Price earnings ratio (P/E ratio) is the ratio between market price per equity share and earnings per share. Earnings per share is calculated by dividing the net profit after taxes and preference dividend by the total number of equity shares. Earnings per share (EPS) is the portion of a company’s profit allocated to each outstanding share of common stock. Note that EPS can be from the last four quarters (trailing P/E) or the sum of the last two actual quarters and the estimates of the next two quarters, but it is important to note that the P/E ratio is a measure of investors’ expectations as to future earnings and not for current earnings. In many cases, the ratio of a stock price to earnings per share or the price which must be paid for each pound of the firm’s earnings is used as basis for comparing the investment characteristics of different shares. A share price on its own tells us little or nothing about its investment value. Two companies with identical prospects, assets and aggregate equity value may have different share prices quite simply because one firm has fewer shares outstanding than the other. This may be the result of a company having fewer shares issued at a higher price than the other or it may mean that a company paid out fewer dividends in order to finance its past growth through retentions, while the other company paid out higher dividends and raised capital by issuing more shares to fund its investment programmes.
In other words, two identical companies can have different prices as a result of the number of shares outstanding. Since EPS and share prices can be affected by the number of shares outstanding P/E will neutralize the impact of these differences. By dividing the stock price by earnings per share a simple way has been found of standardizing share prices that otherwise cannot be meaningfully compared. For example, the Barclays PLC which is a major global financial services provider is currently trading (Po) at 315p a share and the Earnings per share expected in the next four quarters (E1) are 34.99p per share. The P/E ratio for the stock of Barclays PLC will be equal to 9 times (315p/34.99p). In our case, which Barclays PLC is currently trading at a multiple (P/E) of 9 times, the interpretation is that an investor is willing to pay 9 pounds for each pound of current earnings.
In order to identify and briefly discuss the theoretical determinants of P/E ratio the Gordon growth model will be utilized. The Gordon growth model, named after its inventor Myron Gordon, makes the dividend valuation model easier to use by combining it with additional assumptions, which will be given later in our discussion. Shares are valued on the basis of the payoffs which they are expected to generate for investors. In principle the value of the payoff expected from holding a share is simply the present value of the cash flows anticipated by investors. What investors expect to get out of any share they hold are dividends (Dt) and the proceeds (PN) from the sale of the share at the end of the planned holding period (N). The present value of the expected cash flows (the dividends expected and the proceeds from the sale) is determined by using a discount rate which is equivalent to the rate of return which investors can earn on investments in other shares of similar risk (r). The value of the share (Po) may be determined by using a model of the following nature:
A simple valuation equation can also be developed for the shares of a firm that retains some of its earnings to finance investment as long as its assets, earnings and dividends can be expected to grow at a constant rate (g). This produces the following model, referred as the Gordon Model (see Gordon, 1959).-
where D1 = D0 (1+g)
This model suggests that the price of share is a function of the dividend expected in the next period (D1), the rate of growth of dividends (g) and the discount rate (r).
By specifying the dividend, in terms of earnings per share (E1), the retention ratio (b) and the payout ratio (1-b) the above model can be demonstrated as below:
Some insights into why price-earnings ratios can be expected to vary from firm to firm can be derived form a consideration of the previous model. This particular model suggests that the prospective P/E ratio will be higher the lower the discount rate (r), the greater the expected rate of growth (g), and the lower the retention ratio (b).
In the case that the expected growth rate (g) is the same as the historical growth the prospective P/E ratio can be adjusted to obtain a ratio based on the last reported earnings:
At first sight it is evident that there is an inverse relationship between the P/E ratio and the retention ratio (b), but this cannot be true since firms can not influence their P/E ratios by manipulating their retention ratios. Stockholders will pay more per pound of earnings the greater the proportion of earnings paid out in dividends all else being equal, but any reduction in retention will lead to a fall in investment, which will lead to a decrease in the expected rate of growth of dividends. The constant growth model has become the most widely employed theoretical model because of its simplicity. The simplicity of the constant growth model is a reflection of the assumptions on which the model is based, and the awareness of these assumptions is essential for the recognition of its weaknesses and strengths. It is assumed that:
all investment is financed from retentions and a constant proportion of earnings is retained in each time period;
the rate of return on the firm’s investments is constant over time, as the rate of return on existing assets; and
the cash flow produced from investments is constant in perpetuity.
