Module 4
Common Stock
Valuation &
Performance
Measurement
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Table of Contents
Study Plan/Syllabus ... 1
Learning Activities ... 2
Exam Formula Sheet ... 4
Chapter 1: Dividends on Stock ... 5
Importance of Dividends ... 5
Dividend Basics ... 6
Chapter 2: Equity Valuation ... 13
Definitions ... 13
DDM Alternatives ... 15
The Zero Growth Model ... 17
Constant Growth DDM ... 18
The Non-Constant Growth Model ... 25
Valuation Exercise—Merck & Co. ... 29
P/E Ratio ... 32
Summary ... 35
Chapter 3: Security Performance Evaluation ... 38
Investment Policy Statements (IPS) ... 38
Security and Portfolio Performance Evaluation ... 45
Risk/Return ... 47
Jensen Index (alpha) ... 50
Determining the Market Rate ... 57
Asset Class Benchmarks ... 61
Risk-Adjusted Performance ... 65
Mutual Fund Comparison ... 67
Summary ... 75
Module Review ... 77
Questions ... 77
Answers ... 93
About the Author ... 127
References ... 128
Study Plan/Syllabus
he efficient market hypothesis is one of the most controversial elements of modern portfolio theory, and its proponents argue that beating the indexes is next to impossible. This module will deal with its detractors who argue that the anomalies to the theory support active portfolio management. This module will discuss stock valuation techniques and how to make securities decisions using these techniques. Performance measurement approaches are discussed, including how to use those approaches to improve security selection. The chapters in this module are:
Dividends on Stock Equity Valuation
Security Performance Evaluation
Upon completion of this module you should be able to apply the dividend growth model to compute a security’s intrinsic value, and be able to apply security performance measures to evaluate how well a security performed against various market indexes. You should also be able to determine which market indexes are appropriate for evaluating different asset classes within a portfolio.
This module starts with a discussion of dividends, which then leads into the various valuation models that are used extensively by investment analysts to determine if a particular stock is overvalued, undervalued, or appropriately valued. You are expected to understand the valuation concepts, apply the concepts, and then use the concepts to help clients make investment decisions. The ability to determine value is essential, and you should experiment with your own scenarios to test the depth of your understanding of the concepts.
Next we cover the basics of investment policy statements, the use of which has
introduced including Jensen (alpha), Treynor, and Sharpe. You should become very familiar with these measurements including how and when to use them. Choosing the appropriate benchmark is important, as is understanding when or when not to use beta. This is an extremely important module, and you should take the time necessary to master its learning objectives. For those in the investment field, this is knowledge that you should have in order to better serve your clients.
Learning Activities
Learning Activities
Learning Objective Readings
Module Review Questions 4–1 Analyze the impact of different
types of cash and stock
distributions on shareholders and on the company.
Module 4, Chapter 1:
Dividends on Stock
1–13
4–2 Explain terminology related to equity investment valuation models.
Module 4, Chapter 2: Equity Valuation
14–18
4–3 Calculate the intrinsic value of a stock using various stock valuation techniques or calculate the expected return of a stock.
19–23
4–4 Evaluate the appropriateness of investment decisions based on stock valuation models.
24–33
4–5 Explain the various components of the Investment Policy Statement (IPS). Module 4, Chapter 3: Security Performance Evaluation 34, 35
4–6 Explain the characteristics, uses, and limitations of stock
performance measurement indexes. Module 4, Chapter 3: Security Performance Evaluation 36–40
Learning Activities
Learning Objective Readings
Module Review Questions 4–7 Calculate one or more stock
performance measurement indexes for given portfolio returns and risk.
41–43
4–8 Specify relationships among various indicators of security returns.
44–49
4–9 Evaluate the risk-adjusted performances of alternative investment securities or portfolios to recommend the most
appropriate selection for a given client situation.
Exam Formula Sheet
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PLEASE NOTE: You do not need to memorize these formulas for the exam. An exact copy of this formula sheet will be provided to you when you log on to take your IP exam. Also, the formula sheet for the CFP Certification Examination will be different from this exam formula sheet. Prior to taking the exam, please check with the CFP Board regarding their current exam formula sheet.
Chapter 1: Dividends on Stock
Reading this chapter will enable you to:4–1 Analyze the impact of different types of cash and stock distributions on shareholders and on the company.
Importance of Dividends
uring the investment market of the mid-1990s, many investors tended to minimize the relevance of dividends. One of the reasons they did this was the fact that dividends took a back seat to capital appreciation during the bull market run of the decade. Another reason was that many corporations reduced their dividend payout rate, which led to the lowest historical dividend yield on stocks in the 20th century.
In spite of this trend, dividends play an important role in both theory and practice in the investment area. Historically, dividends have accounted for approximately 40% of the total return on securities (Dow Jones & Company website, 2006). One of the EMH anomalies mentioned in Module 3 is that stocks with high dividend rates often have historically outperformed stocks with low dividend rates. For example, the “Dogs of the Dow” investment strategy uses the 10 Dow Industrial Average stocks with the highest dividend yields to form a portfolio. Dividends play an important role in the valuation of stocks, as you will see in the next chapter. The dividend discount model is the key element used by many professional investment managers in determining stock valuation. Famed Omaha investor Warren Buffett uses the model in his valuation computations.
Dividend Basics
The focus of most investment analysis is earnings per share. A company’s earnings, and especially its earnings surprises, drive the performance of the company’s stock.
Many companies, especially the large, mature companies typically found in the major stock market indexes such as the S&P 500 average, pay a portion of their earnings per share to shareholders in the form of dividends. Unlike interest payments on a company’s bonds, a company does not have a legal requirement to pay dividends. The company’s board of directors determines if a dividend should be paid. As a practical matter, once established, boards tend to be reluctant to cut or eliminate dividend payments to stockholders, but will do so if slumping business conditions make that prudent. Dividends on both preferred stock and common stock normally are paid quarterly so a company that, say, pays $1.00 per share annually would pay $0.25 per share every three months.
Preferred stockholders receive a fixed annual dividend amount per share. Some preferred stock have a feature called “cumulative” which means if a dividend is missed, all such dividends must be made up before common stockholders receive their dividends.
Common stockholders receive a dividend only after the preferred stockholders receive their dividends. Since common shareholders are entitled to a claim on the residual earnings after bondholders and preferred stockholders are paid,
hopefully their dividends will increase over time as the company’s earnings increase, a major attraction to owning common stock. Some dividend-paying companies aim to pay a common stock dividend that is a set percentage of earnings.
