A closed form formula for equity valuation model based on differential equation

I-Cheng Yeh ()
Additional contact information
I-Cheng Yeh: Department of Civil Engineering of Tamkang University

OPSEARCH, 2025, vol. 62, issue 2, No 22, 1039-1060

Abstract: Abstract The valuation of intrinsic value is the cornerstone of value investing. When shareholders purchase a company’s stock, they are essentially buying claims to its future earnings and shareholder equity. Two main approaches, income-based and asset-based, have been developed to value equities. However, these approaches focus solely on either the company’s earnings or its shareholder equity. To overcome these limitations, the Growth Valuation Model (GVM) was developed, which incorporates both income and asset-based aspects. While the GVM model has the advantage of a closed-form solution, it still relies on a discrete infinite series, a common limitation of equity valuation models. In contrast, continuous differential equations have been successfully employed to develop a variety of option pricing models. However, there is a scarcity of equity valuation models derived using continuous differential equations, which is a gap in the current financial modeling landscape. This paper addresses this gap by developing a theoretical equity valuation model, the Continuous Growth Value Model (CGVM), based on a continuous differential equation, and deriving its closed-form solution. Our study concludes: (1) The GVM and CGVM models are developed under three discrete-typed and three continuous-typed assumptions, respectively. Therefore, they can be considered as the discrete and continuous versions of a valuation approach based on the same core principle: mean reversion of return on equity (ROE). (2) The reciprocal of the exponential decay rate in CGVM plays a similar role to the growth coefficient in GVM. (3) The theoretical curves between ROE and P/B ratio of CGVM and GVM are close to each other, and when ROE equals the required return rate, both models will have a P/B ratio of 1.0. (4) Only when the current ROE is greater than the required return rate, the persistence of ROE does have a positive effect on intrinsic value.

Keywords: Stock price; Valuation model; Mean reversion; Differential equation (search for similar items in EconPapers)
JEL-codes: G12 G14 M41 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12597-024-00833-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:opsear:v:62:y:2025:i:2:d:10.1007_s12597-024-00833-6

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/12597

DOI: 10.1007/s12597-024-00833-6

Access Statistics for this article

OPSEARCH is currently edited by Birendra Mandal

More articles in OPSEARCH from Springer, Operational Research Society of India
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().