The differences in P/E ratios reported in the financial press cannot all be explained by the determinants of the P/E ratios identified by the valuation models. For example, one of the reasons for those differences can be the differences in the accounting methods employed by firms. The valuation models are based on an idealised notion of expected earnings per share; the firm’s expected cash flows minus an allowance for depreciation, calculated on an economic basis, while observed P/E ratios, reflect more pragmatic definitions of earnings. It is well known that differences in accounting methods have a significant impact on earnings per share but do not have any impact on share prices (the market sees through the effect of accounting differences). Generally, differences in earnings per share arise from differences in accounting methods which lead in differences in reported P/E ratios. Those firms employing depreciation policies with high charges have lower reported earnings per share (since depreciation is charged against revenues as an operating expense) and higher price earnings ratios than firms using straight line depreciation. Another factor that might influence the value of the company’s reported P/E ratio is transitory changes in earnings. Beaver and Morse (1978) at a later study realised that the observed spread of P/E can be explained by the difference between equilibrium and actual earnings. Changes in earnings which are of temporary nature will not lead to proportionate change in the share price but to higher P/E ratio if negative transitory earnings occur and lower P/E ratio if positive transitory earnings occur. As a result, firms with low earnings will have high P/E ratios, without being growth firms at all.
The sample of shares chosen to discuss and explain the possible reasons for the differences in the reported price-earnings ratio belong to the banks operating in the United Kingdom. It is important to choose companies that are in the same industry since this is the only way that P/E ratio analysis can have any significant comparable meaning.
The data gathered are presented in the table below:
Royal Bank of Scotland Group
Lloyds Banking Group
Price – earnings ratios were calculated based on the companies’ current share price and the estimated earnings per share for year 2011. P/E ratios calculated this way are known as forward price earnings ratios. Forward P/E ratios can give investors a more meaningful result than do trailing P/E ratios that are calculated by dividing the current share price by the trailing earnings per share for the last 12 months. Trailing P/E ratio is a historic measure while forward P/E is more useful and informative. After all, it is the future that counts; you are paying what the company will do in the future rather than what the company did in the past. Another reason that forward P/E ratios are used in this case is that the P/E for Lloyds could not be calculated by using EPS of the past 12 months because the firm had a bad year. Lloyds suffered a loss of 0.5p per share and calculation of P/E based on this figure would give a meaningless result.
The figures presented at the table above suggest that the market has more confidence in the ability of RBS to continue increasing its earnings, but at the other side it believes the outlook for Barclays is unpromising. A high P/E ratio indicates that investors are paying more for each unit of earnings, so the stock is more expensive compared to those stock with low P/E ratios. The P/E ratio is commonly used to assess the level of confidence investors have in a company. It represents the market’s view of the company’s growth potential. A high price-earnings ratio indicates that investors have a high level of confidence in a company’s future prospects. As we can see from the table presented, RBS has the highest price-earnings ratio, indicating that investors of the Banking sector have a high level of confidence in the company’s growth potential prospects, it might equally be considered to be overvalued depending on prevailing market circumstances. RBS has a P/E ratio of about 13, implying that investors are currently willing to pay £13 for every pound of earnings RBS generates. Similarly, Barclays P/E ratio of around 9 implies that investors are currently willing to pay 9 pounds for each pound Barclay makes.
For a different perspective, try flipping the P/E ratio to an E/P ratio, commonly referred to as the earning yield. Like a yield on a bond, this number shows a company’s annual earnings as a proportion of its market value. Buying one share of RBS at 44.66p, with EPS 3.4p equates to an earnings yield of 7.6% (3.4p divided by 44.66p). For Barclays, the earning yield is 11.1%, because each share, currently trading at 315p is expected to generate a 34.99p in earnings per share. In long run, Barclays investors theoretically should earn a better rate of return than RBS investors for each pound invested. Yet the true outcomes could be different.
The question that arises is whether the difference in P/E ratios alone makes one company a better investment than the other. Fundamental problems exist with the P/E ratio. First, the share price (P) doesn’t consider debt since it is the equity price of a business. That is fine with companies without debt, like Google or Microsoft but not for the companies chosen. For instance, business with a market cap of £5 billion, with £1 million of net debt on the balance sheet, has an enterprise value of £6 billion. If this company earns £500 million in profit in a given year, the P/E ratio will be 10; but in reality, investors should see 12. The logic embodied in the conventional wisdom that high P/E ratios are good and low P/E ratios bad, is given by the dividend growth rate equation at which dividends (D) is expressed in terms of EPS (E) and retention ratio (b).
