VALUATION – BONDS AND STOCKS
1
 We
 BONDS
hear a lot about the stock market in
the popular press, but not much about the
bond market
 It may surprise you to learn that the U.S.
bond market is over twice the size of the
U.S. stock market


Total outstanding debt in 2007: $29.2 trillion
Total market value of common stock: $14.2
trillion
 In general, bonds are less risky than stocks
 But, like all assets, high-yield bonds have
higher risk
2
 Corporate
Bonds
 Bond ratings go from AAA(Best credit) to
CCC. If the rating is D, then it is
considered in default. BBB or better is
considered investment grade, 0.5% or less
chance of default. BB and below,
historically default rate is around 4% but
has reached above 10% in 90-91, 2001 for
example.
3
WHICH TO BUY?
 High
Yield vs Investment grades
 Example
 AAA 5% with .2% historical default
 B, 9% with 4% historical default rate
 40% recovery rate on defaults
 Return = (1 – default rate) * interest rate
– default rate * (1-recovery rate)
 Return for A, .998 * .05 - .002*.6 = 4.87%.
 Return for B, .96 * .09 - .04 * .6 = 6.24%
 Link
to corporate and Treasury quotes
5
BOND VALUATION
The value of a bond represents the present value
of future cash flows.
 Bonds are easier to value than stocks because in
the case of bonds, the cash flows are known

Coupon amount
 Par value


Investors also know the time remaining to
maturity, and the prevailing market interest rate
for bonds of similar risk
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 Examples
 Calculate
Price, Annual coupon, semiannual coupon.
 What happens when interest rates
change?
 How does maturity affect risk?
 How does coupon affect risk?
 Discount, Premium, at Par
7
Holding period return
 Assume you buy a 10 year 8% annual
coupon bond yielding 8%. 2 years later
it is yielding 6%. What is your return?
8

Other Issues: Yield to Call
The YTM calculation assumes that the bond is held to
maturity
 What if the bond is called by the issuer prior to
maturity? The investor would receive only the coupon
payments up to the point of call, plus the call price
 This is called the Yield to Call

9



Callable bonds are an advantage for the issuer, but a
disadvantage for the investor
 If interest rates fall, the issuer can recall the more
expensive debt and issue new debt at the new lower
interest rate
 The investor is left with cash, just when interest rates
are lower
The call provision effectively puts a ceiling on the price of
a bond
 If interest rates fall enough, the bond will be called
Investors are not stupid – they require higher yields from
callable bonds versus otherwise equivalent non-callable
bonds
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
Example:
 20-year bond with 7 percent coupons, semiannual
 The bond can be called in 5 years at a call price of
1,070
 The bond’s market price is $1,106.38.
 Calculate the Yield to Call:
-1106.38 35
I/YR
PV
PMT
OUTPUT
2.875
 YTC = 2 x 2.875 = 5.75%
INPUT
40
N
1070
FV
11
MUNICIPAL BONDS AND YIELD

Municipal bonds appear to offer low yields
compared with corporate bonds and Treasury
securities.


This is because the interest from municipal bonds is
tax exempt at the federal level, and generally at the
state level as well
In order to compare yields, we must compute the
after-tax yield on municipal bonds
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 Taxable
equivalent yield
Muni yield
Equivalent Taxable Yield 
1 - tax rate
 Example:
Pre-tax yield on municipal bond
is 5%, and investor’s marginal tax rate is
35%

Equivalent taxable yield = 5 / (1-.35) = 7.69%
 Municipal
bonds are more attractive to
high-income investors (with high marginal
tax rates)
13
DURATION




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
DURATION: CALCULATION
wt  CF t (1  y )
t
Price
T
D   t wt
t 1
CFt  Cash Flow for period t
DURATION CALCULATION
8%
Time
Bond years
Sum
Payment PV of CF Weight C1 X
(10%)
C4
1
80
72.727
.0765
.0765
2
80
66.116
.0690
.1392
3
1080
811.420
.8539
2.5617
950.263
1.0000
2.7774
USES OF DURATION
Summary measure of length or effective maturity
for a portfolio
 Immunization of interest rate risk (passive
management)