For example, assume that a company’s earnings per share is $2.00 and that the company has decided that it likes to pay approximately 30% of its earnings as a dividend. In this example, the company would pay 30% of $2.00, or $.60, per share to common stockholders. This percentage is called the dividend payout
Special Dividend
Sometimes a company will pay a special dividend beyond their regular dividend if they have had especially strong earnings in a year. Usually this is due to a buildup of corporate cash, with the board deciding this is an appropriate way to share the company’s success with the common stockholders.
For example, on October 24, 2012, Wynn Resorts Ltd. declared a cash dividend of $8 a share, which included the usual $0.50 quarterly dividend and $7.50 per share of a special dividend. This dividend was payable November 20 of that year to shareholders on record as of November 7.
Key Dividend Distribution Dates
Many dates are associated with dividends. On the declaration date, the board of directors of the corporation declares that a dividend will be paid and identifies the key dates. On the distribution date, the dividend is actually paid to
shareholders. These dates are easy to remember.
The dates that students have difficulty with are the ex-dividend date and the record date. The record date is the date that the corporation closes its books and identifies who the shareholders are. Anyone who is a shareholder on the record date is entitled to receive the dividend.
Securities laws require that all trades be cleared (settled) in three business days. That is, anyone who receives a confirmation that a trade has been executed will not actually be the owner of record until three business days later, when all financial aspects of the trade are settled. Therefore, anyone who buys a security three business days before the record date will be a registered shareholder on the record date.
An investor who buys a security two business days before the record date will have his or her trade cleared one day after the record date and will not be entitled
who receives confirmation that a trade has been executed two business days before the record date will not receive the dividend that is to be paid on the next distribution date.
Example. Cash Cow Inc. is going to pay out a dividend with a distribution date
of September 10 to shareholders who were on the corporation’s books as shareholders on the record date of August 10. Assuming that August 10 was a Monday, two business days before that date was Thursday, August 6. Therefore, August 6 will be the ex-dividend date because trades executed on August 6 would not be cleared until three business days thereafter, on August 11, which was one day after the record date. Note that if you buy on Wednesday, August 5th, your trade will settle on August 10th—in time for the dividend.
Wednesday Aug. 5th Thursday Aug. 6th Ex-dividend Tuesday Aug. 11th Business Day 3 Business Day 2 Business Day 1 Friday Aug. 7th Monday Aug. 10th record date
A trade that will settle on the example record date of Aug.10th—in time for the dividend.
Stock Dividend
Most dividends are paid in cash. Some are paid in additional shares of a
company’s stock, called a stock dividend. (Be aware that cash dividend and stock dividend are precise terms that refer to different types of dividends. Often
investors will loosely use the term stock dividend when they actually are
referring to a cash dividend.) The payment of a stock dividend may occur when a company wants to conserve cash but does not want to alienate shareholders. It could be that a company is having financial difficulties or it may simply decide
there are better uses for its cash. In these situations, the company does not want to increase the cash dividend, so it provides a stock dividend instead.
Many stockholders perceive that their wealth has increased because they own more shares after the stock distribution. Actually, shareholder wealth is unchanged because the market price of the stock is lowered on the distribution date to reflect the fact that the overall market value of the company remains unchanged; it is now simply divided over an increased number of shares. Each shareholder’s proportionate share of ownership of the company is unchanged because each shareholder has experienced the same proportionate increase in the number of shares owned.
Example—10% stock dividend. Assume an investor originally owns 100 shares
at $50 per share ($5,000 value). Immediately after a 10% stock dividend the investor would own 110 shares priced at $45.45 (still a $5,000 value).
Stock Split
A stock split is somewhat like a stock dividend, in that each shareholder owns more shares after the split than before. However, unlike a stock dividend, a stock split is not authorized in lieu of paying cash dividends.
A stock split occurs when corporate management decides to lower the market price of a stock in order to encourage more investors to purchase shares of the company. By splitting the stock, management communicates to the investment community that the company must be successful because its shares have appreciated so much that the stock must split to lower its price to a more reasonable level. It is both a psychological and a practical move for company management.
The most common stock splits are two-for-one splits or three-for-two splits. In a two-for-one split, the investor who owns 200 shares before the split will own 400
market price of the stock is $40 per share on the day before the split, it will be $20 per share on the day of the split. Therefore, the investor’s total market value is unchanged ($8,000).
To calculate the new price per share in a stock split you would divide the original price per share by the ratio of the new stock to the old. Here are a few examples (assume a $100 original stock price in each example):
2 for 1 split $100/(2/1) = $50
3 for 2 split $100/(3/2) = $66.67
3 for 1 split $100/(3/1) = $33.33
Reverse Split
For various reasons some companies have their stock price decline to low levels. The problem with this is twofold. First, there is a perception problem with potential shareholders. Many investors do not want to invest in “penny stocks.” A low share price does not exude success. Another problem is with analysts and brokerage firms. Many firms will not even look at a stock that is trading at less than $5 or $10 per share. A way to address this problem is a reverse split,
converting a certain number of “old” shares into one “new” share. For example, a company trading at 50 cents per share could do a 1-for-20 reverse split,
converting 20 old shares into 1 new share. An investor with 100 pre-split shares valued at $50 (100 × $0.50) would now have 5 shares valued at $50 (5 × $10). A reverse split may temporarily help the share price, but the marketplace will continue to punish the stock price if the company does not correct the issues that drove down the price in the first place!
Dividend Reinvestment Plans (DRIPs)
Mutual fund investors have become accustomed to reinvesting all dividend and capital gains distributions by converting them into additional shares of the fund. Many individual companies also allow investors in their stocks to reinvest their cash dividend distributions by converting them into additional shares of the
Just as with mutual fund reinvestments, the reinvested dividend distributions are taxable dividend income to the investor. The investor is assumed to have
received the cash dividend and then reinvested that cash into additional shares of the company’s stock. The investor’s basis would then increase by the amount reinvested.
The first share must be purchased from a broker or directly from the company before an investor can participate in a DRIP program. Most DRIP investors have purchased their first shares from a broker; increasingly, companies that offer DRIP programs are setting up their own direct-stock-purchase programs. Two principal advantages accrue to an individual investor who participates in a DRIP. First, the investor is able to purchase a small number of shares
periodically without having to pay a brokerage commission on each of the purchases. Since brokerage commissions on purchases of less than 100 shares are quite expensive (in proportion to the dollar value of stock purchased), this can mean significant savings, especially in the early years of a DRIP program. As the account grows, and more than 100 shares are purchased with each transaction, this savings becomes less significant.