The firm’s required rate of return r, can be given as follows:
where i is the firms expected rate of return on future investments.
From this equation is obvious that for any given r and b, the smaller the fraction [E1/P0] is, the larger i must be. Since [E1/P0] is the inverse of the P/E ratio, a small [E1/P0] corresponds to a high P/E ratio. Therefore, all else being equal, the higher the P/E ratio, the higher must be the expected rate of return on future investments; or, more simply, a “high” P/E ratio such as RBS’s corresponds to good future investment opportunities, while Barclays with the lowest P/E ratio doesn’t correspond to good future investment opportunities. Remember the P/E ratios are calculated based on estimated (average) earnings per share. But actual values almost never equal the average. A firm can have a very “high” P/E ratio during a bad year and a very “low” during a good year, yet in both cases, the firm may not have changed fundamentally. A “high” P/E ratio of 13.1 times for RBS is the result of “low” earnings (3.4p) rather than “high” expected rate of return on future investment. Note that RBS with the smallest share value (44.66), has a P/E ratio that is the highest due to very low EPS, the smallest of all companies. The conventional wisdom about P/E ratio can be altered also by the possibility that earnings are not reflecting the actual outcome.
For example, a land sold would create large profits due to the large difference between its historic cost listed on its balance sheet and the current market value. Or, the firm recognizing a bad debt that has existed for several years. Another possibility that can alter the conclusions about P/E ratios is changes in the firm’s accounting procedures. For example, a change of how the firm estimates its inventory, from the First-in-First-out basis (FIFO) to the Last-in-First-out basis (LIFO), lead to a decrease of the firm’s reported earnings in times of inflation. A change in the measure of earnings can cause a change in the P/E ratio that really indicates nothing new about the value of the firm. It can also be suggested that risk will influence the P/E ratio to the direction of influence needs careful consideration. Responsible for differences between the reported P/E ratios is also the expected growth and the way it depends in part on the level of investment and in part on the profitability of the investment. Specifically, one can conclude that a lot more information is needed than just the P/E ratio to estimate the value of a share of stock.
Almost all quoted companies in UK that wish to raise money do so by means of a right issue. A right issue offers existing stockholders the right to buy new shares in proportion to their existing holdings. Rights issues allow stockholders to maintain their interest or proportionate share, in the ownership of the company, by ensuring that new shareholders are not brought in the company to the disadvantage of existing shareholders. Existing shareholders can exercise or sell their rights to other investors who would like to subscribe to the issue.
Specifically, RBS wish to raise £12 billion of new equity capital and will do so by means of a rights issue. RBS shareholders are invited to subscribe to the right issue with an entitlement of 11 new shares for every existing 18 shares they hold at an issue price (PS) of 200p. The subscription price – the price of the new shares – is pitched below the current market price of 372.5p (P0). The discount offered as an inducement to shareholders to subscribe to the new issue is equal to approximate 46.31% (d). The 200p subscription price is calculated as given below:
Once RBS decided on the level of funds (F) to be raised and the subscription price (PS), the number of new shares to be issued can be calculated quite easily:
£ 12 bil / £ 2 = £ 6 billion of shares
And once the number of new shares to be issued is known, the number of shares [N(R)] which an investor must hold to be granted one right can be calculated:
The number of shares outstanding prior to the right issue (N0) must also be calculated in order to determine the ex-rights price. The determination is given below:
The ex-rights price will be a weighted average of the pre-issue price and the subscription price: the weights being given by the ratios of the number of pre-issue shares to the total number shares outstanding following the issue:
The market value of a right [V(R)] depends on the difference between the subscription price (PS) and the expected price of the share following the new issue (PX).
Rights issues are made at a discount, partly to make them “look” attractive and plus encourage stakeholders to subscribe, and partly against the risk of a fall in the market price during the offer period. Whether to invest in the rights or to sell them is the best choice for an investor will be analyzed furthermore.
Assuming that a shareholder owns 900 shares of RBS, through the rights issue he can buy 550 shares at 200p (11 new shares for every 18 existing).
