Post on 21-Dec-2015
Review
Bond Yields and PricesBond Yields and Prices
Learning ObjectivesCalculate the price of a bond.Calculate major bond yield measures,
including yield to maturity, current yield, coupon rate
Account for changes in bond prices.Explain and apply the concept of duration.
Bond Valuation PrincipleIntrinsic value
Is an estimated value Present value of the expected future cash flowsRequired to compute intrinsic value
Expected future cash flows Timing of expected cash flows Discount rate, or required rate of return by
investors
Bond ValuationValue of a coupon bond with semi-annual
payments:
2n
2n
1tt
t
/2)r(1
MV
r/2)(1
/2C V
2n
2n
1tt
t
/2)r(1
MV
r/2)(1
/2C V
• Biggest problem is determining the discount rate or required yield
• Required yield is the current market rate earned on comparable bonds with same maturity and credit risk
Yield to MaturityYield to maturity (YTM)
Rate of return on bonds most often quoted for investors
Promised compound rate of return received from a bond purchased at the current market price and held to maturity
Equates the present value of the expected future cash flows to the initial investment Similar to internal rate of return
Yield to MaturitySolve for YTM (semi-annual coupons):
2t
2n
1tt
t
YTM/2)(1MV
YTM/2)(1
/2CP
2t
2n
1tt
t
YTM/2)(1MV
YTM/2)(1
/2CP
• Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
For: (1) longer-term bonds
(2) bonds with higher coupon rates
(i.e., have more money to reinvest)
NO reinvestment risk for “Zeroes”
Bond Price ChangesOver time, bond prices that differ from face
value must changeBond prices move inversely to market yieldsThe change in bond prices due to a yield
change is directly related to time to maturity and inversely related to coupon rate
Measuring Bond Price Volatility: Duration
Important considerationsDifferent effects of yield changes on the prices
and rates of return for different bondsMaturity inadequate measure of a bond’s
economic lifetimeA measure is needed that accounts for both
size and timing of cash flows
DurationA measure of a bond’s lifetime, stated in
years, that accounts for the entire pattern (both size and timing) of the cash flows over the life of the bond
The weighted average maturity of a bond’s cash flowsWeights determined by present value of cash
flows
Calculating DurationNeed to time-weight present value of cash
flows from bond
tPriceMarket
)PV(CFD
n
1t
t
tPriceMarket
)PV(CFD
n
1t
t
• Duration depends on three factors Maturity of the bond Coupon payments Yield to maturity
Duration RelationshipsDuration increases with time to maturity,
but at a decreasing rateFor coupon paying bonds, duration is always
less than maturityFor zero coupon-bonds, duration equals time
to maturityDuration increases with lower couponsDuration increases with lower yield to
maturity
Why is Duration Important?Allows comparison of effective lives of bonds
that differ in maturity, couponUsed in bond management strategies,
particularly immunizationMeasures bond price sensitivity to interest
rate movements, which is very important in any bond analysis
ConvexityRefers to the degree to which duration
changes as the yield to maturity changesPrice-yield relationship is convex
Duration equation assumes a linear relationship between price and yield
Convexity largest for low coupon, long-maturity bonds, and low yield to maturity
Duration ConclusionsTo obtain maximum price volatility, investors
should choose bonds with the longest duration
Duration is additivePortfolio duration is just a weighted average
Duration measures volatility, which is not the only aspect of risk in bonds
Review part 2
Common Stock ValuationCommon Stock ValuationCompany AnalysisCompany Analysis
Learning ObjectivesThe dividend discount model to estimate
stock pricesExplain the P/E ratio approach.Fundamental Analysis : estimate share’s
intrinsic value
Estimated intrinsic value compared to the current market priceWhat if market price is different than
estimated intrinsic value?
