Infinance, the T-model is a formula that states the returns earned by holders of a company's stock in terms of accounting variables obtainable from its financial statements.^[1] The T-model connects fundamentals with investment return, allowing an analyst to make projections of financial performance and turn those projections into arequired return that can be used in investment selection.

Mathematically the T-model is as follows:

${\displaystyle \mathit{T}=\mathit{g}+\frac{\mathit{R}OE-\mathit{g}}{\mathit{P}B}+\frac{\mathrm{\Delta }PB}{PB}\mathit{(}1+g)}$

where${\displaystyle T}$ = total return from the stock over a period (appreciation + "distribution yield" — see below);

${\displaystyle g}$ = the growth rate of the company's book value during the period;

${\displaystyle PB}$ = the ratio of price / book value at the beginning of the period.

${\displaystyle ROE}$ = the company's return on equity, i.e. earnings during the period / book value;

The return a shareholder receives from owning a stock is:

${\displaystyle (2)\mathit{T}=\frac{\mathit{D}}{\mathit{P}}+\frac{\mathrm{\Delta }P}{P}}$

Where${\displaystyle \mathit{P}}$ = beginning stock price,${\displaystyle \mathrm{\Delta }P}$ = price appreciation or decline, and${\displaystyle \mathit{D}}$ = distributions, i.e. dividends plus or minus the cash effect of company share issuance/buybacks. Consider a company whose sales and profits are growing at rateg. The company funds its growth by investing in plant and equipment and working capital so that its asset base also grows atg, and debt/equity ratio is held constant, so that net worth grows atg. Then the amount of earnings retained for reinvestment will have to begBV. After paying dividends, there may be an excess:

${\displaystyle \mathit{X}CF=\mathit{E}-\mathit{D}iv-\mathit{g}BV}$

whereXCF = excess cash flow,E = earnings,Div = dividends, andBV = book value. The company may have money left over after paying dividends and financing growth, or it may have a shortfall. In other words,XCF may be positive (company has money with which it can repurchase shares) or negative (company must issue shares).

Assume that the company buys or sells shares in accordance with itsXCF, and that a shareholder sells or buys enough shares to maintain her proportionate holding of the company's stock. Then the portion of total return due to distributions can be written as${\displaystyle \frac{\mathit{D}iv}{\mathit{P}}+\frac{\mathit{X}CF}{\mathit{P}}}$. Since${\displaystyle \mathit{R}OE=\frac{\mathit{E}}{\mathit{B}V}}$ and${\displaystyle \mathit{P}B=\frac{\mathit{P}}{\mathit{B}V}}$ this simplifies to:

${\displaystyle (3)\frac{\mathit{D}}{\mathit{P}}=\frac{\mathit{R}OE-\mathit{g}}{\mathit{P}B}}$

Now we need a way to write the other portion of return, that due to price change, in terms ofPB. For notational clarity, temporarily replacePB withA andBV withB. ThenP${\displaystyle \equiv }$AB.

We can write changes inP as:

${\displaystyle \mathit{P}+\mathrm{\Delta }\mathit{P}=(\mathit{A}+\mathrm{\Delta }\mathit{A})(\mathit{B}+\mathrm{\Delta }\mathit{B})=\mathit{A}B+\mathit{B}\mathrm{\Delta }\mathit{A}+\mathit{A}\mathrm{\Delta }\mathit{B}+\mathrm{\Delta }\mathit{A}\mathrm{\Delta }\mathit{B}}$

SubtractingP${\displaystyle \equiv }$AB from both sides and then dividing byP${\displaystyle \equiv }$AB, we get:

${\displaystyle \frac{\mathrm{\Delta }P}{P}=\frac{\mathrm{\Delta }\mathit{B}}{\mathit{B}}+\frac{\mathrm{\Delta }\mathit{A}}{\mathit{A}}\left(\mathit{1}+\frac{\mathrm{\Delta }\mathit{B}}{\mathit{B}}\right)}$

A isPB; moreover, we recognize that${\displaystyle \frac{\mathrm{\Delta }\mathit{B}}{\mathit{B}}=\mathit{g}}$, so it turns out that:

${\displaystyle (4)\frac{\mathrm{\Delta }P}{P}=\mathit{g}+\frac{\mathrm{\Delta }PB}{PB}\mathit{(}1+g)}$

Substituting (3) and (4) into (2) gives (1), the T-Model.

