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VALUATION – BONDS AND STOCKS

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BONDS We 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 marketTotal outstanding debt in 2007: $29.2 trillionTotal market value of common stock: $14.2

trillion In general, bonds are less risky than

stocksBut, like all assets, high-yield bonds have

higher risk

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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.

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%

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Link to corporate and Treasury quotes

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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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ExamplesCalculate Price, Annual coupon,

semi-annual coupon.What happens when interest rates

change?How does maturity affect risk?How does coupon affect risk?Discount, Premium, at Par

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Holding period returnAssume you buy a 10 year 8%

annual coupon bond yielding 8%. 2 years later it is yielding 6%. What is your return?

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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

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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,

semiannualThe bond can be called in 5 years at a call

price of 1,070The bond’s market price is $1,106.38. Calculate the Yield to Call:

YTC = 2 x 2.875 = 5.75%

INPUT 40 -1106.38 35 1070N I/YR PV PMT FV

OUTPUT 2.875

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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

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)

rate tax - 1

yield Muni Yield Taxable Equivalent

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

t tt

w CF y ice ( )1 Pr

D t wt

T

t

1

CF CashFlow for period tt

DURATION CALCULATION

8%Bond

Timeyears

Payment PV of CF(10%)

Weight C1 XC4

1 80 72.727 .0765 .0765

2 80 66.116 .0690 .1392

Sum

3 1080 811.420

950.263

.8539

1.0000

2.5617

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

P/P = -D x [(1+y) / (1+y)D* = modified durationD* = D / (1+y)P/P = - D* x y

PRICING ERROR FROM CONVEXITY

Price

Yield

Duration

Pricing Error from

Convexity

CORRECTION FOR CONVEXITY

)(21 2yConvexityyD

P

P

Modify the pricing equation:

Convexity is Equal to:

N

tt

t tty

CFP 1

22 )1(y)(1

1

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.

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COMMON STOCK Equity securities (stocks) represent

ownership in a corporation Common stockholders are residual

claimantsThe 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 potentialCurrent market interest ratesConditions 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

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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 liabilitiesCurrent 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 / Inventoryor

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

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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

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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

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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

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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 growthStocks are classified as growth stocks or value

stocks based on the PE ratio

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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)

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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

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

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

V0 = Value of StockDt = Dividendk = required return

NO GROWTH MODEL

VD

ko

Stocks that have earnings and dividends that are expected to remain constant

Preferred Stock

NO GROWTH MODEL: EXAMPLE

VD

ko

E1 = D1 = $5.00

k = .15V0 = $5.00 / .15 = $33.33

CONSTANT GROWTH MODEL

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

g = constant perpetual growth rate

CONSTANT GROWTH MODEL: EXAMPLE

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

E1 = $5.00 b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

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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

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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 D2 = 5.50(1.10) = 6.05 D3 = 6.05(1.10) = 6.655 D4 = 6.655(1.04) = 6.92

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Now we can calculate the present value of all of the dividends in periods 4 to ∞, where the growth

is constant foreverP3 = 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

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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

ESTIMATING DIVIDEND GROWTH RATES

g ROE b 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.doc

Another interesting site you may want to use:http://caps.fool.com/Ticker.aspx?source=icaedilnk9950012&ticker=LOW

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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

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The P/E ratio is simply the current price of the stock divided by the last four quarters of earnings per share:

The P/E ratio is used as an indication of expected growth of a companyLarger growth rates lead to larger P/E ratiosHigh P/E stocks are called growth stocks,

whereas low P/E stocks are called value stocks

months 12last for earnings sharePer

pricestock Current P/E

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Estimating Future Stock Prices Multiplying the P/E ratio by expected earnings

results in an expected stock price

nn gEE

PP )1( x x )( 0

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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

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.

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I leave you with the following:“When it comes to investing, the

rear-view mirror is always a lot clearer than the windshield.”

Warren Buffett