Valuing Stocks
Because cash flows are risky, discounting is necessary with equity cost of capital (expected return of
other equivalent risk investments) instead of risk-free interest rate.
Dividend yield: Div (expected annual dividend) / P0 (current price) → the percentage return the
investor expects to earn from the stocks’ dividend
Capital gain rate: P1 - P0 / P0
The expected total return (dividend yield+capital gain rate) of the stock should equal the expected
return of other investments available in the market with equivalent risk
Dividend-discount model: the price of the stock is equal to the present value of the expected future
dividends it will pay
1 year : P0 = (Div + P1) / (1+r)
Re (because return on equity) = Div/P0 (dividend yield) + (P1-P0)/P0 (capital gain rate
Multiple years : P0 = Div / ( 1 + r ) + Div / (1+r)^2 + .. Div / (1+r)^n + P / (1+r)^n
Constant dividend growth model: value of the firm depends on the dividend level for the coming year,
divided by the equity cost of capital adjusted by the expected growth rate of dividends
P0 = Div / (r-g)
A simple model of growth:
Div = earnings / shares outstanding x dividend payout rate
Sustainable growth rate (rate at which it can grow using only retained earnings) g = Retention rate x
Return on new investment
Cutting the firm’s dividend to increase investment will raise the stock price if and only if the new
investments have a positive NPV
Slow growth, earnings exceed investments → paying dividends
Dividend-Discount Model with Constant Long-Term Growth (GORDON)→ see page 319
Limitation of the Dividend-Discount model: lot of uncertainty in forecasting future dividends
Small changes in assumed dividend growth rate → big changes estimated stock price
Total payout model: ignores the firm’s choice between dividends and share repurchases, values all of
the firm’s equity. Discount total dividends and share repurchases and use the growth rate of total
earnings (rather than earnings per share) when forecasting the growth of the firm’s total payouts
Share repurchases: using excess cash to buy back its own stock → less cash available to pay dividends
and decreasing share count which increases earnings and dividends per share
P0=PV(future total dividends and repurchases) / shares outstanding
Discounted free cash flow model: focuses on cash flows to investors, debt and equity holders →
valuing a firm without forecasting its dividends, share repurchases or use of debt. Ignoring interest
income and expenses but adjusting for cash and debt
Enterprise value V0 =market value of equity + debt - cash = PV(future free cash flow of firm)
Free cash flow = EBIT x (1 - t) - net investment - increases in net working capital
P0=V0+Cash0-Debt0/shares outstanding
Since we are discounting the free cash flow paid to both debt and equity holders we should use
weighted average cost of capital Rwacc (weighted average of the firm’s debt and equity cost of
capital) → Rwacc < equity cost of capital
Firm’s enterprise value is the total NPV that the firm will earn from continuing and starting projects
→ accept projects with NPV>0
MOST IMPORTANT DIFFERENCE: you do not need to forecast the dividends + share repurchases.
Method of comparables: estimate value of the firm based on comparable firm
Valuation multiple: ratio of the value to some measure of the firm’s scale (price per square foot etc)
Price-Earnings ratio: share price / earnings per share
Trailing earnings: earnings over the prior 12 months
Enterprise value multiples: represents entire value of firm before paying debt
Limitations: differences in expected future growth rates, profitability, risk, only relative to others
Valuation model: using two variables to explain the other one (share value, future cash flows, cost of
capital)
Efficient markets hypothesis: competition among investors eliminates all positive-NPV trading
opportunities especially with public, easily interpretable information
