FIN 360: Corporate Finance Topics 10: Stocks and their Valuation Larry Schrenk, Instructor

Stock Valuation Stock Basics Valuing Common Stock Valuing Preferred Stock ‘Implied’ Required Rate of Return

Stock Basics

Common Equity Dividends Required Rate of Return Ownership Residual Status Absolute Priority Rule

Preferred Shares (PS) Features Dividend (d) Two Types of Dividends Required Rate of Return History Uses

Common Stock: Owners, Directors, and Managers Represents Ownership Ownership Implies Control Stockholders Elect Directors Directors Hire Management Since Managers are ‘Agents’ of Shareholders, their Goal Should Be: Maximize Stock Price

Ownership of Common Stock Mostly owned (70%) by institutional investors Institutional investors include: Pension Plan Funds (CALPERS) Insurance Companies Mutual Funds Hedge Funds

Pros of Equity Financing No obligation to pay dividends. Risk averse management doesn’t like debt Reduces financial risk (e.g. total debt ratio) This may be a more important advantage to firms that already are relatively risky due to the kind of business they do (e.g. high tech has high business risk)

Cons of Equity Financing Dilution of ownership and power due to more shares of stock outstanding. Lower earnings per share/stock price More work than debt offering Flotation costs (expensive) Fees paid to investment bankers, lawyers, accountants, printers Usually much higher than for debt issues.

Comparison

Valuing Common Stock

Valuing Common Stock Methods Discounted Dividend Model (DDM) P/E Ratio Methodologies Other Ratio Methodologies Capital Asset Pricing Model (CAPM) Relative Valuation Free Cash Flow

Stock Valuation Issues Stock cash flows are less certain than that of bond cash flows because: Bond cash flows are fixed and defined by contract Whereas stock cash flows are: Dividends: residual and determined by the Board of Director’s vote Proceeds from sale of stock: Not guaranteed Difficulties in Stock Valuation: Dividend cash flows are not known in advance Life of stock is essentially forever No easy way to observe the rate of return required for a stock

Discounted Dividend Model (DDM)

Capital Gains vs. Dividends▪

Discounted Dividend Model (DDM) Motivation Dividends are the cash flows derived from common stock. The price is the present value of cash flows. Thus, the price of a common share should be the present value of its dividends Problems Dividends (especially far future ones) are not easily estimated.

Discounted Dividend Model (DDM) Constant Model Dividends remain constant Growth Model Dividends change at a constant rate Mixed Model Dividends change at different rates.

Constant Model If dividend is constant, then stock is a perpetuity.

Constant Model If a stock is always expected to pay an annual dividend of $4.00 and r = 7%, then

Growth Model If dividend is changing at a constant rate, then stock is a growing perpetuity.

Growth Model If a stock has just paid an annual dividend of $4.00, and the dividend is expected to increase (infinitely) at 2% (r = 7%), then

Growth Model The same methodology applies if the dividend is expected to decline. If a stock has just paid an annual dividend of $4.00, and the dividend is expected to decrease (infinitely) at 2% (r = 7%), then

Mixed Model Both patterns possible, but not likely to apply to very many firms. Generally, expect the firm’s dividend to change at different rates over time. A high growth firm might increase is cash flows at 30% for a few years, but this could not be sustained for any extended period.

Mixed Model Problem Estimate year-by-year dividends for an extended period, e.g., ten years, this would become a pure, unfounded guess at values. What will the dividend be for IBM 8 years from now?

Mixed Model Strategy Short Term Long Term To alleviate this problem, we divide the forecast of dividends into two periods: Short Term Prediction/Horizon Long Term Prediction/Horizon Short Term Long Term 1 2 3 t d0 d1 d2 d3 dt

Mixed Model: Short Term Period over which we can reasonably estimate the expected dividends: As specific dollar amounts, or E.g., $4.00 $4.15 $4.25 $4.90 As subject to some growth forecast E.g., $4.00 growing at 10% for 4 years Dividend ‘Smoothing’

Mixed Model: Long Term Period over which we cannot predict dividends. We cannot ignore the long term, For many firms the long term provides much of the value of the firm. NOTE: The more value is derived from the future, the harder to use the DDM as a method.

The Long Term Solution Estimate the long term dividends as growing at a reasonable, constant growth rate. Estimate as growing perpetuity. Infinite growth rate cannot be very large. One good estimate is the long term growth for the economy, perhaps 3 or 4%.

Calculations Value of the short term dividends is PV of the individual dividends. 2) Value of the long term dividends is a delayed growing perpetuity. NOTE: It is a delayed growing perpetuity because the long term dividends do not begin until after the short term dividends end. 3) Stock price = PVshort term + PVlong term

Mixed Model Example EXAMPLE A firm has just paid an annual dividend of $2.00. That dividend is expected to grow at a rate of 30% for one year, 20% for the next two years, then level off to a long term growth rate of 3%. If the discount rate is 12%, what should be the price of the stock?

Mixed Model Example Data: d0 = 2 g1 = 30% g2-3 = 20% g4+ = 3% r = 12%

Mixed Model Example Data Dividends Calculation d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Dividends Calculation d1 = 2(1.30) = 2.60 d2 = 2(1.30)(1.20) = 3.12 d3 = 2(1.30)(1.20)2 = 3.74 d4 = 2(1.30)(1.20)2 (1.03) = 3.85 etc.

Mixed Model Example The Timeline Short Term Long Term 1 2 3 4 d0 d1 d2 1 2 3 4 d0 d1 d2 d3 d4 2.00 2.60 3.12 3.74 3.85

Mixed Model Example EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Short Term d1 = 2.60 d2 = 3.12 d3 = 3.74

Mixed Model Example EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Long Term d4 = 3.85

Mixed Model Example EXAMPLE or Short Term Long Term Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% or Short Term Long Term

Mixed Model Formula

Valuing Preferred Stock

Valuing Preferred Stock Unlike common stock, the cash flows on preferred stock are typically of the form of a perpetuity, so we can use that formula for pricing:

Valuing Preferred Stock EXAMPLE If a preferred share pays an annual dividend of $3.00 and r = 15%, then

The ‘Implied’ Required Rate of Return

‘Implied’ Required Rate of Return The term ‘implied’ sometimes has a semi-technical meaning. Recall implied future interest rates Normally We use a formula of the form: Price = … to determine the price of an asset. Then compare the predicted price with the asset’s market value

‘Implied’ Required Rate of Return An alternative Use the market price to estimate what the ‘market’ assumes to be one of the ‘implied’ input variables We have already used this in the YTM of bonds. Given the market price of a bond, what ‘implied’ discount rate, i.e., YTM What discount rate must the market apply to arrive at the market price. YTM is the implied required rate of return on a bond.

‘Implied’ Required Rate of Return If the stock (common or preferred) is modeled as a (growing) perpetuity, Solve the equation for i) the ‘implied’ required rate of return or ii) the ‘implied’ growth rate:

‘Implied’ Required Rate of Return Example If a share is selling for $75 and it is paying a constant, annual dividend of $6.00, then

‘Implied’ Required Rate of Return If the stock dividends are not constant, Then the implied rate of return is internal rate of return (IRR) The IRR calculation (in a later topic) is analogous to finding the YTM of a bond.