Last updated

In finance, 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 a required return that can be used in investment selection. Mathematically the model is as follows:


where = total return from the stock over a period (appreciation + "distribution yield" — see below);
= the growth rate of the company's book value during the period;
= the ratio of price / book value at the beginning of the period.
= the company's return on equity, i.e. earnings during the period / book value;


When ex post values for growth, price/book, etc. are plugged in, the T-Model gives a close approximation of actually realized stock returns. [2] Unlike some proposed valuation formulas, it has the advantage of being correct in a mathematical sense (see derivation); however, this by no means guarantees that it will be a successful stock-picking tool. [3]

Still, it has advantages over commonly used fundamental valuation techniques such as price–earnings or the simplified dividend 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 the ROE term. With an eye toward making forecasting more robust, in 2003 Estep published a version 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 the capital 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 regard expected return as the sum of a risk-free rate plus a premium for exposure to return variability.


The return a shareholder receives from owning a stock is:

Where = beginning stock price, = price appreciation or decline, and = 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 rate g. The company funds its growth by investing in plant and equipment and working capital so that its asset base also grows at g, and debt/equity ratio is held constant, so that net worth grows at g. Then the amount of earnings retained for reinvestment will have to be gBV. After paying dividends, there may be an excess:

where XCF = excess cash flow, E = earnings, Div = dividends, and BV = 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 its XCF, 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 . Since and this simplifies to:

Now we need a way to write the other portion of return, that due to price change, in terms of PB. For notational clarity, temporarily replace PB with A and BV with B. Then PAB.

We can write changes in P as:

Subtracting PAB from both sides and then dividing by PAB, we get:

A is PB; moreover, we recognize that , so it turns out that:

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

The cash-flow 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:



He provided a proof [4] 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.

Relationship to other valuation models

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:

Since and we are assuming in this case that , , 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's ROE.

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 rate 1 – D/E. Then if PB doesn't change:

Substituting E/BV for ROE, this turns into:

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

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

From this relationship we recognize immediately that P–E cannot be related to growth by a simple rule of thumb such as the so-called "PEG ratio" ; it also depends on ROE and the required return, T.

The T-model is also closely related to the P/B-ROE model of Wilcox [5]

See also


  1. Estep, Preston W., "A New Method For Valuing Common Stocks", Financial Analysts Journal, November/December 1985, Vol. 41, No. 6: 26–27
  2. Estep, Tony (July 1987), "Security Analysis And Stock Selection: Turning Financial Information Into Return Forecasts", Financial Analysts Journal, 43 (4): 34–43, doi:10.2469/faj.v43.n4.34, JSTOR   4479045
  3. Dwyer, Hubert and Richard Lynn, "Is The Estep T-Model Consistently Useful?" Financial Analysts Journal, November/December 1992, Vol. 48, No. 6: 82–86.
  4. Estep, Preston, "Cash Flows, Asset Values, and Investment Returns", The Journal of Portfolio Management, Spring 2003
  5. Wilcox, Jarrod W., "The P/B-ROE Valuation Model," Financial Analysts Journal, Jan–Feb 1984, pp 58–66.

Further reading

Related Research Articles

The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with some adjustments, by options market participants.

Time value of money value of current money with interest after time

The time value of money is the greater benefit of receiving money now rather than an identical sum later. It is founded on time preference.

In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will overall rise in value, while overvalued stocks will generally decrease in value.

Rational pricing is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, the second derivative of the price of the bond with respect to interest rates. In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance.

In finance, the beta of an investment is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors.

The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.

In corporate finance, the return on equity (ROE) is a measure of the profitability of a business in relation to the equity. Because shareholder's equity can be calculated by taking all assets and subtracting all liabilities, ROE can also be thought of as a Return on Assets Minus Liabilities. ROE measures how many dollars of profit are generated for each dollar of shareholder’s equity. ROE is a metric of how well the company utilizes its equity to generate profits.

Proportional control

Proportional control, in engineering and process control, is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value and the measured value. Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor.

Earnings growth is the annual compound annual growth rate (CAGR) of earnings from investments. For more general discussion see: Sustainable growth rate #From a financial perspective; Stock valuation #Growth rate; Valuation using discounted cash flows #Determine the continuing value; Growth stock; PEG ratio.

The dividend discount model (DDM) is a method of valuing a company's stock price based on the theory that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In other words, it is used to value stocks based on the net present value of the future dividends. The equation most widely used is called the Gordon growth model (GGM). It is named after Myron J. Gordon of the University of Toronto, who originally published it along with Eli Shapiro in 1956 and made reference to it in 1959. Their work borrowed heavily from the theoretical and mathematical ideas found in John Burr Williams 1938 book "The Theory of Investment Value."

In electrochemistry, the Butler-Volmer equation, also known as Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction, considering that both a cathodic and an anodic reaction occur on the same electrode:

The trinomial tree is a lattice based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing. For fixed income and interest rate derivatives see Lattice model (finance) #Interest rate derivatives.

The Grinold and Kroner Model is used to calculate expected returns for a stock, stock index or the market as whole. It is a part of a larger framework for making forecasts about market expectations.

Velocity Vector that measures the rate of change in position over time of a moving point

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

Enthalpy of fusion enthalpy

The enthalpy of fusion of a substance, also known as (latent) heat of fusion is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure. For example, when melting 1 kg of ice, 333.55 kJ of energy is absorbed with no temperature change. The heat of solidification is equal and opposite.

Residual income valuation is an approach to equity valuation that formally accounts for the cost of equity capital. Here, "residual" means in excess of any opportunity costs measured relative to the book value of shareholders' equity; residual income (RI) is then the income generated by a firm after accounting for the true cost of capital. The approach is largely analogous to the EVA/MVA based approach, with similar logic and advantages. Residual Income valuation has its origins in Edwards & Bell (1961), Peasnell (1982), and Ohlson (1995).

The sum of perpetuities method (SPM) is a way of valuing a business assuming that investors discount the future earnings of a firm regardless of whether earnings are paid as dividends or retained. SPM is an alternative to the Gordon growth model (GGM) and can be applied to business or stock valuation if the business is assumed to have constant earnings and/or dividend growth. The variables are:

The public market equivalent (PME) is a collection of performance measures developed to assess private equity funds and to overcome the limitations of the internal rate of return and multiple on invested capital measurements. While the calculations differ, they all attempt to measure the return from deploying a private equity fund's cash flows into a stock market index.

In corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or stock buybacks—after all expenses, reinvestments, and debt repayments are taken care of. Whereas dividends are the cash flows actually paid to shareholders, the FCFE is the cash flow simply available to shareholders. The FCFE is usually calculated as a part of DCF or LBO modelling and valuation. The FCFE is also called the levered free cash flow.