This is a chapter from the Bloomsbury Professional book Practical Share Valuation, 5th Edition, which provides an in-depth view of the very latest techniques and procedures for assessing the worth of a company's shares and intangible assets. Tax considerations, practical tips and suggestions, and the accountancy best practice guidelines are all examined in this one essential handbook. A clear and concise layout, along with practical information and suggestions will allow the reader to supply accurate and reliable valuations effectively. This 5th edition covers the Companies Act 2006, new case law at the time of printing, details of the latest Accounting Standards, new chapters on options valuations and matrimonial valuations, the Finance Act 2008 and additional commentary on fair value assurance.
Table of Contents
The cases referred to in the earlier part of this book have shown that there are a number of factors to be taken into account in share valuation.
Many of these factors are important in determining the rate to be used in capitalising the earnings and in arriving at the appropriate dividend yield. Other factors of importance are the net assets of the company from which are derived the net assets value per share and any sales of the shares which have, in fact, taken place, provided that those sales are at arm's length in conditions which approximate to the 'open market' requirement.
The final value may be a combination of these four factors: earnings, dividends, assets and previous sales. The skill of the valuer comes in ascertaining the appropriate rates of capitalisation and the weighting to be given to each of these factors in the light of the size of the shareholding and the circumstances of the valuation.
Nevertheless, the valuer should appreciate that sometimes a single factor will by itself determine both the method of valuation and the value to be adopted. For example:
(i) no earnings and no possibility of earnings
(ii) the existence of a bid for the company as a whole.
In the case of (i) above the break-up value will be of prime importance and for (ii) it is unlikely that anyone would sell his shares for less than the bid price – or that anyone would pay more.
The following graphs show the weighting which might be given to assets, earnings, dividends and prior sales in the case of a trading company and an investment company.
Based on the American cases referred to in Chapter 8, The Foreign Influence, this would indicate that in the case of, for example, a 30% shareholding in a trading company, which, because the other shares are not held in very small numbers by a large number of shareholders, could not be regarded as carrying de facto control, some 10% of the overall value would be based on prior sales, 60% by reference to dividends or notional dividends, 18% by reference to earnings and 12% by reference to assets. On the other hand if the 30% holding because of the splintering of the other shares, did carry de facto control then the percentages would be more akin to a 70% holding. In the case of a 70% holding, 8% of the value would be by reference to prior sales, 4% by reference to dividends, 70% by reference to earnings and 18% by reference to assets. If the asset value were greater than the capitalised earnings value the asset weighting would increase from 18% to 24% with a corresponding reduction to 54% by reference to earnings. If there is a 90% shareholding prior sales would represent say, 5% of the overall value, dividends 3%, earnings 74% and assets 18%. If, however, the asset basis value were greater than the capitalised earnings basis of a holding of this order it would be reasonable to reduce the influence of the earnings to 12% and increase the asset weighting to 80%. This would of course follow from the fact that with a shareholding of this size the company could be put into liquidation. In each case the capitalisation factor could be adjusted to take account of a minority interest or it may be preferable to capitalise in full, then make an overall reduction for non-marketability.
It is emphasised that these suggested proportions should be regarded merely as general examples and in no way considered the hard and fast rule, as each company must be looked at individually in accordance with all the circumstances, including the general economic conditions prevailing at the valuation date. If, for example, a controlling interest in a run-down company was being acquired and that company had substantial under-utilised assets it could well be sensible to attach a greater weighting to the asset value which could be liberated once control was obtained even though there would not be sufficient power to place the company in liquidation. Similarly, in the case of the company providing services, the net tangible assets may be totally insignificant in relation to the earning power and in that case it would be appropriate to attach a lower than normal proportion to the assets; for example, providing financial services, stock broking, and advertising are all sectors in which it is the skill and experience of the operative which generates the profit.
It will be seen from the graphs that in the case of an investment company the assets would tend to have a much greater influence than in the case of a trading company, which is only to be expected.
Indeed, for an investment company, the quality of the portfolio and the spread of investment both by industry and location are of prime importance. It is instructive to consider how the actual open market – and there can be little doubt that, generally speaking, the Stock Exchange has been accepted by the courts as an almost perfect example of an open market required by tax legislation even with, in most decided cases, the necessary intervention of broker and market maker between vendor and purchaser – deals with the shares of listed investment companies. It is usual for the shares to change hands at a price which constitutes a discount from the net asset value. Such an approach to valuation is reasonable when it is remembered that the underlying investments are valued on what are considered to be the reasonable expectations of earnings, dividends, assets and potential. It must also be remembered that listed investment companies generally distribute a large part of their income but this is not always true of private investment companies. In such cases greater weight should be attributed to the dividend policy of the company.