Second, and most important, the DRIP investor must have a long-term perspective, since he or she is participating in a buy-and-hold program and is adding to his or her stock holdings using a dollar-cost-averaging approach over a long period of time. This allows an investor to build a significant position in one or more individual stocks and to increase his or her personal net worth using a disciplined investment strategy, without worrying about day-to-day gyrations in the stock’s price.
A potential disadvantage of DRIPs is that an investor is adding to his or her position in a single stock, thereby increasing unsystematic risk. This can be minimized if the investor participates in DRIP programs for stocks in a number of different industries.
introduced into the marketplace, which reduces the percentage of ownership of nonparticipating shareholders. This dilution will also impact earnings, which will be spread over an increased number of shares.
Stock Repurchases
Sometimes a firm will repurchase some of its outstanding shares of stock as an alternative to paying dividends. This would then increase earnings per share since the earnings would now be spread over a decreased number of shares. There can be various reasons for a stock repurchase. There may be stock options that have been granted to employees for which the shares are needed. The shares may also be repurchased to ward off an unwanted takeover attempt. If the company has too much cash this can attract suitors, so by repurchasing shares the company will reduce its cash amount while reducing the number of outstanding shares, which in turn will increase earnings. This should also result in a higher stock price, making the stock a less-likely takeover candidate.
Chapter 2: Equity Valuation
Reading the first part of this chapter will enable you to:4–2 Explain terminology related to equity investment valuation models.
Definitions
he total return a security should achieve is determined by calculating its required return. Required return is calculated by multiplying the market risk premium by the security’s beta and then adding the risk-free return. The security’s required return, then, is a function of its beta (systematic risk). This is the capital asset pricing model (CAPM) that we have already covered:
i f m f i r (r r ) r = + − β
Expected return is the total return an investor can expect from a security, given its current price, the growth rate of its dividend, and the capital appreciation expected (which is assumed to be the same as the expected growth rate of its dividend). The calculation for this will be covered in more detail later in this chapter:
g P D r = 1+
The intrinsic value of a security is the value of a security that is computed using a discounted cash flow approach to valuation. Dividends have been accepted by the investment community as the critical cash flow element to discount.
An important assumption in this computation is that dividends are a constant percentage of a corporation’s earnings; in other words, the payout ratio is constant. If this assumption is considered valid, then the growth rate of earnings
annual rate. If both dividends and earnings grow, then it can be assumed that the value of the company’s stock will also continue to grow.
The equation used to compute a company’s intrinsic value using the discounted cash flow approach is called the dividend discount model (DDM). It is also called the dividend growth model or the constant growth dividend discount model:
g r D V − = 1
The calculation for this will be covered in more detail later. Once a company’s intrinsic value is computed, then an investor will buy the stock if the current market price is equal to or below the intrinsic value; the investor will not buy, and indeed may sell, if the current market price is higher than the intrinsic value. The two most difficult aspects of the dividend discount model computation are estimating the appropriate discount rate to be used for the computation and estimating the future growth rate of dividends.
The net discount rate used is the required return minus the dividend growth rate. The assumption here is that the required return is the gross discount rate to be used in computing the total return of a security. However, a percentage of the required return is earned by the growth rate of the dividend; only the amount of the required return that represents growth above the dividend growth rate (i.e., capital gain) needs to be represented as the net discount rate used in the equation. Estimating dividend growth can be frustrating. In reality, neither earnings nor dividends grow systematically and steadily. One year, earnings may grow at 24% and dividends may grow at 15%; another year, earnings may decline and
dividends may remain constant. Every investor must derive some method of smoothing out dividend growth so that a compound annual rate can be determined.
DDM Alternatives
A popular alternative to using dividends in the model is to use cash flow,
especially when a company does not pay dividends. Details of this approach will not be discussed here. Different assumptions may have to be made regarding the appropriate required return rate and the growth rate of cash flow.
A second approach to determining the intrinsic value of a stock is to use the P/E ratio. This is one of the most popular valuation methods that investors use. If a company has positive earnings but pays no dividends, then this method must be used because the dividend discount model can be used only when a company pays dividends (assuming that the cash flow model is not used).
When using the P/E ratio approach, two benchmarks are considered—the industry P/E ratio and the market P/E ratio. The ratio for the company in question is computed and compared against both of these benchmarks. If the company ratio is lower than either or both benchmarks, then the stock may be undervalued. If the company ratio is higher than either or both, then the stock may be overvalued. A third approach is the price-to-sales ratio (PSR). Like the P/E ratio, this method can be used with any company; it is especially useful when a company pays no dividends and has no earnings. To use the ratio, net sales are divided by the number of shares outstanding to determine the sales per share. That number is then divided into the price per share to determine the PSR. In general, stocks with PSRs of less than 1.0 are undervalued; those with PSRs that are greater than 3.0 may be overvalued.
Another popular approach to valuation is the growth-adjusted P/E ratio, known as the PEG (PE/growth) ratio. The PEG ratio is calculated by dividing the P/E ratio by the earnings growth rate (EGR). The PEG ratio allows investors to compare companies with different growth expectations. In other words, in an industry where the average P/E ratio is 18, the P/E ratio of a stock with an expected earnings growth rate of 26% should be higher than the P/E ratio of a
Using the PEG ratio is more complex than using the other ratios. A general rule is that a PEG ratio of less than 1.0 may identify an undervalued company. However, one cannot assume that a company’s P/E ratio is too low simply because the company’s PEG ratio is lower than the S&P 500 PEG ratio. For example, the S&P 500 PEG ratio was approximately 1.5 in late 2006. If a growth company has an estimated earnings growth rate of 30%, one might be tempted to say that it is undervalued if its P/E ratio is less than 45 (1.5 × 30). The PEG ratio is not a directly proportional relationship. The PEG ratio actually decreases as the earnings-per-share growth rate increases.
Finally, an approach that has a rich historical basis is the price-to-book (P/B) ratio. To calculate book value per share, the shareholders’ equity section of the balance sheet is divided by the number of shares outstanding. The stock’s price per share is divided by the book value per share to obtain the P/B ratio. A P/B ratio of less than 1.0 was a common benchmark for identifying possibly undervalued companies.