Net worth immunization
 Target date immunization


Measure of price sensitivity for changes in
interest rate
DURATION/PRICE RELATIONSHIP
Price change is proportional to duration and not to
maturity
DP/P = -D x [D(1+y) / (1+y)
D* = modified duration
D* = D / (1+y)
DP/P = - D* x Dy
PRICING ERROR FROM CONVEXITY
Price
Pricing Error from
Convexity
Duration
Yield
CORRECTION FOR CONVEXITY
Modify the pricing equation:
DP
  D  Dy  1  Convexity (Dy )2
2
P
Convexity is Equal to:
 CF t

2
  t 
2 
t t
P  (1  y) t 1  (1  y )

1
N
Where: CFt is the cashflow (interest and/or
principal) at time t.
Stock Investing:
October, this is one of the peculiarly
dangerous months to speculate in stocks.
The others are July, January September,
April, November, May, March, June,
December, August and February.
Mark Twain, 1899.
COMMON STOCK
 Equity
securities (stocks) represent
ownership in a corporation
 Common stockholders are residual claimants

The have a claim on cash flows only after all
other claimants (employees, suppliers,
debtholders, the government) have been paid
 At
any point in time the market value of a
firm’s common stock depends on many
factors including:




The company’s profitability (cash flows)
The company’s growth potential
Current market interest rates
Conditions in the overall stock market
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VALUATION APPROACH
Examine Economic Environment(Federal
Reserve Forecasts is a good place to start)
 Examine Industry/Sector Environment
 Examine Company
 Examine Price



Best of all worlds: Finding a good company in a
growing industry within an expanding economy
that is undervalued. A tall order.
We will not focus on the economic and industry
environment in this class, but will start with
some simple financial statement analysis to
determine if we are dealing with a good
company, and then look at valuation models to
see if it is selling at an attractive price.
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ANALYSIS OF FINANCIAL STATEMENTS
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INTRODUCTION

The real value of financial statements lies in the
fact that managers, investors, and analysts can
use the information in the statements to:
Analyze firm performance
 Plan changes to improve performance


Ratio Analysis

Calculating and analyzing financial ratios to assess a
firm’s performance
25

Ratios fall into five groups:






Liquidity ratios
Asset management ratios
Debt management ratios
Profitability ratios
Market value ratios
After managers, analysts, or investors calculate
a firm’s ratios they make two comparisons:


Trend – comparison to the same firm over time
Competitors – comparison to other firms in the
same industry
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LIQUIDITY RATIOS
Liquidity ratios provide an indication of the ability
of the firm to meet its obligations as they come
due
 The two most common liquidity ratios are the
current ratio and the quick (or acid-test) ratio.

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 The
broadest liquidity measure is the current
ratio, which measures the dollars of current
assets available to pay each dollar of current
liabilities
Current Ratio = CA / CL
 Inventory
is the least liquid of the current
assets, and is the current asset for which book
values are the least reliable measure of market
value. The quick, or acid-test ratio excludes
inventory in the numerator, and measures the
firm’s ability to pay off short-term obligations
without relying on inventory sales:
Quick Ratio = (CA – Inventory) / CL
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ASSET MANAGEMENT RATIOS
Asset management ratios measure how efficiently
a firm uses its assets
 Many of these ratios are focused on a specific
asset, such as inventory or accounts receivable.
 We will examine inventory and total asset
turnover.

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
Inventory Management
The inventory turnover ratio
measures the dollars of sales produced per dollar
of inventory. Often this ratio uses cost of goods
sold in the numerator rather than sales since
inventory is listed on the balance sheet at cost
Inventory Turnover = Sales / Inventory
or
Inventory Turnover = Cost of Goods Sold / Inventory


Total Asset Management
 The Total Asset Turnover ratio measures the dollars
of sales produced per dollar of total assets
Total assets turnover ratio = Sales / Total assets
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DEBT MANAGEMENT RATIOS
Debt management ratios
measure the extent to which
the firm uses debt (financial
leverage) versus equity to finance its assets. We will
examine the following four:


The debt ratio measures the percentage of total
assets financed with debt.
Debt ratio = Total debt / Total assets

The debt-to-equity ratio measures the dollars of
debt financing used for every dollar of equity
financing.
Debt-to-equity ratio = Total debt / Total equity
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
The Equity Multiplier ratio measures the dollars of
assets on the balance sheet for every dollar of equity
financing
Equity multiplier ratio = Total assets / Total equity

The Times Interest Earned ratio measures
the number of dollars of operating earnings
available to meet each dollar of interest
obligations
Times interest earned = EBIT / Interest expense
32
PROFITABILITY RATIOS
These ratios show the combined effect of liquidity,
asset management, and debt management on the
overall operating results of the firm
 These ratios are closely monitored by investors



