Valuing Securities

FIN 591: Financial Fundamentals/Valuation Pricing in General Investors value financial instruments based on discounting expected future cash flows Why? Financial markets provide an alternative to real investments Discounting the cash flows allows you to compare the alternatives Three types of securities: Bonds Stocks Derivatives. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Types of Bonds Pure discount or zero bonds Single promised payments (face value) at a maturity date Examples: Treasury bills, corporate zeros, strips Consols Pay a fixed “coupon” each period forever Coupon bonds Pay regular (6 month) coupon payments + face value at maturity Coupons = interest for tax purposes Examples: Most corporate and long-term government bonds. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Pricing Zero Bonds Price is equal to PV For a zero coupon bond with T years to maturity and a face value of F and a constant discount rate of r, price equals: F / (1 + r)T Example: Face value = $1,000 Discount rate r = 10% Years until maturity T = 8 1000 / (1.10)8 = $466.51. FIN 591: Financial Fundamentals/Valuation

Another Example: Pricing Discount Bonds Example: Suppose we have two discount (zero) bonds: 0 1 2 1-year PV = $93.46 $100 0 2-year PV = $84.17 0 $100 What can we infer about the 1- and 2-year spot interest rates at time 0? FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Pricing Consol Bonds Receive coupon payments in perpetuity Face amount is never paid For a consol with T years to maturity and a face value of F and a constant discount rate of r, price equals: St=1 $C / (1 + r)t = $C / r Example: $50 received monthly, in perpetuity Stated annual rate = 8% Monthly rate r = 8% / 12 = .6667% PV = $C / r = $50 / .6667% = $7500. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Pricing Coupon Bonds What is the PV of a two-year $100 par value bond paying 10% interest semi-annually if the required return is 8% compounded semiannually? $100 $5 $5 $5 $5 0 1 2 3 4 Note: c = r Price = face Par c < r Price < face Discount c > r Price > face Premium FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Value of Risky Debt I. Risky Debt = Assets – Equity (call option) FIN 591: Financial Fundamentals/Valuation

Common Stock Valuation Different valuation models exist All follow time value of money concepts: Discount all expected future cash flows at an appropriate market risk-adjusted rate Future cash flows consist of: Dividends Future selling price. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Determining Price For a single holding period: P0 = (Div1 + P1) / (1 + r1) But what determines P1? P1 = (Div2 + P2) / (1 + r2) But what determines P2? Well, doing this over and over again, we get P0 = S Divt / (1 + rt)t Value of stock depends on the size, timing, and riskiness of expected future dividends. FIN 591: Financial Fundamentals/Valuation

Valuation of a Non-constant Dividend Stream... Value = PV dividends in period 1 + PV dividends in period 2 + ... + PV dividends in period n + PV expected price in period n Example: A stock is expected to pay dividends of $4 in 1 year and $5 in 2 years. Expected price of the stock in 2 years is $90. The discount rate is 10%. How much is the stock worth today? Answer: $4 / 1.10 + $5 / (1.10)2 + $90 / (1.10)2 = $3.64 + $4.13 + $74.38 = $82.15. FIN 591: Financial Fundamentals/Valuation

Valuation of Constant, No-Growth Perpetual Dividend Stream All future dividends are expected to be constant in perpetuity A simple model emerges: Price = Expected dividend next period Required market rate Example: Dividend next period is forecasted to be $3. The market’s required return is 10%. How much is the stock worth today? Answer: $3 / .10 = $30. FIN 591: Financial Fundamentals/Valuation

Valuation of Constant Growth Dividend Stream in Perpetuity All future dividends are expected to grow at a constant rate in perpetuity A simple model emerges: Price = Expected dividend next period . Required market rate - growth rate Example: Dividend next period is forecasted to be $3 and grow in perpetuity at 4%. The market required return is 10%. How much is the stock worth today? Answer: $3 / (.10 - .04) = $50. FIN 591: Financial Fundamentals/Valuation

Valuation of a Two-Stage Dividend Growth Stream Combine the non-constant stream and perpetual stream models Example: A stock is expected to pay dividends of $2 and $3 each of the next 2 years. The dividend in year 3 will be $4 and grow thereafter at 5%. The market rate is 8%. How much is the stock worth? Answer: $2 / 1.08 + $3 / (1.08)2 + $4 / (1.08)3 + [$4 (1.05) / (.08 - .05)] / (1.08)3 = $1.85 + $2.57 + $3.18 + $111.14 = $118.74. FIN 591: Financial Fundamentals/Valuation