Wealth Effects: the initial wealth with 900 shares at value P0 = £3.72 is:
Initial Wealth = 900 * £3.725
Invest in the rights:
This will happen only if the shareholder has the resources to acquire the additional shares and believes this is the best way to invest his money. Moreover a shareholder may invest in the rights because there are bi stamp or duty brokers’ commissions payable, and the desire to maintain one’s existing share of voting power.
Value of new investment = £3,352.5 + £1,100 = £4,452.5
The value of investment at the ex-rights price will be:
Value of investment at PX = (900+550 shares) * £3.07 = £4,452.5
Thus, the impact on the shareholders wealth will be £0.
Sell the rights
This will happen if the shareholder wants to maintain his existing investment in the company in value terms. In the beginning the shareholder will lose from the fall of the share but he will cover from the loss through selling the rights.
If the shareholder sells the rights, the value of his share at the ex-rights price will be:
Value of shares at PX = 900 shares * £3.07 = £2,763
The declines in the shareholder’s wealth will be:
Decline in shareholder’s wealth = £3,352.5 -£2,763 = £ 589.5
The amount that the shareholder will acquire from the sale of the right at VR = £1.07 will be:
Value from sale of the right = 550 shares * £1.07 = £589.5
Thus, the impact on the shareholders wealth will be £0
From the above analysis it is obvious that the shareholder wealth remains unchanged after the rights issue ether if e invests in the rights or sells the rights. The wealth of the shareholder will change only when the new issue leads to the re-appraisal of the firm’s value. This happens because issue of new shares at a discount leads to the fall in the value of existing shares thereby offsetting the value of the right.
The Royal Bank of Scotland (RBS) announced a rights issue in order to raise £12 billion, which is considered the largest UK equity issue at that time. Under the terms of the rights issue, 11 new shares will be offered to existing shareholders for every 18 shares they hold. The subscription price is pitched well below the current market price of 372.5p. The discount offered as and inducement to shareholders to subscribe to the new issue is equal to 46.13%, well above the conventional level o f 15 to 20 per cent. The discount is pitched at this level in order to assure that the subscription price of 200p [372.5 (1-1.46310)] will remain below the market price over the offered period. The size of the typical discount drifted upward since the stock market at that time became more volatile and because of the size of funds needed to be raised.
At first sight it might appear that the rights issue mentioned above is an attractive proposition for shareholders. The right issue allows the shareholders to increase their holdings of shares in the company at a discounted price, but a closer look at the mechanics of a rights issue reveals that it leaves the wealth of the shareholder unchanged, because the value of the existing shares falls, and this fall offsets the gains provided by the subscription. If the market price of the shares of RBS remains sufficiently above the subscription price of 200p the issue is likely to be successful, otherwise underwriters guarantee to take up any shares which the shareholders decline to acquire.
Specifically, in the case of RBS, the bank agreed with its lead banks that fees would be 1.75 per cent of the proceeds of the average issue. These investment banks that lead the issue will only absorb some of the risk since most of it is passed onto the sub-underwriters of other merchant banks and institutional investors such as insurance companies for a fee of 1%. The question that arises is whether the company will be obtaining value for money for the underwriters’ fee of 1.75 per cent of the proceeds of the issue. In later study, Marsh (1980) found out that underwriting is highly profitable on an ex post basis. In 671 rights issues, only 35 led to losses with an average loss of 4.2%. In the case of RBS, the underwriters were left with unsold shares of less than 5 per cent since 95.11 percent of the shares offered had been taken by the investors. The remaining 299.4m shares were sold at profit by the underwriters, at a price of 230p a share, raising an additional £688.6m (299.4 m shares times £2.3p)
As Merret, Howe and Newbould (1967) comment in one of their first studies, the underwriting charges in the case of rights issues seems somewhat excessive for the minimal risks actually borne bye the underwriters. To incorporate the effects of risk mentioned above the underwriting contract should be viewed as a put option (Marsh 1980). RBS, the issuing firm is in the same position as an investor holding a put option, while the underwriter of the right issue is considered as the writer of a put option. The potential losses or gains of the underwriter are equal to the potential gains and losses of the issuing firm. Marsh found that the cost of underwriting produced an average excess return to the underwriters of 0.7 percent and only in 14% out of 539 underwritten issues the value of the put option element of the underwriting agreement appears to be greater than the fees charged. It seems logical to conclude that underwriting fees are used to compensate for other services provided by the merchant banks, for which explicit charge is not being made. Underwriting cannot be considered too expensive if this is the case.
