Roe discount model

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The Roe Discount Model (RDM) is an equity valuation model that conceptually splits the value of the share into two components:

1. The Current Value, the capitalization of the stream of dividends.
2. The Growth Value, the capitalization of the reinvestment of retained earnings.

RDM is a parsimonious model that uses 4 inputs to compute the price of the stock or the implied rate of return on equity.

Inputs

1. Forecasted (next 4 quarters) earnings per share $(Eps)$ or return on equity $(Roe)$.
2. Forecasted (next 4 quarters) dividend per share $(Dps)$ or payout ratio $(Py)$.
3. Current book per share $(Bps)$.
4. Implied cost of equity $(Ke)$ or current market price $(P)$.

Limitations

1. The model assumes a costant return on equity and payout ratio, that is an unrealistic presumption.
2. The model requires as imput a positive earnings per share or return on equity, excluding firms with negative values.
3. The model requires earnings greater than dividends.
4. The model requires as imput a positive book per share, excluding firms with negative values.

Equations

Ke (closed form formula)

$Ke={\frac {\mathrm {E} ps*Py}{\mathrm {P} }}+{\frac {\mathrm {E} ps*(1-Py)}{\sqrt {P*Bps}}}$

$Ke={\frac {\mathrm {D} ps}{\mathrm {P} }}+{\frac {\mathrm {E} ps*(1-Py)}{\sqrt {P*Bps}}}$

$Ke={\frac {\mathrm {R} oe*Py}{\frac {\mathrm {P} }{\mathrm {B} ps}}}+{\frac {\mathrm {R} oe*(1-Py)}{\sqrt {\frac {\mathrm {P} }{\mathrm {B} ps}}}}$

Price (recursive formula)

$P={\frac {\mathrm {E} ps*Py}{\mathrm {K} e}}+{\frac {\mathrm {E} ps*{\sqrt {\frac {\mathrm {P} }{\mathrm {B} ps}}}*(1-Py)}{\mathrm {K} e}}$

$P={\frac {\mathrm {D} ps}{\mathrm {K} e}}+{\frac {\mathrm {E} ps*{\sqrt {\frac {\mathrm {P} }{\mathrm {B} ps}}}*(1-Py)}{\mathrm {K} e}}$

$P={\frac {\mathrm {R} oe*Bps*Py}{\mathrm {K} e}}+{\frac {\mathrm {R} oe*{\sqrt {{\mathrm {P} }*{\mathrm {B} ps}}}*(1-Py)}{\mathrm {K} e}}$

See also

• Dividend discount model
• Sum of perpetuities method
• Residual income valuation

Further reading

• Sanna, Dario. "A Fast and Parsimonious Way to Estimate the Implied Rate of Return on Equity" (PDF). mpra.ub.uni-muenchen.de.

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