tailieunhanh - Generalization of the annuity factor

The well-known Annuity Factor, restricted to constant payments only, can be generalized for time dependent payments. A Generalized Annuity Factor (GAF) broadens the application potential considerably as is shown exemplarily for the valuation of loans and pension obligations. | http afr. Accounting and Finance Research Vol. 7 No. 2 2018 Generalization of the Annuity Factor Joerg Wilde1 1 Pension Fund of Water Associations Ruhrverband Essen Germany Correspondence Joerg Wilde Ruhrverband 45128 Essen Kronprinzenstr 37 Germany. Received January 10 2018 Accepted January 29 2018 Online Published February 6 2018 doi URL https Abstract The well-known Annuity Factor restricted to constant payments only can be generalized for time dependent payments. A Generalized Annuity Factor GAF broadens the application potential considerably as is shown exemplarily for the valuation of loans and pension obligations. For the first time for such linear and nonlinear payments over time compressed closed-form formulae for important financial key numbers such as present value duration convexity or value at risk can be derived. Moreover easy computation makes General Annuity Factors a useful valuation tool especially in the field of finance and accounting. As General Annuity Factors can be implemented as User Defined Functions in a spreadsheet program calculations can also be done in smaller firms or public services. Because of its computational efficiency the new instrument is also suitable for far-sighted economical models such as Asset Liability Management models ALM or life-cycle valuation models concerning products investments or stocks. Keywords General annuity factor Present value Value at risk Loans Pension obligations Life cycle JEL Classification C02 G12 G17 L11 M41 1. Introduction and Literature Review The Annuity Factor is routinely used in many economical fields to calculate the present value of an annuity which is a cash flow stream with a limited number of periodic payments of the same amount. The annuity factor concept allows an easy computation of the present value as a simple product of the constant payment amount and the Annuity Factor. Annuity Factor tables for different discount .