Stock prices react very quickly to unexpected changes
in these ratios. We will look at the profit margin,
ROA, and ROE.
The Profit Margin is the percent of sales left after all
firm expenses are paid
Profit margin = Net income available to common
stockholders / Sales
33

The Return on Assets (ROA) measures the
overall return on the firm’s assets, inclusive of
leverage and taxes
Return on Assets (ROA) = Net income available to
common stockholders / Total Assets

The Return on Equity (ROE) measures the
return on common stockholders’ investment
Return on Equity (ROE) = Net income available to
common stockholders / Common stockholders’ equity


ROE is affected by net income as well as the amount of
financial leverage
A high ROE is generally considered to be a positive sign of
firm performance
 Unless it is driven by excessively high leverage
34
MARKET VALUE RATIOS
 While
ROE is a very important financial
statement ratio, it doesn’t specifically
incorporate risk.
 Market prices of publicly traded firms do
incorporate risk, and so ratios that
incorporate stock market values are
important.
 We will look at two, Market to book and PE
35
 The
Market-to-Book ratio measures the
amount that investors will pay for the firm’s
stock per dollar of equity used to finance the
firm’s assets
Market-to-book ratio = Market price per share / Book value per
share



Book value per share is an accounting-based
number reflecting historical costs
This ratio compares the market (current) value
of the firm's equity to their historical costs.
If liquidity, asset management, and accounting
profitability are good for a firm, then the
market-to-book ratio will be high
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 The
Price-Earnings ratio is the best
known and most often quoted figure
Price-earnings ratio = Market price per share / Earnings per share


Measures how much investors are willing to
pay for each dollar of earnings
A high PE ratio is often an indication of
anticipated growth

Stocks are classified as growth stocks or value
stocks based on the PE ratio
37
DUPONT ANALYSIS
DuPont analysis is a decomposition model
 ROA and ROE can be broken down into
components in an effort to explain why they may
be low (or high).
 ROE = profit margin x total asset turnover x
equity multiplier
 ROE = NI/Sales x Sales/Total Assets x Total
Assets/Total Equity
 The DuPont model focuses on




Expense control (Profit Margin)
Asset utilization (TA turnover)
Debt utilization (Equity Mult)
38
TIME SERIES AND CROSS-SECTIONAL
ANALYSIS
To analyze ratios in a meaningful way they must
be compared to some benchmark
 There are two types of benchmarks:

Performance of the firm over time (time series
analysis)
 Performance of the firm against other companies in
the same industry (cross-sectional analysis)


Comparative ratios for industries are available from Value
Line, Robert Morris Associates, Dun & Bradstreet, Hoover’s
Online, and MSN Money
39
FUNDAMENTAL STOCK ANALYSIS: MODELS OF
EQUITY VALUATION: IS IT UNDERVALUED?

Basic Types of Models
Balance Sheet Models
 Dividend Discount Models
 Price/Earning Ratios


Estimating Growth Rates and Opportunities
DIVIDEND DISCOUNT MODELS:
GENERAL MODEL

Dt
t
t  1 (1  k )
Vo  
 V0
= Value of Stock
Dt = Dividend
k = required return
NO GROWTH MODEL
D
Vo 
k
 Stocks
that have earnings and dividends
that are expected to remain constant
 Preferred Stock
NO GROWTH MODEL: EXAMPLE
D
Vo 
k
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
CONSTANT GROWTH MODEL
Do (1  g )
Vo 
kg
g
= constant perpetual growth rate
CONSTANT GROWTH MODEL: EXAMPLE
Do (1  g )
Vo 
kg
E1 = $5.00 b = 40%
k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
ADDITIONAL VALUATION METHODS

Variable Growth Techniques
For high-growth firms, we can’t use the constant
growth formula because we know that the firm can’t
sustain the high growth forever
 These firms may have two different growth rates

Growth during the supernormal growth period
 Steady growth after the firm matures


We can use a multistage growth formula for these
firms, but we can also use discounted cash flows in
combination with the constant growth model
46

Example: Suppose a firm currently has a dividend
of D0 = $5. We expect the firm to grow at a rate of
10% for three years, after which it will grow at 4%
forever. The required return is 9%.