The strong stock market performance of the late 1980s and 1990s pushed the average P/B ratio of the S&P 500 average to more than 5.0. By 1999, very few stocks had P/B ratios near 1.0, other than those of companies that were near bankruptcy. As a consequence, this method had fallen into disuse by all except diehard Graham and Dodd value investors (Cottle, Murray, and Block 1988). In late 2006, however, after the 2000–2002 correction and subsequent recovery, the S&P 500 P/B ratio was at about 3.0.
No single equity valuation method should be used alone. Even if a company has positive earnings and pays dividends, an investor should calculate the intrinsic value using most or all of the previously listed methods. At times, each method will lead you to the same conclusion; at other times, the methods may leave you in limbo, wondering if your analysis is flawed. In the latter case, you may decide that no rational decision can be made at the moment.
Reading the next part of this chapter will enable you to:
4–3 Calculate the intrinsic value of a stock using various stock valuation techniques or calculate the expected return of a stock.
There are basically three different types of dividend growth valuation models that you should be familiar with:
1. the zero growth or dividend in perpetuity, 2. the constant dividend growth model, and 3. the non-constant dividend growth model.
The Zero Growth Model
The zero growth model is also known as the dividend in perpetuity model. This is commonly used to evaluate stocks whose dividend is fixed and will never grow. This situation is most frequently encountered with preferred stocks that have a fixed dividend rate with no maturity date. This formula breaks down to a very simple form, where we just take the cash flow (the annual dividend amount) and divide it by the required return:
r D V= 0
To illustrate this method we will look at a preferred stock trading on the NYSE: Xcel Energy Series A $3.60 preferred stock. The stock has a stated dividend rate of $3.60. This is a fixed rate and will not grow in the future. An investor who required a return of 7% on his investment would use this for his “r” (required return). The formula would yield the following valuation:
43 51 07 60 3 . . . =
stock is overpriced. Another even easier way to assess valuation on a preferred stock would be to simply look at the yield. If the yield is less than your required return, it would be considered overvalued. A quick look at the yield on Xcel Energy Series A preferred confirms this. The yield is 4.83%, which is lower than the required return of 7%, making the stock overvalued at $74.50. The stock would have to trade at $51.43 or below for the yield to equal or exceed the required return of 7%.
There is a great amount of interest rate risk with preferred stocks, since there is no stated maturity. For example, using the same Xcel preferred, let’s say interest rates increase from 7% to 8%. To find the intrinsic value:
45 08 60 3 $ . . =
The intrinsic value of the preferred when interest rates were 7% was $51.53. With interest rates a point higher at 8% the intrinsic value drops to $45.00, a decrease of $6.53 or 12.7%. Investors sometimes think of preferred stocks as “safe,” but as can be seen by this 1% change in interest rates preferred stocks do have quite a bit of interest rate risk.
Constant Growth DDM
The second type of dividend growth valuation is the constant growth dividend discount model, which is used to calculate the intrinsic value of dividend paying stock. It is essentially an extension of the zero growth model already covered. The difference is that we now have a cash flow (annual dividend) that is growing over time rather than a cash flow (annual dividend) that stays the same. To take into account this growth, we introduce a growth rate into the formula, so
r D V= 0 becomes: D V = 1
The D1 in the numerator stands for “D(1 + g)”—in other words we are now going to increase the dividend by the amount we anticipate it will grow each year by taking the annual dividend and multiplying by 1 plus the growth rate. Note: On the denominator, we are going to subtract the growth rate from the required return rather than just using the required return as we did in the zero growth model.
With the constant growth dividend discount model, the assumption made is that the dividends will continue to grow at the same rate in perpetuity.
Calculation
Calculating the intrinsic value of a stock using the constant growth DDM requires three inputs:
1. current-year dividends
2. estimated growth rate of dividends 3. required return
Current-year dividends are the easy part. Calculating the estimated growth rate of dividends is more difficult. If we assume that the payout ratio will remain
constant (an important assumption in the DDM), then we can use the estimated growth rate of earnings as the estimated growth rate of dividends.
g r D g r ) g ( D V − = − + = 0 1 1 where
V = Intrinsic value of the stock D0 = Current-year dividend
r = Required return g = Dividend growth rate
To thoroughly understand the formula and its application, you should experiment with different assumptions of growth rate and required return to see what impact they have on the final result for V.
The dividend growth rate is a function of the company’s return on equity (ROE) and the retention rate of earnings (rr), which is 1 minus the dividend payout ratio. Specifically, g = ROE × rr. It makes sense that, everything else held constant, the higher the ROE, the faster dividends can grow. Likewise, the more earnings retained to generate additional growth, the faster dividends can grow in the future. This will be covered further in the next module on security analysis. For the preceding equation to work, the required return must exceed the dividend growth rate. If that is not the case, a different valuation method must be used.
Example. Thor Industries pays an annual dividend $2.00 per share, and its dividends are expected to grow at 6% annually. If your required return is 10% then what is the intrinsic value of Thor?
06 10 06 1 00 2 . . ) . ( . V − =
Note that we use the decimal form, not a whole number, for the growth rate, so 6% is .06. Also note that since we are using the decimal form for the growth rate, we must also do so for the required return, so this is expressed as .10.
06 10 06 1 00 2 . . ) . ( . V − = = 04 12 2 . . = $53.00
This then tells us that the intrinsic value of Thor Industries is $53.00, meaning if it is priced in the marketplace at $53 or lower we would purchase it. If it is trading above $53 a share we would not purchase it because it would be overvalued, and we would be paying too much for it.
Fair Market Value Relative Value Action
Less than $53 Undervalued Buy
$53 Fairly valued Buy
Greater than $53 Overvalued Do not buy, or sell short
Expected Return
While we are looking at the constant growth DDM, let’s take a look at another formula, the expected return formula:
g P D r = 1+
The formula for the expected return of a security is derived from the formula for computing a security’s intrinsic value. The distinction between the two formulas is that in the intrinsic value formula, the objective is to compute the price at which the security should sell; in the expected return formula, the security’s current price is one of the known factors, and the objective is to determine the total return that the security should achieve given its current price and its expected dividend growth (current income) and market value growth
(appreciation). The dividend growth and the appreciation are assumed to be at the same rate.
to earn the required return) and undervalued securities lie above the capital market line (their prices are so low that you will earn more than the required return rate).