The profit and loss associated with an underwriting agreement as a function of the share price are illustrated in the figures below:
(a) PROFIT – LOSS FOR RBS
Market share price
(b) PROFIT – LOSS FOR UNDERWRITERS
Alex Porter of Collins Stewart views that investors should take up the rights offered by RBS because buying shares at 200p is incredibly cheap since the 2009 estimated earnings per share of 37p and a price-earnings of 9 indicate that the price of share will be raised to 333p (374p x 9). RBS rights issue seems as an attractive proposition for shareholders since they are given the right to subscribe to additional shares at a discount above the conventional level of 15% to 20%. On the other hand, RBS has employed a large price discount (46.31%) and faces the risk of the dilution of earnings, dividends and assets. The lower the subscription price the larger the number of shares that must be sold in order to raise the fund required by the company. In the case of RBS, 6 billion shares must be issued in order to raise £12 bil of equity capital. There is a fear that the increased claims of the firm’s earnings, dividends and assets will lead the stock market to react adversely to this dilution. An adverse reaction implies that the investors are unable to differentiate between nominal and real changes and that the stock market is inefficient. The fall in earnings per share, as more shares have to be issued to raise the funds required, will be matched by the fall in share price. The fall in share price will be compensated by the increase in the number of shares, leaving the earnings yield of the stockholders’ overall stake in the company unchanged. As a conclusion I believe that Porter’s statement is misleading and creates a misunderstanding, since it implies a share price of 333p which is far greater than the expected ex-rights price of 307p calculated.
The belief that the price of share will have a future value of 333p is very optimistic since the financial crisis of 2007 is considered by most economists the worst financial crisis since the great Depression to the 1930s. There is a fear that the European banking system may collapse as did large financial institutions in the United States. Specifically, S& P no longer considers the UK banking sector to be one of the lowest risk and secure banking systems because of “the country’s weak economic environment, the reputational damage experienced by the banking industry, and high dependence on state support programs”. The risk profile of UK banks is affected by “anticipated system-wide, domestic non-performing and impaired loans” that will remain high throughout 2009 and 2010, linked to high levels of household and corporate debt. The uncertainty surrounding the banking industry must be taken into consideration in analyzing the statement of Porter which is in my opinion very optimistic. One, before deciding buying RBS shares offered at 200p, should consider whether RBS will remain in the following years, structurally strong, and a business that will continue making profits under the conditions discussed above.
An option gives the holder the right to buy or sell on asset by a certain date for a certain price. The option that gives the holder the right to buy is called call option and the one that gives the holder the right to sell is called put option. The price in the contract is known as the exercise or strike price (x), and the date in the contract is known as the expiration, expiry or maturity date. The fact that distinguishes options from other contracts (futures of forwards) is that the holder does not have to exercise the right that the option gives him.
For an option contract an investor must pay an up-front price, known as the option premium (c). In the specific question we are asked to explain why call option traded on Marks & Spencer shares are trading in November than those trading in September.
There are many factors that influence stock option prices, and the most important are given below:
The current stock price (S0)
The strike price (x)
The time to expiration (T)
The volatility of the stock price (AÆ’)
The risk-free rate (r)
The dividends expected during the life of the option
Specifically in order to give an adequate answer to the question involved, we will discuss what happens to the call option prices of Marks & Spencer when one of these factors changes (the time to expiration) while the others remain fixed.
Options are referred to as in the money, at the money or out of the money. A call option is in the money when s>k, at the money when s=k, and out of the money when s<k. Clearly the option will be exercised when it is in the money and the payoff will be the amount by which the stock price exceeds the strike price (s-x>0), which is called the intrinsic value of an option. As the stock price increases, than call option becomes more valuable. Therefore the longer the time that a call has to run to maturity, the greater the scope for the price to rise above the exercise price. The probability to notice big variation between the share price at expiration and the strike price is higher, the longer the maturity period of the option. Another important element is that in call options there is a limit to what can be lost – which is the call premium – while the gains are unlimited. In other words, gains and losses are not symmetrically distributed for a call option. Although European call options usually become more valuable as the time to expiration increases, this is not always the case. Consider two European call options on a stock: one with an expiration date in one month, the other with expiration date in two months. If a very large dividend is expected in six weeks, this expected dividend will cause the stock price to decline, so that the short-life option could be worth more than the long-life option.
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