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2013 | OriginalPaper | Chapter

2. Does a Positive Perpetual Growth Rate Exist?

Author : Zhiqiang Zhang

Published in: Finance – Fundamental Problems and Solutions

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter explores a common variable, perpetual grow rate, in financial or valuation models and reveals that it is not sure to be positive or negative, which is referred to as a growth paradox. Based on Moody’s default rate data, this chapter further reveals some insights related to this growth paradox and concludes that finance as a science is just on its initial stage, which is similar to Astronomy in the time of Nicolaus Copernicus (1473-1543).

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previous chapter Finance and its Fundamental Problems

next chapter Valuation Based on Required Payback Period

We will discuss it further in Chap. 3 [1].

Choice of other column will not change the results too much. Note that most of the standpoints here related to the negative growth rate are logically sound. The calculations are mainly for illustrative purposes, and some impreciseness in assumptions or data will not hurt the conclusions. Therefore, we prefer the simpler assumption or data processing for simplifying the illustrating as long as it is not far from reality.

Although we need not to stress on the preciseness, we do consider the significant differences or changes in various concepts and calculations.

Note that there are 7 ratings listed here, and 70 % × 1 + 5% × 6 = 100 %, and adjusting downward of the “70 %” and consequently adjusting upward of the “5 %” will increase the constant one year bankruptcy probabilities of A firms and decrease the constant one year bankruptcy probabilities of C firms.

According to the survey of O’Hara (2002), only 3 companies have been living over 1000 years so far.

See Fama Eugene F. and French Kenneth R. [4, 5].

See among others, Dichev, Ilia D [6].

Based on the data of Aswath Damodaran (2008), yearly data of the S&P 500 from 1960 to 2007 (http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/spearn.htm), the author find that the compound annual growth rate (capital gain) of the S&P 500 was 7.12 %, the average annual dividend yield was 3.26 % and the average annual total return was 10.38 %.

Gordon MJ (1962) The savings investment and valuation of a corporation. Rev Econ Stat 44(1):37–51CrossRef

Cantor R, Hamilton DT, Tennant J (2007) Confidence intervals for corporate default rates. Special Comment of Moody’s, April 2007

Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33:3–56

Fama EF, French KR (1996) Multifactor explanations of asset pricing anomalies. J Financ 51:55–84

Dichev ID (1998) Is the risk of bankruptcy a systematic risk? J Financ 53:1131–1147

Ibbotson RG, Chen P (2003) Long-run stock returns: participating in the real economy. Financ Anal J 59(1)

Title: Does a Positive Perpetual Growth Rate Exist?
Author: Zhiqiang Zhang
Publisher: Springer Berlin Heidelberg
Book: Finance – Fundamental Problems and Solutions
Print ISBN: 978-3-642-30511-5

Electronic ISBN: 978-3-642-30512-2

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-642-30512-2_2