The required return is often confused with the expected return. In fact, the term expected return is used by some analysts when what they really mean is required return. Rather than trying to change people’s habits, which is impossible, you will have to develop an ear for knowing when someone really means required return instead of expected return.
Required return is the return required by an investor to induce him or her to part with the dollars that will be required to invest in any particular security. If an investor cannot feel some degree of comfort that a security’s required return can be achieved, then the investor should not invest in the security. Required return can be computed using the capital asset pricing model formula
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.Expected return is the return that can be expected given the current price of a security and the security’s expected growth (the “g” in the DDM). If the security is undervalued using the DDM, then the expected return, as computed, will exceed the required return; if the security is overvalued using the DDM, then the expected return will be less than the required return.
Returning to our Thor Industries example, let’s see what happens using three different market prices, $50, $53, and $56 in the formula:
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Note that when the stock is priced at $53 (the intrinsic value we came up with earlier) the expected return is 10%, which matches our required return of 10%. When the stock is undervalued (at $50) note that the expected return (10.24%) is now greater than our required return. When the stock is overvalued (at $56) the expected return (9.79%) is now less than our required return.
It is important to note the relationships here. If we calculate the intrinsic value of a stock using the DDM, and know that this stock is fairly valued (trading at intrinsic value), then we know our expected return will match our required return. Or, approached another way, if we were to do the expected return calculation first and the expected return matched our required return, we would know that the current market price of the stock is equal to its intrinsic value.
If we calculate the intrinsic value of a stock using the DDM, and know that the stock is undervalued, then we know that our expected return is going to exceed our required return. If we were to do the expected return calculation first and the expected return was more than our required return, we would then know that the stock is undervalued.
If we calculate the intrinsic value of a stock using the DDM, and know that the stock is overvalued, then we know that our expected return is going to be less than our required return. If we were to do the expected return calculation first and the expected return was less than our required return, we would then know that the stock is overvalued.
Let’s look at a hypothetical scenario.
Example—Intrinsic Value
Victor and Helga Leichtenstein want to begin investing in stocks. They believe that 12% is a reasonable required rate of return. They are considering buying one of the following two stocks, which have the following characteristics:
XYZ Corp. Dividends are currently $1.80 annually and are expected to increase by 6% annually; the current market price is $26.
Which stock should they purchase and why? Stock ABC: $33.75 .05 .12 (1.05) 2.25 V = − = 10.63% .1063 .05 42 (1.05) 2.25 r = + = = Stock XYZ: $31.80 .06 .12 (1.06) 1.80 V = − = 13.34% .1334 .06 26 1.80(1.06) r= + = =
Stock ABC has an intrinsic value of $33.75, but is trading in the marketplace at $42. It is clearly overvalued and should not be purchased. Note also that the expected return of 10.63% is lower than their required return of 12%. Stock XYZ, however, has an intrinsic value of $31.80, but is trading in the marketplace at just $26, so it is undervalued and should be purchased. Note also that the expected return of 13.34% is greater than their required return of 12%. If their required rate of return were to decrease from 12% to 11%, would you make the same selection?
$39.37 .05 .11 (1.05) 2.25 V = − = 10.63% .1063 .05 42 (1.05) 2.25 r = + = = Stock XYZ: $38.16 .06 .11 (1.06) 1.80 V = − = 13.34% .1334 .06 26 (1.06) 1.80 r = + = =
Now stock XYZ is even more undervalued, and would remain the correct choice for the Leichtensteins. As the required return goes down, the intrinsic value of the stock will go up. Conversely, as the required return goes up, the intrinsic value of a stock will go down.
The Non-Constant Growth Model
The third type of dividend growth model, the non-constant or multistage growth model, has been tested on the CFP® Certification Examination in recent exams. Since there is no formula for it on the exam formula sheet, you will have to memorize the steps. The theory behind this model is that many companies in their earlier growth stages will have dividend growth rates that are not
sustainable over long periods of time. At some point the growth rate will slow as the company enters a more mature stage of growth.
Example. Let’s look at a hypothetical company that recently paid a dividend of $0.35 per share for the year just completed. The company is expected to grow this dividend at a rate of 20% for the next three years, after which the growth rate is expected to level off at 8% for subsequent years. The required return is 12%.
Step One
What is the dollar amount of the dividend at the end of the first three years of super normal growth?
Year 1 0.35 × 1.20 0.42
Year 2 0.42 × 1.20 0.504
Year 3 0.504 × 1.20 0.6048
You should take note of a common trap here. Make sure you don’t use the dividend most recently paid as your dividend for Year 1. You must multiply by the growth rate to get the dividend for Period D1.
Step Two
What is the value of the stock at the end of Year 3 based on the dividend at the end of Year 3?
Use the constant growth formula for this step:
( )
1633 08 12 08 1 6048 . . . . . = −Make sure to realize that you are using the dividend at the end of Year 3 to calculate the value for the stock at the end of Year 3.
Step Three
Use your calculator to solve for “NPV”—net present value, of an irregular cash flow. The “NPV” key is the alternate function on the “PRC” key (found just below the payment key) on the HP-10BII+. On the HP-12C the NPV key is the alternate function on the “PV” key —“f, NPV.”
The cash flow key “CFj” on the HP-10BII+ is the second key below the “PV” key. This is the key you will use for any cash flow entries.
On the HP-12C there are two cash flow keys. The initial cash flow is always entered as “CFo,” and any subsequent cash flows are always entered as “CFj.” On the HP-12C the “CFo” key is the alternate function on the “PV” key (g, CFo), and the “CFj” key is the alternate function on the “PMT” key (g, CFj).
The keystrokes are as follows:
HP-10BII+ HP-12C 12 I/YR 12 i 0 CFj 0 CFo 0.42 CFj 0.42 CFj 0.504 CFj 0.504 CFj 0.6048 + 16.33 = 16.9348 CFj .6048 + 16.33 = 16.9348 .CFj SHIFT, NPV 12.83 f, NPV 12.83
Note that in Year 3 you combine the dividend for that year with the discounted value of the stock at the end of Year 3 based on the constant growth formula, and enter just this one number (in this case 16.9348). Do not enter them separately! This sum is then discounted back to the present using the discount rate of 12%. Another way to think of this is in terms of a time line:
Here is another example of the non-constant growth dividend discount model:
Example. Robert Robertson III is interested in buying a stock that currently pays a dividend of $0.60 cents per share annually. His required return on investments is 9%. The dividend is expected to grow 15% annually for the next two years, followed by an expected growth rate of 6% thereafter. What is the most that Robert should pay for the stock?