Valuing a Stock that Pays No Dividends for a Period of Time Example: A stock is expected to pay no dividends the next 2 years. The dividend in year 3 will be $4 and grow thereafter at 5%. The market rate is 8%. How much is the stock worth? Answer: $4 + $4 (1.05) / (.08 - .05) (1.08)3 = $114.31. FIN 591: Financial Fundamentals/Valuation

Ex-Dividend Behavior of Price Stock price should drop by the amount of the dividend on the ex-date Evidence indicates that it declines by a lesser amount Tax reasons? Clientele effects? FIN 591: Financial Fundamentals/Valuation

Valuation and Dividend Policy “Dividends do not matter” versus “dividends do matter” views. FIN 591: Financial Fundamentals/Valuation

Why Dividends May Matter Informational signaling Change in dividends signals a corresponding change in management’s expectations for the firm Agency considerations Free cash flow argument and shirking by management Other factors Debt covenants; institutional constraints; IRS; state laws. FIN 591: Financial Fundamentals/Valuation

Some Cautions About Dividend Growth Models Many firms have “life cycles”. When young, they grow fast, then slow and grow at a “normal” rate Finally, they may shrink or go out of business These growth rates are difficult to predict The chosen range has a large impact on value Important to discount dividends and not earnings Cash flows received by shareholders represent value If you use earnings, you may double count some cash flows. FIN 591: Financial Fundamentals/Valuation

Conceptual View of the Firm Balance Sheet Assets Debt Equity Value of firm = Value of debt + value of stock Analyze from several perspectives: Modigliani & Miller model Free cash flow, APV model Dividends not a factor Economic value added Dividends not a factor. FIN 591: Financial Fundamentals/Valuation

Outline of Valuation Models Free cash flow Exhibit 5.5, page 77 in text Economic value added (aka EVA) i.e., economic profit or residual income Market value added Market value of firm – book value of firm PV of EVA’s Exhibits 4.2 – 4.4, pages 60 – 62. Shareholder value added. Reconciled: Exhibit 3.5, Page 50 FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Free Cash Flow Definition: After-tax operating earnings + non-cash charges - investments in operating working capital, PP&E and other assets It doesn’t incorporate financing related cash flows Operating free cash flow Represents cash flow available to service debt and equity. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Economic Value Added Reorders cash flows to allow shareholders to relate company operating performance directly to shareholder value Adjusts capital to eliminate distortions Financing perspective Capital = Debt + equity Operating perspective Capital = Fixed assets + working capital EVA = Operating profits - capital charge. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Calculating EVA Two methods lead to the same answer Method 1: EVA = (ROIC% - WACC%) * Invested operating capital Profitability captured by the spread: ROIC% - WACC% Growth captured by the invested operating capital Method 2: EVA = (Operating profits after taxes) - WACC% * Invested operating capital Similar to the economist’s definition of profit. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation Advantage of EVA Investment objective: Maximize the NPV of all available projects Issue is how to measure cash flow generating abilities? Interpreting annual free cash flow is difficult Negative free cash flow could be Value depleting or value enhancing Temporary EVA aids the understanding Will be examined in greater detail later. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation EVA & Market Value Market value of a company reflects: Value of invested capital Value of ongoing operations Present value of expected future economic profits Captures improvement in operating performance EVA related to market value by: Measuring all the capital Seeing what the firm is going to do with the capital Turn those free cash flow forecasts into EVA forecasts Discount EVA to find market value added. FIN 591: Financial Fundamentals/Valuation

Relationship Between EVA & MVA EVA EVA EVA EVA Year 1 Year 2 Year 3 .... Year n MVA MVA Market Value Market value EVA + EVA + EVA + ... + EVA 1 + r (1 + r)2 (1 + r)3 (1 + r)n = Capital Market value is based on establishing the economic investment made in the company (capital), making a best guess about what economic profits (EVA) will be in the future, and discounting those EVAs to the present. FIN 591: Financial Fundamentals/Valuation

FIN 591: Financial Fundamentals/Valuation The End FIN 591: Financial Fundamentals/Valuation