# The First Difference Property of the Present Value Operator

Stephen A. Buser, Bjarne Astrup Jensen

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

### Resumé

This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results.
We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.
Originalsprog Engelsk 1750012 Quarterly Journal of Finance 7 4 41 2010-1392 https://doi.org/10.1142/S2010139217500124 Udgivet - 2017

### Emneord

• Present value
• First difference property
• Recursive calculation
• Duration
• Convexity

### Citer dette

@article{1a3393883ec5496dacd68634c9ea2138,
title = "The First Difference Property of the Present Value Operator",
abstract = "This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.",
keywords = "Present value, First difference property, Recursive calculation, Duration, Convexity, Present value, First difference property, Recursive calculation, Duration, Convexity",
author = "Buser, {Stephen A.} and Jensen, {Bjarne Astrup}",
year = "2017",
doi = "10.1142/S2010139217500124",
language = "English",
volume = "7",
journal = "Quarterly Journal of Finance and Accounting",
issn = "1939-8123",
publisher = "World Scientific",
number = "4",

}

I: Quarterly Journal of Finance, Bind 7, Nr. 4, 1750012, 2017.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - The First Difference Property of the Present Value Operator

AU - Buser, Stephen A.

AU - Jensen, Bjarne Astrup

PY - 2017

Y1 - 2017

N2 - This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.

AB - This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.

KW - Present value

KW - First difference property

KW - Recursive calculation

KW - Duration

KW - Convexity

KW - Present value

KW - First difference property

KW - Recursive calculation

KW - Duration

KW - Convexity

U2 - 10.1142/S2010139217500124

DO - 10.1142/S2010139217500124

M3 - Journal article

VL - 7

JO - Quarterly Journal of Finance and Accounting

JF - Quarterly Journal of Finance and Accounting

SN - 1939-8123

IS - 4

M1 - 1750012

ER -