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 constant return on equity and payout ratio, that is an unrealistic presumption.
2. The model requires as input 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 input a positive book per share, excluding firms with negative values.

Equations

Ke (closed form formula)

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

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

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

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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