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Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus Chapter 13 Equity Valuation

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No Slide TitleFourth Edition
Irwin / McGraw-Hill
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Basic Types of Models
Essentials of Investments
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Intrinsic Value
Market Price
Trading Signal
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No Growth Model
Stocks that have earnings and dividends that are expected to remain constant
Preferred Stock
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V0 = 3.00 / (.15 - .08) = $42.86
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ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)
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D0 = $2.00 g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = 2.88 D3 = 3.46 D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / (.15 - .05) ( (1.15)3
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Specified Holding Period Model
PN = the expected sales price for the stock at time N
N = the specified number of years the stock is expected to be held
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PVGO = Present Value of Growth Opportunities
E1 = Earnings Per Share for period 1
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g = .20 x .40 = .08 or 8%
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PVGO = Present Value of Growth Opportunities
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Required Rates of Return (k)
Expected growth in Dividends
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E1 - expected earnings for next year
E1 is equal to D1 under no growth
k - required rate of return
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b = retention ration
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P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
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E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
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Coverage ratios
Leverage ratios
Liquidity ratios
Profitability ratios
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T = number of periods to maturity
r = semi-annual discount rate or the semi-annual yield to maturity
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Ct = 40 (SA)
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Bond Prices and Yields
Prices and Yields (required rates of return) have an inverse relationship
When yields get very high the value of the bond will be very low
When yields approach zero, the value of the bond approaches the sum of the cash flows
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Avg. Income = Int. +(Par-Price) / Yrs to maturity
Avg. Price = (Price + Par) / 2
Using the earlier example
Approx. YTM = 65.10/1074.50 = .0606 or 6.06%
Actual YTM = 6.00%
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Relationship between yields to maturity and maturity
Yield curve - a graph of the yields on bonds relative to the number of years to maturity
Usually Treasury Bonds
Have to be similar risk or other factors would be influencing yields
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Active strategy
Trade on market inefficiencies
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Inverse relationship between price and yield
An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield
Long-term bonds tend to be more price sensitive than short-term bonds
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As maturity increases, price sensitivity increases at a decreasing rate
Price sensitivity is inversely related to a bond’s coupon rate
Price sensitivity is inversely related to the yield to maturity at which the bond is selling
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A measure of the effective maturity of a bond
The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
Duration is shorter than maturity for all bonds except zero coupon bonds
Duration is equal to maturity for zero coupon bonds
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Price change is proportional to duration and not to maturity
DP/P = -D x [D(1+y) / (1+y)
D* = modified duration
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Summary measure of length or effective maturity for a portfolio
Immunization of interest rate risk (passive management)
Net worth immunization
Target date immunization
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In the Money - exercise of the option would be profitable
Call: market price>exercise price
Put: exercise price>market price
Out of the Money - exercise of the option would not be profitable
Call: market price>exercise price
Put: exercise price>market price
At the Money - exercise price and asset price are equal
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American vs European Options
American - the option can be exercised at any time before expiration or maturity
European - the option can only be exercised on the expiration or maturity date
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Notation
Payoff to Call Holder
0 if ST < X
Profit to Call Holder
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Payoff to Call Writer
0 if ST < X
Profit to Call Writer
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Payoffs to Put Holder
0 if ST > X
Profit to Put Holder
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Payoffs to Put Writer
0 if ST > X
Profits to Put Writer
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Investment Strategy Investment
Leveraged Buy calls @ 10 100 options $1,000
equity Buy T-bills @ 2% $7,000
Yield
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Microsoft Stock Price
$75 $80 $100
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Microsoft Stock Price
$75 $80 $100
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Payoff for
Total Payoff ST - X ST - X
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Long Call
Short Put
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Arbitrage & Put Call Parity
Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal.