In 2003, Estep published a version of the T-model that does not rely on estimates of return on equity, but rather is driven by cash items: cash flow from the income statement, and asset and liability accounts from the balance sheet. The cash-flow T-model is:

${\displaystyle \mathit{T}=\frac{\mathit{C}F}{\mathit{P}}+\mathbf{\Phi }g+\frac{\mathrm{\Delta }PB}{PB}\mathit{(}1+g)}$

where

${\displaystyle \mathit{C}F=cashflow}$${\displaystyle \text{(net income + depreciation + all other non-cash charges),}}$

and

${\displaystyle \mathbf{\Phi }=\frac{\mathit{M}ktCap-grossassets+totalliabilities}{\mathit{M}ktCap}}$

He provided a proof^[2] that this model is mathematically identical to the original T-model, and gives identical results under certain simplifying assumptions about the accounting used. In practice, when used as a practical forecasting tool it may be preferable to the standard T-model, because the specific accounting items used as input values are generally more robust (that is, less susceptible to variation due to differences in accounting methods), hence possibly easier to estimate.

Some familiar valuation formulas and techniques can be understood as simplified cases of the T-model. For example, consider the case of a stock selling exactly at book value (PB = 1) at the beginning and end of the holding period. The third term of the T-Model becomes zero, and the remaining terms simplify to:${\displaystyle \mathit{T}=\mathit{g}+\frac{\mathit{R}OE-\mathit{g}}{1}=ROE}$

Since${\displaystyle \mathit{R}OE=\frac{\mathit{E}}{\mathit{B}V}}$ and we are assuming in this case that${\displaystyle \mathit{B}V=\mathit{P}}$,${\displaystyle \mathit{T}=\frac{\mathit{E}}{\mathit{P}}}$, the familiar earnings yield. In other words, earnings yield would be a correct estimate of expected return for a stock that always sells at its book value; in that case, the expected return would also equal the company'sROE.

Consider the case of a company that pays the portion of earnings not required to finance growth, or put another way, growth equals the reinvestment rate1 – D/E. Then ifPB doesn't change:

${\displaystyle \mathit{T}=\mathit{g}+\frac{\mathit{R}OE-\mathit{R}OE(1-D/E)}{\mathit{P}B}}$

SubstitutingE/BV for ROE, this turns into:

${\displaystyle \mathit{T}=\mathit{g}+\frac{D}{\mathit{P}}}$

This is the standard Gordon "yield plus growth" model. It will be a correct estimate ofT ifPB does not change and the company grows at its reinvestment rate.

IfPB is constant, the familiar price–earnings ratio can be written as:

${\displaystyle \frac{\mathit{P}}{\mathit{E}}=\frac{\mathit{R}OE-\mathit{g}}{\mathit{R}OE(\mathit{T}-\mathit{g})}}$

From this relationship we recognize immediately thatP–E cannot be related to growth by a simple rule of thumb such as the so-called "PEG ratio"${\displaystyle \frac{\mathit{P}/E}{g}}$; it also depends onROE and the required return,T.

The T-model is also closely related to the P/B-ROE model of Wilcox^[3]

Whenex post values for growth, price/book, etc. are plugged in, the T-Model gives a close approximation of actually realized stock returns.^[4] Unlike some proposed valuation formulas, it has the advantage of being correct in a mathematical sense (seederivation); however, this by no means guarantees that it will be a successful stock-picking tool.^[5]

Still, it has advantages over commonly used fundamental valuation techniques such asprice–earnings or the simplifieddividend discount model: it is mathematically complete, and each connection between company fundamentals and stock performance is explicit so that the user can see where simplifying assumptions have been made.

Some of the practical difficulties involved with financial forecasts stem from the many vicissitudes possible in the calculation of earnings, the numerator in theROE term. With an eye toward making forecasting more robust, in 2003 Estep published aversion of the T-Model driven by cash items: cash flow, gross assets, and total liabilities.

Note that all "fundamental valuation methods" differ from economic models such as thecapital asset pricing model and its various descendants; fundamental models attempt to forecast return from a company's expected future financial performance, whereas CAPM-type models regardexpected return as the sum of a risk-free rate plus a premium for exposure to return variability.

• Residual income valuation
• Clean surplus accounting

• Asikoglu, Yaman and Metin R. Ercan, "Inflation Flow-Through and Stock Prices," Journal of Portfolio Management, Spring 1992
• Erzegovesi, Luca, "Come impostare la previsione dei rendimenti azionari: il T-model," Economia & Management 1988, v. 2, p. 93–104
• Estep, Tony, "Cash Flows, Asset Values, and Investment Returns: Brief Summary", Banc of America Capital Management, March 2003
• Wilcox, Jarrod and Philips, Thomas K., "The P/B-ROE Model Revisited" (March 10, 2004)
• Yamaguchi, Katsunari "Supply-side Estimate of Expected Equity Return on Industrial Japan", Security Analysts Journal, September 2005Archived 2011-10-04 at theWayback Machine

• Investment
• Financial models

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