n
1ttk) (1
Flows Cash security of Value
n
1ttk) (1
Flows Cash security of Value
• Intrinsic value of a security isPresent Value Approach DDM
Expected cash flows Dividends paid out of earnings
Earnings important in valuing stocksRetained earnings enhance future earnings
and ultimately dividends Retained earnings imply growth and future
dividends Produces similar results as current dividends in
valuation of common shares
Required Inputs
Current value of a share of stock is the discounted value of all future dividends
1tt
cs
t
cs2
cs
21
cs
1cs
)k(1
D
)k1(D
...)k1(
D
)k1(D
P
1tt
cs
t
cs2
cs
21
cs
1cs
)k(1
D
)k1(D
...)k1(
D
)k1(D
P
Dividend Discount Model
Problems:Need infinite stream of dividendsDividend stream is uncertain
Must estimate future dividendsDividends may be expected to grow over time
Must model expected growth rate of dividends and need not be constant
Dividend Discount Model
Assume constant growth rate in dividendsDividends expected to grow at a constant rate,
g, over time
gkD
P 10 gk
D P 1
0
Dividend Discount Model
D1 is the expected dividend at end of the first period
D1 = D0 x (1+g)
Multiple growth rates: two or more expected growth rates in dividendsUltimately, growth rate must equal that of the
economy as a wholeAssume growth at a rapid rate for n periods,
followed by steady growth
nt
t
)k1(
1g-k
)g(1D
k)(1
)g(1D P cn
n
1t
100
nt
t
)k1(
1g-k
)g(1D
k)(1
)g(1D P cn
n
1t
100
Dividend Discount Model
To estimate share value
1o1
o
/EP E ratio P/E justified
earnings estimatedP
1o1
o
/EP E ratio P/E justified
earnings estimatedP
• P/E ratio can be derived from
g - k/ED
/EP or g - k
DP 11
1o1
o g - k/ED
/EP or g - k
DP 11
1o1
o
Indicates the factors that affect the estimated P/E ratio
P/E Ratio Approach
Market-to-book ratio (M/B)Ratio of share price to per share
shareholder’s equity as measured on the balance sheet
Price paid for each $1 of equityPrice-to-sales ratio (P/S)
Ratio of company’s market value (price times number of shares) divided by sales
Market valuation of a firm’s revenues
Other Valuation Techniques
Company AnalysisCompany Analysis
g-k
DP̂ valueIntrinsic 1
0 g-k
DP̂ valueIntrinsic 1
0
Earnings multiple could also be usedP0 = estimated EPS justified P/E ratio
Stock is under- (over-) valued if intrinsic value is larger (smaller) than current market price
Focus on earnings and P/E ratioDividends paid from earningsClose correlation between earnings and
stock price changes
Fundamental Analysis
A function of the riskless rate of return and a risk premium
k = RF + RPConstant growth version of dividend discount
model can be rearranged so thatk = (D1/P0) + g
Growth forecasts are readily available
Required Rate of Return
Risk premium for a stock regarded as a composite of business, financial, and other risks
If the risk premium rises (falls), then k will rise (fall) and P0 will fall (rise)
If RF rises (falls), then k will rise (fall) and P0 will fall (rise)
Discount rates and P/E ratios move inversely to each other
Required Rate of Return
Five types of ratios used to analyze a firm:1. Liquidity: ability to generate cash and
meet short-term debt2. Asset Management: ability to effectively
manage its assets to generate sales and profits
3. Debt Management: ability to effectively handle its debt
4. Profitability: ability to generate profits5. Value: market value versus accounting
values
Appendix 17-A Financial Ratio Analysis
DuPont AnalysisXYZ (2004)
ROE = (NI/Sales) (Sales/TA) ((TA/Equity) = (.0299)(1.042)(4.339) = 13.51%
Industry averages (2004) ROE = (NI/Sales) (Sales/TA) ((TA/Equity)
= (.0568)(1.23)(1.74) = 12.16% This analysis suggests that XYZ displays an
above average ROE due to its higher leverage factor, and despite the fact it has below average profitability and asset turnover