C - P = S0 - X / (1 + rf)T
If the prices are not equal arbitrage will be possible
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Stock Price = 110 Call Price = 17
Put Price = 5 Risk Free = 10.25%
Maturity = .5 yr X = 105
C - P > S0 - X / (1 + rf)T
17- 5 > 110 - (105/1.05)
12 > 10
Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative
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Position Cashflow ST<105 ST> 105
Buy Stock -110 ST ST
Borrow
Sell Call +17 0 -(ST-105)
Buy Put -5 105-ST 0
Total 2 0 0
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Option Strategies
Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration
Vertical or money spread
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Option Values
Intrinsic value - profit that could be made if the option was immediately exercised
Call: stock price - exercise price
Put: exercise price - stock price
Time value - the difference between the option price and the intrinsic value
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Option
value
X
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Factor Effect on value
Time to expiration increases
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d2 = d1 - (s T1/2)
So = Current stock price
N(d) = probability that a random draw from a normal dist. will be less than d.
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e = 2.71828, the base of the nat. log.
r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option.
T = time to maturity of the option in years.
ln = Natural log function
s = Standard deviation of annualized cont. compounded rate of return on the stock
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s = .50 d = 0
= .43
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Call Option Value
Co = Soe-dTN(d1) - Xe-rTN(d2)
Co = 100 X .6664 - 95 e- .10 X .25 X .5714
Co = 13.70
Implied Volatility
Using Black-Scholes and the actual price of the option, solve for volatility.
Is the implied volatility consistent with the stock?
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Using the sample data
P = $95e(-.10X.25)(1-.5714) - $100 (1-.6664)
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P = C + PV (X) - So
= C + Xe-rT - So
r = .10 T = .25
P = 6.35
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Hedging: Hedge ratio or delta
The number of stocks required to hedge against the price risk of holding one option
Call = N (d1)
Option Elasticity
Percentage change in the option’s value given a 1% change in the value of the underlying stock
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Buying Puts - results in downside protection with unlimited upside potential
Limitations
Maturity of puts may be too short
Hedge ratios or deltas change as stock values change
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Futures and Forwards
Forward - an agreement calling for a future delivery of an asset at an agreed-upon price
Futures - similar to forward but feature formalized and standardized characteristics
Key difference in futures
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Futures price - agreed-upon price at maturity
Long position - agree to purchase
Short position - agree to sell
Profits on positions at maturity
Long = spot minus original futures price
Short = original futures price minus spot
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Foreign currencies
Financial futures
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Clearinghouse - acts as a party to all buyers and sellers.
Obligated to deliver or supply delivery
Closing out positions
Reversing the trade
Most trades are reversed and do not involve actual delivery
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Initial Margin - funds deposited to provide capital to absorb losses
Marking to Market - each day the profits or losses from the new futures price and reflected in the account.
Maintenance or variance margin - an established value below which a trader’s margin may not fall.
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Margin and Trading Arrangements
Margin call - when the maintenance margin is reached, broker will ask for additional margin funds
Convergence of Price - as maturity approaches the spot and futures price converge
Delivery - Actual commodity of a certain grade with a delivery location or for some contracts cash settlement
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Hedging -
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Basis and Basis Risk
Basis - the difference between the futures price and the spot price
over time the basis will likely change and will eventually converge
Basis Risk - the variability in the basis that will affect profits and/or hedging performance
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Futures Pricing
Spot-futures parity theorem - two ways to acquire an asset for some date in the future
Purchase it now and store it
Take a long position in futures
These two strategies must have the same market determined costs
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no storage costs
no seasonal patterns in prices
Strategy 1: Buy the stock now and hold it until time T
Strategy 2: Put funds aside today to perform on a futures contract for delivery at time T that is acquired today
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Buy stock -So ST
Long futures 0 ST - FO
Invest in Bill
Total for B - FO(1+rf)T ST
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Since the strategies have the same flows at time T
FO / (1 + rf)T = SO
FO = SO (1 + rf)T
The futures price has to equal the carrying cost of the stock
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Implications for business and corporate finance
Implications for investment
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Random Walk - stock prices are random
Actually submartingale
Positive trend and random about the trend
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Prices react to information
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Once information becomes available, market participants analyze it
Competition assures prices reflect information
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Types of Stock Analysis
Technical Analysis - using prices and volume information to predict future prices
Weak form efficiency & technical analysis
Fundamental Analysis - using economic and accounting information to predict stock prices
Semi strong form efficiency & fundamental analysis
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Active Management
Security analysis
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Market Efficiency and Portfolio Management
Even if the market is efficient a role exists for portfolio management
Appropriate risk level