A valuation prepared on this basis might be set out as follows:
30% shareholding in trading company
In order to proceed with a valuation along these lines it is necessary to arrive at the capitalised values appropriate for the assets, earnings, dividends and prior sales.
So far as the valuation of assets is concerned, this depends on the value of each individual asset considered on its own, either on the basis of a value to the business as a going concern, or on the open market depending on whether or not there is any likelihood of the asset being sold rather than retained for use in the business. For example, it may be that one of the sites occupied by the company is very ripe for development. Similarly, with prior sales, any weighting to be attached to this factor will be factual and it is only necessary to consider whether there are, in fact, any arm's length prior sales to influence the weighting. Clearly, if there are no such sales, the proportionate weighting attached to assets, earnings and dividends would be increased.
It is therefore necessary to consider the capitalisation of earnings and dividends.
If a company is making a loss it is obviously difficult to calculate a dividend yield or price/earnings ratio. The first question that must be asked is whether or not the company is likely to go back into profit in the foreseeable future. If so, it should be possible to calculate a potential notional dividend and potential future earnings which would require a further discount to bring them back to the present value at an appropriate rate per annum in the same way as for deferred shares. On the other hand, if the company is unlikely to go back into profit it will presumably be sensible to sell the business or put the company into liquidation, in which case it would be necessary to estimate the time scale for this to happen, and the likely net proceeds which could then again be discounted to their net present value, perhaps with a further discount for uncertainty.
A popular method of analysis which was the earnings yield which was of particular importance in the valuation of unquoted company shares where, in the majority of cases, dividends are either not declared at all or are a purely nominal amount.
The earnings yield is calculated by taking the profit after corporation tax and dividing this by the total capitalisation (the nominal share capital multiplied by the price per share) and multiplying by 100 to give the earnings yield per cent.
Tornado Ltd, motor vehicle component factors, had the following results for the year ended 31 December 2007.
Earnings yield on par value of the share
The valuer must then decide what earnings yield is required for the particular company. If, bearing in mind the earnings yield of other companies in similar business on the price of their shares and any factors peculiar to the particular company, eg the quality of the management, the valuer considers an earnings yield of 32% reasonable, the price per share will be £3, eg:
Earnings are also expressed in pence per share which is simply the net profit after tax divided by the number of shares. It is important in computing the earnings per share to ensure that the net profits are divided by the correct number of ordinary shares in issue, particularly where the nominal value of each share is other than £1.
If Tornado Ltd's share capital was divided into 200,000 shares of 25p each, the earnings per share were:
However it may be preferable to use the average share capital for the year.
Tornado Ltd had 120,000 shares in issue on 1 January 2007 and made a bonus issue of 2 for 3 on 1 April 2007. The average share capital was:
The average share capital is often used in practice to calculate earnings per share but a valuer must be extremely careful in using it. He is valuing the shares after the bonus issue and is looking to the past as a guide to the future. So far as the shares he is valuing are concerned, the past results indicate future earnings per share of 24p not 26.7p.
If instead of the bonus issue there had been an allotment of 80,000 shares, either at par or at a premium, he needs to consider what effect the additional cash injected will have on the profit figure. For example if that cash were used to pay off an overdraft thereby saving (say) £9,000 of interest charges the anticipated future profit, based on past figures, would be £48,000 plus £9,000 less any additional taxation if all other things are equal, so affecting the anticipated earnings per share.
Reference has been made to the capitalisation of earnings to arrive at the going concern value of the company, but it is necessary to arrive at the factor to be applied.
Some guidance can be obtained by a consideration of take-overs, amalgamations and reorganisations. The financial press, the Financial Times in particular, give details of the purchase price and the form it takes (either cash or shares or a mixture of the two) so that the purchase price can be expressed as a multiple of the pre-tax profit. This is often termed the 'exit P/E' and is of course entirely different to the normal P/E ratio which is based on sales of minority holdings. Care must be taken to compare like with like and to make due allowance for differences in the companies but it does give a suitable multiple. Shares and Assets Valuation division maintains a survey of Acquisitions and Mergers and its Manual instructs HMRC valuers to report to its Information Library any useful information regarding prices at which unquoted companies change hands, gathered from taxpayers or the Inspector of Taxes. There can be no doubt that HMRC put the resulting information to good use.
As a dividend is normally declared as a percentage of the nominal value of the share this has to be related to the market value to give the actual true yield. This is arrived at by dividing the nominal value of the shares in pence by the price of the share in pence and multiplying by the dividend as a percentage to give the yield as a percentage.
Tornado Ltd for the year ended 31 December 2007 paid a dividend of 36% on the 25p shares. The shares were valued at 75p per share.