Step 1: Find the amount of the dividend at the end of each of the two years of non-constant growth: 0.7935 1.15 0.69 0.69 1.15 0.60 = × = ×
Step 2: Find the value of the stock at the end of Year 2 based on the dividend to be paid at the end of Year 3:
28.04 0.06 0.09 1.06 0.7935 = − ×
Step 3: Using the calculator, solve for the PV of unequal cash flows as follows: HP-10BII+ HP-12C 9 I/YR 9 i 0 CFj 0 CFo 0.69 CFj 0.69 CFj 0.7935 + 28.04 = 28.8335 CFj 0.7935 + 28.04 = 28.8835 CFj SHIFT, NPV 24.90 SHIFT, NPV 24.90
Reading the next part of this chapter will enable you to:
4–4 Evaluate the appropriateness of investment decisions based on stock valuation models.
Valuation Exercise—Merck & Co.
To demonstrate the calculation of the intrinsic value of a stock, we will use 2009 financial data from Merck & Co. (as of 9/30/2009), drawn from the Morningstar and Smart Money websites.
Calculating the intrinsic value of MRK using the constant growth DDM requires three inputs:
1. current-year dividends of MRK
2. estimated growth rate of MRK’s dividends 3. required return for MRK
Current-year dividends are the easy part. The annual dividend reported was $1.52 per share.
Calculating the estimated growth rate of dividends is more difficult. If we assume that the payout ratio will remain constant (an important assumption in the DDM), then we can use the estimated growth rate of earnings as the estimated growth rate of dividends. The data for MRK shows that earnings are expected to grow at a 3.3% rate over the next five years according to SmartMoney. We will use a required return for large-cap stocks (the asset class of which MRK is a member) of 9.6%, which is the long-term return number for large-caps from Ibbotson. Using these inputs for the equation, the computation of the intrinsic value of MRK using the DDM is as follows:
$24.92 .033 .096 .033) (1 1.52 g r g) (1 D V 0 = − + = − + = where
V = Intrinsic value of the stock D0 = Current-year dividend
r = Required return g = Dividend growth rate
The intrinsic value of MRK is approximately $25 per share, based on the inputs used. This compares with a recent market quote of $35, which would indicate that the stock is approximately $10 overvalued. Note the importance of accurate assumptions when using the formula. Let’s do the calculation assuming a 4.5% earnings growth rate, which is Merck’s 5-year earnings growth rate according to Morningstar: $31.15 .045 .096 .045) (1 1.52 g r g) (1 D V 0 = − + = − + =
Or if we use the 10-year average earnings growth rate, which is 5.4%: $38.15 .054 .096 .054) (1 1.52 g r g) (1 D V 0 = − + = − + =
So you can see that the formula is very sensitive to relatively small changes in the input. With a growth rate of 4.5%, the intrinsic value comes out to be $31.15, which is below the $35 market current price, meaning that the stock is
overvalued. However, if we use a growth rate of 5.4%, then the stock’s intrinsic value is $38.15, which is above the current market price, meaning the stock is undervalued.
To thoroughly understand the formula and its application, you should experiment with different assumptions of growth rate and required return to see what impact they have on the final result for V.
Using the same data for MRK, we can compute the expected return as follows for the various growth rates:
3.3% growth rate: 7.79% .0779 .033 35 .033) (1 1.52 g P g) (1 D r= 0 + + = + + = = where r = Expected return D0 = Current-year dividend P = Current price
g = Dividend growth rate 4.5% growth rate: 9.04% .0904 .045 35 .045) (1 1.52 g P g) (1 D r= 0 + + = + + = = 5.4% growth rate: 9.98% 0998% .054 35 .054) (1 1.52 g P g) (1 D r= 0 + + = + + = =
Remember that our required return is 9.6%, and note that only the last scenario, using 5.4% as our estimated growth rate, gives us an expected return greater than 9.6%. This, of course, is also the only scenario we looked at where the stock comes out to be undervalued. If a stock is undervalued, then the expected return will be greater than the required return. If a stock is overvalued, then the expected return will be less than the required return.
P/E Ratio
To compute the projected value of MRK using the P/E (price to earnings) ratio, the input factors are the current price of the stock and the current and projected earnings of the company. The P/E ratios of the industry and of the market are also required.
The projected 2009 annual earnings (from SmartMoney) for Merck were $3.27, so to arrive at a P/E ratio we simply take the current price of $35 per share and divide by $3.27.
10.7 $3.27
$35 =
When this analysis was done the P/E ratio for the market was approximately 20.9, and the P/E ratio for the drug industry was approximately 11.3.
For our P/E ratio calculation above, we used estimated 2009 earnings of $3.27 per share, and we should also look at the earnings estimate for 2010, which is $3.46 per share. The value of MRK using P/E multiples is shown in Table 1. The earnings per share are multiplied by the P/E ratios to obtain the valuation
estimates.
Table 1: Valuation Based on P/E Ratios
Factor Based on 2009 Projected Earnings $3.27 Based on 2010 Projected Earnings $3.46 MRK P/E 10.7 $35 $37.02 Industry P/E 11.3 $36.95 $39.10
Using industry and market P/E ratios, MRK has a projected value that is
somewhere between approximately $37 per share and $39 per share. The $37 is close to both the current value of the stock, and the value computed using the DDM with 4.5% and 5.4% growth rates.
The historical 5-year P/E range for Merck is from 6.30 to 41.40, with an average P/E of 19.3. Merck’s current P/E at 10.7 is below the historic average, which means there is a chance for an increase in price if there is an increase in the P/E ratio.
PSR
The total revenues of MRK for the trailing 12-month (ttm) period ending 9/30/2009 were approximately $17.9 billion; total shares outstanding were 2.1 billion. Dividing revenue by shares gives us sales of $8.52 per share. The current market price of the stock is approximately $35 per share. Therefore, the PSR for MRK is calculated as follows:
4.1 $8.52
$35 =
The industry average for price to sales according to Morningstar is 2.7. (This is the average PSR for Merck, Abbott Labs, Bristol-Myers Squibb, Johnson & Johnson, Eli Lilly, and Pfizer.) This indicates that Merck has a high price to sales ratio relative to the industry, which leans to it being overvalued based just on this ratio. The PSR for the general market is 1.2.
