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Corporate Finance Unit 5: Stock Valuation

A share of stock is worth the present value of the cash it will pay its owner. This unit values stocks with dividend models, free cash flow models and multiples, and explains where growth comes from.

Covers: Common and preferred stock features, Dividend discount model and constant growth, Required return: dividend yield and capital gains yield, Nonconstant (multi-stage) growth, Growth opportunities, ROE and P/E ratios, Free cash flow and multiples valuation, Market efficiency

Study guide

Common stockholders own the firm's residual cash flows and elect the board. Preferred stockholders receive a fixed dividend that must be paid before common dividends, and they have priority in liquidation, but they usually cannot vote. Because a share's value comes from what its owner receives, the dividend discount model says P₀ = PV of all expected future dividends. Even an investor who plans to sell soon gets a price that depends on the dividends expected after the sale, so the horizon does not matter. A preferred stock with a fixed dividend is a perpetuity, worth D ÷ R.

If dividends grow at a constant rate g forever, the Gordon growth model gives P₀ = D₁ ÷ (R − g), where D₁ = D₀(1 + g) is next year's dividend. The model requires R > g and becomes very sensitive as g approaches R. Rearranging gives R = D₁ ÷ P₀ + g: the total return equals the dividend yield plus the capital gains yield, which equals g because the price grows at g. Sustainable growth equals ROE × retention ratio (b), because reinvested earnings earn the firm's return on equity.

Many firms grow quickly before settling into steady growth. For nonconstant growth, forecast each dividend during the fast-growth stage, then compute a terminal value at the end of that stage with the Gordon model, using the first dividend of the stable stage. Discount every dividend and the terminal value back to today at R. The terminal value at year N is a year-N amount, so it is discounted N years. If a firm pays no dividends for a while, the same method works: value the first growing perpetuity one year before its first dividend.

Growth creates value only when reinvested earnings earn more than the cost of equity. Price can be split into the no-growth value E₁ ÷ R plus the present value of growth opportunities (PVGO). If ROE equals R, retaining earnings leaves price unchanged; if ROE is below R, retaining earnings destroys value even though growth rises. This explains P/E ratios: forward P/E = payout ratio ÷ (R − g), so firms with valuable growth opportunities and low risk trade at higher multiples. Comparable-firm multiples such as P/E and EV/EBITDA give quick market-based estimates.

The corporate valuation (free cash flow) model values the whole firm by discounting expected free cash flows at the WACC, often with a terminal value: V = FCF₁ ÷ (WACC − g). Equity value equals firm value minus debt (plus excess cash), and dividing by shares gives price per share. This approach works for firms that pay no dividends. All valuations depend on market prices being sensible. In an efficient market, prices quickly reflect available information: weak form (past prices), semistrong form (all public information) and strong form (even private information).

Key ideas

• A stock's value is the present value of all expected future dividends.
• The Gordon model, P₀ = D₁ ÷ (R − g), uses next year's dividend and requires R > g.
• Required return equals dividend yield plus capital gains yield.
• Nonconstant growth is valued with explicit dividends plus a terminal value.
• Growth adds value only when ROE exceeds the required return.
• Free cash flow at WACC values the whole firm; subtract debt to get equity.
• In efficient markets, prices react quickly and fully to new public information.

Formulas and rules

Common mistakes

• Plugging D₀ instead of D₁ into the Gordon model.
• Discounting a terminal value by N + 1 years instead of N years.
• Forgetting to subtract debt after valuing the firm with free cash flows at WACC.
• Assuming faster growth always raises price, even when ROE is below the required return.
• Using the payout ratio instead of the retention ratio in g = ROE × b.

Before the test, make sure you can

• Calculate stock price with the constant-growth model and value preferred stock.
• Calculate the required return as dividend yield plus capital gains yield.
• Value a stock with nonconstant growth using a terminal value.
• Calculate sustainable growth from ROE and the retention ratio.
• Calculate PVGO and explain when growth adds or destroys value.
• Value equity using free cash flows at WACC and subtract debt.
• Use P/E and EV/EBITDA multiples to estimate value per share.
• Explain the three forms of market efficiency.

Words to know

Dividend discount model

Values a stock as the present value of all expected future dividends.

Gordon growth model

P₀ = D₁ ÷ (R − g) for dividends growing at a constant rate forever.

Dividend yield

Next year's dividend divided by the current price, D₁ ÷ P₀.

Capital gains yield

The percentage change in price; equals g in the constant-growth model.

Terminal value

The value at the end of a forecast period of all cash flows after that point.

Nonconstant growth

Dividends that grow at different rates in different periods before settling to a constant rate.

Retention ratio

The fraction of earnings reinvested in the firm, b = 1 − payout ratio.

Sustainable growth rate

g = ROE × retention ratio; growth financed by retained earnings.

PVGO

Present value of growth opportunities: price minus the no-growth value E₁ ÷ R.

P/E ratio

Price per share divided by earnings per share.

Preferred stock

Stock with a fixed dividend and priority over common stock, usually without voting rights.

Common stock

Ownership shares with voting rights and a residual claim on cash flows.

Corporate valuation model

Values the firm as the PV of free cash flows at WACC; equity = firm value − debt.

Enterprise value

Market value of equity plus debt minus cash; the value of the operating business.

Semistrong-form efficiency

Prices reflect all publicly available information.

Weak-form efficiency

Prices reflect all information in past prices and trading volume.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.