valuing securities. fin 591: financial fundamentals/valuation2 pricing in general investors value...
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FIN 591: Financial Fundamentals/Valuation
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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.
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Types of Bonds
Pure discount or zero bonds Single promised payments (face value) at a
maturity dateExamples: 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.
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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 = $1,000Discount rate r = 10%Years until maturity T = 81000 / (1.10)8 = $466.51.
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Another Example:Pricing Discount Bonds
Example: Suppose we have two discount (zero) bonds:
0 1 21-year PV = $93.46 $100 02-year PV = $84.17 0 $100What can we infer about the 1- and 2-year spot interest rates at time 0?
%9117.84$/100$
%7146.93$/100$
1/1/
2/12
1
/1
r
r
PVFrrFPV TT
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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:
t=1 $C / (1 + r)t = $C / r Example:
$50 received monthly, in perpetuityStated annual rate = 8%Monthly rate r = 8% / 12 = .6667%PV = $C / r = $50 / .6667% = $7500.
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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 $50 1 2 3 4
PV C AT F
1 r T
$5 3.6299 $100 / 1.1699 $103.63
Note:
c = r Price = face Par
c < r Price < face Discount
c > r Price > face Premium
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Value of Risky Debt
I. Risky Debt = Assets – Equity (call option)
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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.
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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 = Divt / (1 + rt)t
Value of stock depends on the size, timing, and riskiness of expected future dividends.
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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.
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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.
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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.
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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.
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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.
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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?
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Valuation and Dividend Policy
“Dividends do not matter” versus “dividends do matter” views.
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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.
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Some Cautions AboutDividend 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.
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Conceptual View of the Firm
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.
Balance Sheet
Assets DebtEquity
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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
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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.
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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.
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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.
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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.
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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.
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RelationshipBetween EVA & MVA
EVA EVA EVA EVAYear 1 Year 2 Year 3 .... Year n
MarketValueMarketvalue
MVA
Capital
=EVA + EVA + EVA + ... + EVA1 + r (1 + r)2 (1 + r)3 (1 + r)n
Market value is based on establishing theeconomic 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.
MVA