PEG Ratio
The PEG ratio is calculated by taking the P/E ratio and dividing it by the earnings growth rate. Generally, the lower the PEG ratio, the more likely it is that a stock may be undervalued; however, as with any one ratio or measurement, this number alone will not tell the entire story.
We will look at PEG ratios based on SmartMoney growth estimates as of 11/19/2009:
Table 2: PEG Ratio Forward P/E Ratio Next 5 Years Growth Rate Current Year PEG Ratio MRK 10.8 3.3% 3.3 Drug industry 11.3 15.7% 0.7 Source: Morningstar
Table 2 shows us a couple of things. First, the P/E ratio of Merck is essentially the same as the P/E ratio of the drug industry in general. However, drug stocks in general have higher earnings growth rates than Merck. So this means that the PEG ratio for the drug industry is lower than the PEG ratio for Merck, suggesting that Merck may be overvalued relative to the overall drug industry. There may better values found in other drug stocks, but again remember that this is just one ratio.
P/B Ratio
The book value of a company is the amount reported as shareholders’ equity in the balance sheet of the corporation. Most reporting services do the computation on a per share basis so that investors do not have to search through financial statements to find book value in dollars and make the conversion themselves. The Morningstar website shows a book value for MRK of $7.26 per share. With the current market price of MRK’s stock is approximately $35 per share the P/B ratio is computed as follows:
4.8 $7.26
$35 =
The price to book ratio average for the drug industry is 3.8. This analysis would indicate that the current ratio for Merck is higher than that for the industry average. Traditionally, a P/B ratio closer to 1.0 would indicate an undervalued stock to a strict value investor. In recent years, however, P/B ratios have risen far above 1.0, so an undervalued security would be one with a ratio less than the market ratio or the industry ratio.
Summary
The valuation measures computed above are summarized in Table 3. Table 3: Valuation Summary
Valuation Method Computed Value
DDM $25–$38 P/E projected 2009 $35–$37 P/E projected 2010 $37–$39 PSR 4.1 PEG ratio 3.3 P/B 4.8
During 2009 MRK traded between $20.05 and $38.10 per share. An investor who is considering purchasing MRK stock must make a decision about the stock’s appreciation potential, given the current price. Different analytical tools can lead an investor to different conclusions. Let’s look at the factors we considered in our decision-making process regarding a purchase of MRK stock.
DDM. The DDM shows that MRK stock is currently overvalued by up to $10 per share. If the more favorable growth rate of 5.4% is used, then the stock is undervalued by about $3 a share. The denominator is the key to DDM valuation analysis. The discount rate used for required return was 9.6%. It could be less, or it could be more. Even a scientific approximation of the appropriate required return rate could be questioned by another equally qualified analyst. In our analysis we used different dividend growth rates. If the spread between r and g is smaller than computed, then the intrinsic value is higher than the figure computed; if the spread is larger, then the intrinsic value is lower than the figure computed.
multiple expansion that would increase the price of the stock. The company’s financial statements should be analyzed in greater detail to determine whether this conclusion is justified.
PSR. In the current market environment, the PSR of MRK appears high, coming in at 4.1 compared with an industry average of 2.7. The PSR analysis alone would indicate an overvalued stock with limited upside potential.
PEG ratio. The PEG ratio shows a fairly substantial premium when compared to the PEG ratio for the industry. The PEG ratio does seem to confirm the conclusion from the other analysis that the stock may be overvalued.
P/B ratio. This analysis also indicates that MRK may be overvalued, selling at a P/B ratio of 4.8 compared with an industry average of 3.8. P/B ratios are not as significant to security analysts as they have been in years past, so the P/B ratio should be given the least weight in the analysis.
Overall Conclusion
One can see that different methods of analysis will lead to different conclusions regarding the fair value of a stock. It is important not only to analyze a
company’s current fundamentals, but that analysis should be compared with the historical norms for the company, with the industry averages, and with the market as a whole.
The use of the DDM, and the few ratios we have looked at, is just a start when it comes to analyzing individual securities. There are many more ratios that can and should be considered, such as liquidity and cash flow ratios, inventory turnover ratios, profitability ratios, and return on equity, to name a few. There may also be other fundamental information that is equally important, such as changes in management, products, or competition. For example, Merck went through a major acquisition in the fourth quarter of 2009 and acquired Schering-Plough— a transaction that totals about $41 billion in cash and stock. Merck’s market
capitalization prior to the acquisition was in the neighborhood of $70 billion, so this will have a major impact on Merck.
Many individuals who are interested in analyzing securities obtain the CFA Charter (Chartered Financial Analyst), which is offered through the CFA Institute (ww.cfainstitute.org). The CFP certification is geared more toward helping individuals with their financial planning needs, and not toward becoming an expert on security analysis. For the CFP certification you just need to know the very basics when it comes to ratio analysis.
In the next module we will take a look at Investment Policy Statements, and at three very important ratios: Jensen (alpha), Sharpe, and Treynor.
Chapter 3: Security Performance
Evaluation
Reading the first part of this chapter will enable you to:
4–5 Explain the various components of the Investment Policy Statement (IPS).
Investment Policy Statements (IPS)
ffective portfolio performance evaluation depends upon an appropriate standard against which to evaluate investment decisions and
performance. Many such standards include relative performance against an index, measured by returns on that index. There are also statistical measures available that are discussed below: the Sharpe, Treynor, and Jensen (alpha) indexes.
Absolute performance measures are also used, such as inflation plus some percentage (e.g., inflation plus 5%).
Regardless of which of these absolute and relative performance measurement approaches are used, performance against an investment policy statement should be the first step in the evaluation process.
A well-drafted investment policy statement (IPS) reduces ambiguity and provides guidance to any and all investment professionals needing to interact to implement the IPS. If an IPS exists, a new relationship can be quickly established in the event of an advisor change, providing clarity to the newly hired investment professional. In addition, when investment recommendations are made, the recommendations can be evaluated against the standards set in the IPS to determine suitability.
According to Boone and Lubitz (Creating an Investment Policy Statement, FPA Press), an IPS serves four basic purposes:
1. Setting objectives. This includes establishing and defining client expectations concerning risk and return, and providing guidelines on how the assets are to be invested.
2. Defining the asset allocation policy. This requires identifying various asset classes that will be used to achieve the investor’s objectives, and determining how best to allocate the assets to achieve a diversified portfolio.
