T-model

Overview

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. 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.

Formula

Mathematically the T-model is as follows:

T

=

g

+

R

O E −

g

P

B

+

Δ P B

P B

(

1 + g )

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

where

T

{\displaystyle T}

= total return from the stock over a period (appreciation + "distribution yield" — see below);

Derivation

The return a shareholder receives from owning a stock is:

( 2 )

T

=

D

P

+

Δ P

P

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

Where

P

{\displaystyle {\mathit {P}}}

= beginning stock price,

Δ P

{\displaystyle \Delta P}

= price appreciation or decline, and

D

{\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 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:

Cash-flow variation

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:

T

=

C

F

P

+

Φ

g +

Δ P B

P B

(

1 + g )

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

where

C

F = c a s h f l o w

{\displaystyle {\mathit {C}}F=cashflow\,}

(net income + depreciation + all other non-cash charges),

{\displaystyle {\mbox{(net income + depreciation + all other non-cash charges),}}\,}

Relationship to other 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:

T

=

g

+

R

O E −

g

1

= R O E

{\displaystyle {\mathit {T}}={\mathit {g}}+{\frac {{\mathit {R}}OE-{\mathit {g}}}{1}}=ROE}

Since

R

O E =

E

B

V

{\displaystyle {\mathit {R}}OE={\frac {\mathit {E}}{{\mathit {B}}V}}}

and we are assuming in this case that

B

Use

When ex post values for growth, price/book, etc. are plugged in, the T-Model gives a close approximation of actually realized stock returns. 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. 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.

See also

Residual income valuation Clean surplus accounting

Further reading

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 2005 Archived 2011-10-04 at the Wayback Machine