Valuation Fundamentals
Kerry Back
Growing perpetuity
- Cash flows \(C_1 = c\), \(C_2 = (1+g)c\), \(C_3 = (1+g)^2c\) and so on forever.
- Discount rate \(r>g\)
- PV is
\[ c\left[\frac{1}{1+r} + \frac{1+g}{(1+r)^2} + \frac{(1+g)^2}{(1+r)^3} + \cdots\right] = \frac{c}{r-g}\]
Gordon growth model
- We want to value cash flows to shareholders
- \(r=\) required return on equity
- Payouts to shareholders = dividends + repurchases - net issues
- Assume earnings, payouts, and book equity all grow at rate \(g<r\).
- Define ROE to be earnings divided by lagged (beginning of year) equity.
- Set \(k =\) payout ratio \(=\) payouts / earnings.
- Equity grows by earnings minus payouts = \((1-k) \times\) earnings.
- Earnings \(=\) ROE \(\times\) lagged equity.
- \(g=\) % change in equity \(=\) growth in equity / lagged equity
\[=\frac{(1-k) \times \text{ROE} \times \text{lagged equity}}{\text{lagged equity}}\]
\[= (1-k) \times \text{ROE}\]
- Value of stock is next year’s payout / \((r-g)\).
- Next year’s payout is \(k\) \(\times\) next year’s earnings.
- Next year’s earnings \(=\) ROE \(\times\) current book equity.
- Theoretical price-to-book \(=\) market-to-book
\[=\left.\frac{k \times \text{ROE} \times \text{book equity}}{r-(1-k)\times \text{ROE}}\right/ \text{book equity}\]
\[=\frac{k \times \text{ROE}}{r-(1-k)\times \text{ROE}}\]
Dupont Analysis
\[\text{ROE} = \frac{\text{Net Income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Lagged Assets}} \]
\[\times \frac{\text{Lagged Assets}}{\text{Lagged Equity}}\]
\[= \text{Profit Margin} \times \text{Asset Turnover}\]
\[ \times \text{Leverage}\]