Review
Bond Yields and Prices
Learning Objectives
 Calculate 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 Principle
 Intrinsic value
 Is an estimated value
 Present value of the expected future cash flows
 Required to compute intrinsic value



Expected future cash flows
Timing of expected cash flows
Discount rate, or required rate of return by investors
Bond Valuation
 Value of a coupon bond with semi-annual
payments:
C t /2
MV
V

t
2n
(1

r/2)
(1

r
/2)
t 1
2n
• 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 Maturity
 Yield 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 Maturity
 Solve for YTM (semi-annual coupons):
C t /2
MV
P

t
2t
(1  YTM/2)
t 1 (1  YTM/2)
2n
• Investors earn the YTM if the bond is held to
maturity and all coupons are reinvested at
YTM
Reinvestment Risk
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 Changes
 Over time, bond prices that differ from face value must
change
 Bond prices move inversely to market yields
 The 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 considerations
 Different effects of yield changes on the prices and rates
of return for different bonds
 Maturity inadequate measure of a bond’s economic
lifetime
 A measure is needed that accounts for both size and
timing of cash flows
Duration
 A 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 flows

Weights determined by present value of cash flows
Calculating
Duration
 Need to time-weight present value of cash flows from
bond
PV(CFt )
D
t
t 1Market Price
n
• Duration depends on three factors



Maturity of the bond
Coupon payments
Yield to maturity
Duration Relationships
 Duration increases with time to maturity, but at a
decreasing rate


For coupon paying bonds, duration is always less than
maturity
For zero coupon-bonds, duration equals time to
maturity
 Duration increases with lower coupons
 Duration increases with lower yield to maturity
Why is Duration Important?
 Allows comparison of effective lives of bonds that
differ in maturity, coupon
 Used in bond management strategies, particularly
immunization
 Measures bond price sensitivity to interest rate
movements, which is very important in any bond
analysis
Convexity
 Refers to the degree to which duration changes as the
yield to maturity changes

Price-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 Conclusions
 To obtain maximum price volatility, investors should
choose bonds with the longest duration
 Duration is additive

Portfolio duration is just a weighted average
 Duration measures volatility, which is not the only
aspect of risk in bonds
Review part 2
Common Stock Valuation
Company Analysis
Learning Objectives
 The dividend discount model to estimate stock prices
 Explain the P/E ratio approach.
 Fundamental Analysis : estimate share’s intrinsic value
Present Value Approach DDM
• Intrinsic value of a security is
Cash Flows
Value of security  
(1  k) t
t 1
n
 Estimated intrinsic value compared to the current
market price

What if market price is different than estimated
intrinsic value?
Required Inputs
 Expected cash flows
 Dividends paid out of earnings


Earnings important in valuing stocks
Retained 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
Dividend
Discount
Model
 Current value of a share of stock is the discounted
value of all future dividends
D1
D2
D
Pcs 

 ... 
1
2

(1  k cs ) (1  k cs )
(1  k cs )

Dt

t
t 1 (1  k cs )
Dividend Discount Model
 Problems:
 Need infinite stream of dividends
 Dividend stream is uncertain


Must estimate future dividends
Dividends 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 dividends
 Dividends expected to grow at a constant rate, g, over
time
D1
P0 
kg


D1 is the expected dividend at end of the first
period
D1 = D0 x (1+g)
Dividend Discount Model
 Multiple growth rates: two or more expected growth
rates in dividends


Ultimately, growth rate must equal that of the economy
as a whole
Assume growth at a rapid rate for n periods, followed
by steady growth
n
P0  
t 1
D0 (1  g1 )
(1  k)
t
t
Dn (1  gc ) 1

n
k - g (1  k )
P/E
Ratio
Approach
 To estimate share value
Po  estimated earnings
 justified P/E ratio  E1  Po /E1
• P/E ratio can be derived from
D1
D1/E1
Po 
or Po /E1 
k-g
k-g
 Indicates the factors that affect the estimated
P/E ratio
Other Valuation Techniques
 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 equity
 Price-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
Company Analysis
Intrinsic value  P̂0 
D1
k -g
Fundamental Analysis
 Earnings multiple could also be used
P0 = 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 ratio


Dividends paid from earnings
Close correlation between earnings and stock price
changes
Required Rate of Return
 A function of the riskless rate of return and a risk
premium
k = RF + RP
 Constant growth version of dividend discount model
can be rearranged so that

k = (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
Appendix 17-A Financial Ratio Analysis

Five types of ratios used to analyze a firm:
Liquidity: ability to generate cash and meet shortterm debt
2. 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 profits
5. Value: market value versus accounting values
1.
DuPont
Analysis
 XYZ (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