Acta academica karviniensia 2012, 12(4):85-90 | DOI: 10.25142/aak.2012.060

APPLICATION OF THE LAPLACE TRANSFORM FOR THE EVALUATION OF CONSOLS' PRESENT VALUE

Jiří Mazurek

Mgr. Jiří Mazurek, Ph.D., Odborný asistent Katedra matematických metod v ekonomii, Obchodně podnikatelská fakulta v Karviné, Slezská univerzita v Opavě, Univerzitní náměstí 1934/3, 733 40 Karviná, mazurek@opf.slu.cz

The aim of the article is to demonstrate the use of the Laplace transform to the evaluation of consols' present value under different streams of returns (dividends). Consols (or perpetual bonds, perpetuities) are bonds with no maturity, which means that interest is paid to a bondholder perpetually (usually annually) forever. The present value of a consol, when constant interest is paid, is simply a ratio of this interest and interest rate. However, when interest payments (stream of returns to a bondholder) change in time the evaluation of consol's present value is more complicated. In the first part of this article it is shown that the Laplace transform of a stream of returns can be used to the evaluation present value of a consol under assumption of continuous compounding; and moreover, with the inverse Laplace transform an unknown stream of returns can be reconstructed from the known consol's present value. In the second part of the paper, the use of the Laplace transform for the present value evaluation is illustrated by examples.

Keywords: consol, future value, Laplace transform, present value, stream of returns

JEL classification: C65, G12

Published: December 30, 2012  Show citation