3. Establishing management procedures. A guide needs to be put in place as far as selecting and monitoring the investments, and making changes as necessary. There also needs to be a way to evaluate the performance of whoever is in charge of the investment process.
4. Determining communication procedures. A concise method of
communication needs to be in place so that all parties involved are aware of the process and objectives, and responsibility must be assigned for
implementation. Quoting Boone and Lubitz:
“For the typical investor, a lack of information, the absence of a systematic approach, and emotional and behavioral factors often lead to irrational or inappropriate investment decision. The creation and use of an IPS helps clients and advisors make prudent, rational decisions about their investments. This process will generally help both the investor and the advisor become better and more successful in their respective roles.”
There are no set IPS statement standards, but the following minimum content areas would result in a comprehensive and relatively complete IPS. A properly crafted IPS will keep both the client and the advisor on track, and minimize any disagreements or confusion.
Risk tolerance. At a minimum, this should state if the portfolio volatility is to be low, below average, average, above average, or high. There are two major areas to address with risk tolerance: (1) the ability to take risk, and (2) the willingness to take risk. They are not the same thing. Ability has to do with resources and circumstances. Someone in good health, properly insured, with adequate savings, and $5 million in investments would most likely have a high ability to take risk. However, this same individual may not like to see his account balances move much, and may have a very low willingness to take risk. Or, based on his return objective, he may not need to take much risk to achieve his objective. Other statements reflecting risk tolerance issues also can be addressed. If the risk level is to decline in several years due to an expected change in circumstances—such as retirement—statements to that effect should be included. One caveat here is that the risk tolerance objective should be consistent with the return requirement. For example, if the return requirement needed to meet the client’s goal is 10%, but they have a conservative risk tolerance, something has to give. Either they are going to have to take on more risk, lower their return requirement (thus downsizing their goals), or a combination of the two.
Liquidity. Any liquidity constraints, such as an emergency fund, a fund for a vacation or car purchase, or an amount needed within the next three to five years to fund an anticipated cash expenditure, should be included here. Generally, many advisors do not invest assets in the stock market that will be needed within the next five years.
Time horizon. Short, intermediate, or long-term horizons should be indicated for the achievement of investment goals. All three may be represented due to the existence of short-, intermediate-, and long-term goals. For example, an individual may have a personal short-term time horizon for education cost, and then have a long-term time horizon for retirement. A long-term time horizon may also be applicable to certain assets that are expected to be gifted or willed to family members or charities.
Laws and regulations. Individuals have few laws and regulations with which to be concerned. If an IPS is developed for a retirement plan or endowment, then regulatory issues may be more complex—such as compliance with ERISA.
Taxes. For individuals, the objective generally is to minimize the income tax consequences of all investment transactions. Estate taxes may be an issue for elderly clients. For retirement plans and IRAs, taxes generally are not an issue, at least until required distributions must be made.
Unique preferences and circumstances. This refers to things the client brings up as issues. Included may be statements about outside income that may be received, such as royalties; restrictions on security transactions applicable to insiders; trusts that may provide current or future income or assets; prospective inheritances, especially if expected soon; and concerns about any other issues, such as inflation and depression.
Permitted and excluded investments. All clients have some favorite types of investments and some investments with which they may have had some negative experiences over their investing lives. If the client wants to include or exclude certain of these investment asset classes or types, they should be listed here.
Constructing an IPS
A properly constructed IPS should be designed for that particular client—a “cookie-cutter” or “one-size-fits-all” approach will not work well. One test of a well-written IPS is whether the client could have remained committed to the parameters of the IPS based on what the capital markets have done over the past decades. Given the dramatic decline and volatility of the markets in 2008 and 2009, we may well see a different appreciation of what “risk” means going forward.
Here is a template of how an IPS could be constructed:
Investment Policy Statement for John Doe
I. Investor Circumstances
II. Investment Objectives a. General
b. Portfolio Return Objective c. Rationale and Justification
III. Risk Tolerance a. Ability to take risk b. Willingness to take risk c. Risk Tolerance Objective
IV. Client Liquidity Needs
a. Rationale and Justification
V. Time Horizon
a. Time Horizon Objective b. Rationale and Justification
VI. Income Tax Constraints
VII. Other Unique Needs and Circumstances
VIII. Asset Allocation
For more information on investment policy statements and how to construct them, you can refer to Creating an Investment Policy Statement by Boone and Lubitz (FPA Press) or visit www.ipsadvisorpro.com.
SWOT Analysis
“SWOT” stands for Strengths, Weaknesses, Opportunities, and Threats and helps both the advisor and the client understand the big picture. When an advisor does a SWOT analysis he or she develops an understanding of how both the internal and external environments impact the client. Strengths and weaknesses reflect the internal environment unique to the client, such as income, net worth, too much debt, deficient insurance, etc. These are areas over which the client has varying amounts of control. The opportunities and threats, on the other hand, reflect the external environment, over which the client has no control. These include such things as current interest rates, rate of inflation, or the cost of education and retirement. A well-thought-out SWOT analysis helps to focus the client on their current situation as well as what they are up against. This analysis can also be helpful in constructing a well-designed IPS, since several of the areas that will come up in this analysis also are relevant to an IPS, such as risk and return, and market expectations.
Following is an example of what a SWOT analysis might look like for a fictional couple, Zack and Zoe Jones:
Strengths:
Zack has a steady job in a recession-proof industry that provides over $70,000 a year in income.
Zoe works part-time and supplements the household income while doing work she enjoys.
Zack and Zoe’s net worth is reasonable for their age.
Weaknesses:
Zack is growing restless in his job and wants to pursue a new career, which would lower their household income.
Too much debt relative to their net worth.
Unrealistic goals for the amount of saving and investing.
Investments are inappropriate and do not match their risk tolerance.
Neither Zack nor Zoe have long-term disability.
Estate planning is inadequate.
Opportunities:
Interest rates are historically low making borrowing, such as for a home, more affordable.
Decline in stocks increases the chances for substantial appreciation going forward, and it may be a good time to dollar cost average into the market.
Lower housing prices makes purchasing an affordable home more likely.
Threats:
Unemployment is high, and this may impact raises and/or employment.
Cost of college continues to rise, presenting challenges for sending Zack Jr. to his dad’s alma mater.
Inflation may be increasing in the coming years.
One can see the strategic thinking that needs to go into a SWOT analysis would also be helpful in constructing an IPS.
