Stock Valuation

1. Stock Valuation Learning Module

2. Stock Valuation • Firms obtain their long-term sources of equity financing by issuing common and preferred stock. • The payments of the firm to the holders of these securities are in the form of dividends. • The common stockholders are the owners of the firm and have the right to vote on important matters to the firm, such as the election of the Board of Directors. • Preferred stock, on the other hand, is a hybrid form of financing, sharing some features with debt and some with common equity.

3. Stock Valuation • The value of these securities, as with other assets, is based upon the discounted value of their expected future cash flows. The value of a share of stock is often calculated as the present value of the stream of dividends the stock is expected to provide in the future. • We will illustrate the valuation of a constant growth stock, i.e., a stock whose dividends are growing at a rate. • Preferred stock is a perpetuity and is a little easier to value than common stock.

4. Equations • Constant Growth Stock Price:P0 = [D0(1+g)]/(r – g) = D1/(r-g) • You can also solve for the expected return: r = (D1/P0) + g • Preferred Stock: Pp = Dp / r

5. Equations • where: • P0 = the stock price at time 0 • D0 = the current dividend • D1 = the next dividend (i.e., at time 1) • g = the growth rate of the dividends • r = the required return on the stock • Note that g < r. • Pp = the preferred stock price • Dp = the preferred dividend

6. Constant Growth Stocks • A constant growth stock is a stock whose dividends are expected to grow at a constant rate in the forseeable future. • This condition fits some established firms, which tend to grow over the long run at the same rate as the economy. • There are numerous, more complicated models which we will not discuss in this learning module.

7. An Example • Find the stock price given that the current dividend is $2 per share, dividends are expected to grow at a rate of 5% in the forseeable future, and the required return is 10% • Step 1 – Draw Timeline $5 g = 5% 0 Infinity r = 10%

8. An Example • Step 2 – Write equation P0 = D0(1+g)/(r – g) = D1/(r – g) • Step 3 – Fill in equation P0 = $2 (1 + 5%)/(10% - 5%) • Step 4 – Solve equation P0 = $2.10/5% = $2.10/0.05 = $42 • This means that the value of the stock at time zero is $42 dollars given a required rate of return of 10%, a growth rate of 5% and a dividend at time zero of $2.

9. Preferred Stock • Preferred stock is defined as equity with priority over common stock with respect to the payment of dividends and the distribution of assets in a liquidation. • Preferred stock has the following features: • Par Value - The par value represents the claim of the preferred stockholder against the value of the firm. • Preferred Dividend / Preferred Dividend Rate - The preferred dividend rate is expressed as a percentage of the par value of the preferred stock. The annual preferred dividend is determined by multiplying the preferred dividend rate times the par value of the preferred stock. • Since preferred dividends are generally fixed, preferred stock can be valued as a constant growth stock with a dividend growth rate equal to zero.

10. An Example • Find the price of a share of preferred stock given that the par value is $100 per share, the preferred dividend rate is 10%, and the required return is 12%. • A timeline is not really needed, because the dividends of preferred stock are fixed. However, you can always draw one if it helps. • Step 2 – Write equation Pp = Dp/rNote: The formula is the same as a constant growth stock with g = 0, soP0 = D1/(r – g) = Pp = Dp/r when g = 0.

11. An Example • Step 3 – Fill In Equation Pp = $10/12% • Step 4 – Solve Equation Pp = $83.33