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 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
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.
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
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)
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
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
Price change is proportional to duration and not to maturity
P/P = -D x [ (1+y) / (1+y)
D * = modified duration
D * = D / (1+y)
P/P = - D * x y
PRICING ERROR FROM CONVEXITY Price Yield Duration Pricing Error from Convexity
CORRECTION FOR CONVEXITY Modify the pricing equation: Convexity is Equal to: Where: CF t is the cashflow (interest and/or principal) at time t.
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.
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
Examine Economic Environment(Federal Reserve Forecasts is a good place to start)
Examine Industry/Sector Environment
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.
ANALYSIS OF FINANCIAL STATEMENTS
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
Calculating and analyzing financial ratios to assess a firm’s performance
Ratios fall into five groups:
Asset management ratios
Debt management 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
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.
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
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.
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
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
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
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
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
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
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
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
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
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)
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
Estimating Growth Rates and Opportunities
DIVIDEND DISCOUNT MODELS: GENERAL MODEL
V 0 = Value of Stock
D t = Dividend
k = required return
NO GROWTH MODEL
Stocks that have earnings and dividends that are expected to remain constant
NO GROWTH MODEL: EXAMPLE
E 1 = D 1 = $5.00
k = .15
V 0 = $5.00 / .15 = $33.33
CONSTANT GROWTH MODEL
g = constant perpetual growth rate
CONSTANT GROWTH MODEL: EXAMPLE
E 1 = $5.00 b = 40% k = 15%
(1-b) = 60% D 1 = $3.00 g = 8%
V 0 = 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
Example: Suppose a firm currently has a dividend of D 0 = $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:
D 1 = 5(1+.10) = 5.50
D 2 = 5.50(1.10) = 6.05
D 3 = 6.05(1.10) = 6.655
D 4 = 6.655(1.04) = 6.92
Now we can calculate the present value of all
of the dividends in periods 4 to ∞, where the growth is constant forever
P 3 = D 4 /(kg)
Now we have all the cash flows, and we can find P 0
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 = 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.
F REE 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.
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
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 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
Estimating Future Stock Prices
Multiplying the P/E ratio by expected earnings results in an expected stock price
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.
P 5 = (P/E) x E 0 x (1 + g) 5
= 12.98 x $5.05 x (1.128) 5
OTHER TYPES OF VALUATION
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 rear-view mirror is always a lot clearer than the windshield.”