado fue del 8%
nominal anual que equivale a un 4% semestral.
En el gráfico que figura a continuación se muestran las cantidades a pagar en millones de euros y en los
semestres futuros previstos.
Para calcular el valor actual deberemos hacer lo siguiente:
= 122,06 millones de euros
Lo que quiere decir que el comprador paga una cantidad actual equivalente a 122,06 millones de euros y
en modo alguno los 130 millones que figuran en el contrato.
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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WW*
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
04 - El valor temporal del dinero
Apéndice: Diccionario Español-Inglés
Español
Inglés
Español
Inglés
Amortización de préstamos
Loan rescue
Oferta
Offer
Anualidad
Annuity
Perpetuidad
Perpetuity
Coste de oportunidad
Opportunity cost
Préstamo
Loan
Demanda
Demand
Renta
Rent
Inflación
Inflation
Rentas perpetuas
Perpetual rents
Interés compuesto
Compound interest
Riesgo
Risk
Interés continuo
Continuous interest
Tasa de inflación
Inflation rate
Interés simple
Simple interest
Tasa de interés
Interest rate
Letra del Tesoro
Treasury Bill
Valor futuro
Future value
Valor actual
Present value
Wo*