First we can calculate the dividends:
D1 = 5(1+.10) = 5.50
 D = 5.50(1.10) = 6.05
2
 D = 6.05(1.10) = 6.655
3
 D = 6.655(1.04) = 6.92
4

47
Now we can calculate the present value of all
of the dividends in periods 4 to ∞, where the growth is
constant forever
P3 = D4/(kg)
= 6.92/(.09-.04)
= 138.42
Now we have all the cash flows, and we can find P0
P0 = 5.50/1.091 + 6.05/1.092 + (6.655 + 138.42)/1.093
= $122.17

48


Estimating some key inputs for Multi-Stage Growth Models
Cash flow estimate
Dividends
 Operating Cash Flow
 Free Cash Flow to Equity (what could be paid out and remain a going
concern): NI - (1 – debt ratio) *( Change in Working Capital + Cap.
Expend. – Depreciation)


Cost of Capital/Required Return
Bond Yield + premium, premium 5% or so
 Capm: Return = risk free + B(Expected Market Return – risk free)
 Your own personal required return


Growth
A) Geometric or Average growth rates of Earnings, Sales, Cash Flows
 B) Intrinsic Growth, ROE (1 – payout ratio)
 C) Analyst Estimates

49
ESTIMATING DIVIDEND GROWTH RATES
g  ROE  b
g = growth rate in dividends
 ROE = Return on Equity for the firm
 b = plowback or retention percentage rate


(1- dividend payout percentage rate)
ESTIMATING GROWTH VIA
HISTORICAL INFO.
Dividend in 2000 was $1.
 Dividend in 2006 was $1.80
 Growth is (1.80/1)^(1/6)-1 = 10.29%

FREE CASH FLOW TO EQUITY
A much better model is to apply discount models to
FCFE which may more accurately reflect a firms
value.
FCFE = Net Income + depreciation – Cap. Expend.
– change in working capital – principal debt
repayments + new debt issues.
Apply model as per usual.
FREE CASH FLOW TO EQUITY
 If
the firm finances a fixed percentage of its
capital spending and investments in
working capital with debt, the calculation of
FCFE is simplified. Let DR be the debt ratio,
debt as a percentage of assets. In this case,
FCFE can be written as
 FCFE = NI – (1 – DR)(Capital Spending +
change in Working Capital – Depreciation)
 When
building FCFE valuation models, the
logic, that debt financing is used to finance a
constant fraction of investments, is very
useful. This equation is pretty common.
FREE CASH FLOW TO THE FIRM
 FCFF
= EBIT(1-tax rate) + Dep. – Cap.
Expenditures – Change in WC – Change
in other assets.
 Again, proceed as normal(replace
dividends with FCFF) but discount at
firms cost of capital.
 You find value of firm. To find value of
equity, simply subtract off debt.
LET’S LOOK AT AN EXAMPLE
http://faculty.etsu.edu/trainor/FNCE%203300/Lowes.d
oc
Another interesting site you may want to use:
http://caps.fool.com/Ticker.aspx?source=icaedilnk9950
012&ticker=LOW
THE P/E MODEL
The models we have used so far involve computing
a stock’s intrinsic value using discounted cash
flows to the investor
 Another approach is to assess a stock’s relative
value
 The price-earnings (P/E) ratio represents the most
common valuation yardstick in the investment
industry

56
 The
P/E ratio is simply the current price of
the stock divided by the last four quarters of
earnings per share:
Current stock price
P/E 
Per share earnings for last 12 months
 The
P/E ratio is used as an indication of
expected growth of a company
Larger growth rates lead to larger P/E ratios
 High P/E stocks are called growth stocks, whereas
low P/E stocks are called value stocks

57

Estimating Future Stock Prices

Multiplying the P/E ratio by expected earnings results
in an expected stock price
n
P
Pn  (
) x E0 x (1  g )
E
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 Example:
The P/E ratio for Caterpillar
is 12.98. The company earned $5.05 per
share and paid a $1.10 dividend last
year. Analysts estimate that the
company will grow at an average annual
rate of 12.8% over the next 5 years.
Calculate the expected price of
Caterpillar’s stock price in 5 years.
P5 = (P/E) x E0 x (1 + g)5
= 12.98 x $5.05 x (1.128)5
= $119.70
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OTHER TYPES OF VALUATION
Use Price/sales
 Price/Cash flow
 All relative valuation models rely on the market
to be fairly valued. What is a good Price/Sales
ratio? Relies on comparisons which may or may
not be valued accurately.

I leave you with the following:
“When it comes to investing, the rearview mirror is always a lot clearer
than the windshield.”
Warren Buffett
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