El valor temporal del dinero

Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878

04 - El valor temporal del dinero

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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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Caso real: El manuscrito en el que Einstein escribió su famosa teoría que relacionaba la masa y la energía (E=mc2) fue adquirido en 1987 por 1,2 millones de euros. Su propietario lo puso a la venta me-diante una subasta pública en 1996 pidiendo un mínimo de 4 millones, la mejor oferta sólo llegó a 3,3 mi-llones 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



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Caso real: 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 pa-go 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



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- 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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Apéndice: Diccionario Español-Inglés

Español Inglés Español Inglés

Amortización de préstamos

Anualidad

Coste de oportunidad

Demanda

Inflación

Interés compuesto

Interés continuo

Interés simple

Letra del Tesoro

Loan rescue

Annuity

Opportunity cost

Demand

Inflation

Compound interest

Continuous interest

Simple interest

Treasury Bill

Oferta

Perpetuidad

Préstamo

Renta

Rentas perpetuas

Riesgo

Tasa de inflación

Tasa de interés

Valor futuro

Valor actual

Offer

Perpetuity

Loan

Rent

Perpetual rents

Risk

Inflation rate

Interest rate

Future value

Present value

El valor temporal del dinero

Documents

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