The required yield can conversely be used to arrive at a value per share. If the required yield were 12% and the actual dividend 36% the value per 25p share would be:
After 5 April 1973, all dividends are declared net, even if the company then had to pay over advance corporation tax on the dividend paid, and the recipient was deemed to receive a tax credit in addition to the net dividend. When looking at dividends paid over a number of years, it is extremely important in any comparison to make sure that like is compared with like.
After 5 April 1993, the tax credit given was at the lower rate of 20% and as from 6 April 1999 was reduced further to 10%.
In many cases, the dividend is declared at a rate per share and the dividend yield obtained by dividing the actual dividend in pence by the price of the share in pence and multiplying by 100 to give the net dividend yield per cent.
Tornado Ltd for the year ended 31 December 2007 paid a dividend of 9p per share on the 25p shares. The shares were valued at 75p per share.
9/75 × 100 = 12%
The required yield, and the dividend per share can be used to arrive at a value per share.
9 × 100/12 = 75p per share
In considering the value of a share it is important to look not only at the actual dividends paid and the appropriate dividend yields but also to consider the likelihood of future dividend increases, and it may be possible to calculate the prospective or likely future dividend which in turn would enable the prospective yield to be calculated.
Tornado Ltd was expected to pay a dividend of 10p per share for the year ended 31 December 2008. If the price remains at 75p per share the prospective yield becomes.
10/75 × 100 = 13.33%
If the required yield remains at 12% the likely price will become:
10 × 100/12 = 83.33p per share
In order to work back to a valuation from a dividend yield it is merely necessary, as illustrated above, to transpose the fraction which becomes the dividend percentage divided by the required dividend yield per cent, times the nominal value of the share in pence, to give the price per share in pence. The published figures of dividend yield percentages in the Financial Times and other financial journals are normally on the basis of the gross equivalent of the dividends actually paid in the previous calendar year which may be an interim and final dividend for the last accounting period or a final dividend for the preceding period and an interim dividend for the current period. The valuer must compare like with like. It is pointless to arrive at a dividend yield for A Ltd based on last year's total dividend and attempt to compare it with B Ltd's dividend calculated on last year's final dividend and this year's interim.
It will be observed that in the above examples a net dividend yield of 12% is assumed but one of the difficulties facing the valuer is to arrive at that required yield on a reasoned and logical basis. It is of course perfectly possible simply to adopt a dividend yield on the basis of experience but such a yield would be very difficult to justify before, for example, the courts. The 'inner man' is not a good witness.
For fiscal purposes, valuation in the open market is necessary and there is, in fact, no better open market for shares than the Stock Exchange. If, on the Stock Exchange, an exactly comparable company to Tornado Ltd were listed and the price quoted for it showed a net equivalent dividend yield of 8.8%, what would be the required dividend yield for Tornado Ltd? Since the companies are exactly comparable, the only difference is that the comparable company is listed so that there is a ready market for its shares while Tornado does not enjoy that benefit. The extent of the allowance for that difference must depend on the time, circumstances and the conditions in the market. In times of difficulty, the 35% mentioned in 11.01 could be justified but when conditions and market sentiment improve 35% may be too high and 20–25% reasonable.
It is, however, extremely unlikely that there will be an exactly comparable company. It is much more likely that there will be a number of listed companies showing similarities but also showing variations in size, dividend policy, earnings, range of product, etc. It is certainly not beyond a valuer's competence to make suitable allowance for differences in the companies to arrive at a dividend yield for the particular company on an 'if quoted' basis. Allowance for unmarketability can then be made and the value based on the actual dividend and the expected dividend yield, calculated.
Some professionals consider that there is absolutely no comparison between a listed and an unlisted company. When they reject comparability, they must prefer arbitrary selection of a required dividend yield (unless they consider dividend yield is of no consequence in valuation) but the difficulty of defending an arbitrary selection of the required dividend yield is obvious.
It will be appreciated that so far as valuation is concerned a prospective purchaser of shares is interested in the future dividends he is likely to receive after his purchase and the dividends previously paid are merely an indication of the previous dividend policy of the company and as such an indication to its likely future dividend policy. However, there may be many reasons why the past dividend policy is unlikely to be a reliable guide to the future policy. For example, the company might be trying to resist a takeover bid and therefore increasing its dividends to its existing shareholders. On the other hand the new management might be more or less interested in an immediate return in the form of dividends than the previous management. Therefore, it is important to remember that past dividends are, at best, a mere indication of likely future dividends and it is important to take account of all available evidence in calculating prospective future dividends.
So far as dividend yield calculations are concerned, where no dividend is actually paid it is suggested that the best approach is to assume that the board of the company had to consider the payment of a dividend, in view of the existence of hypothetical outside shareholders, and to decide what dividend would be declared by a reasonable board in such circumstances.
In his book entitled Share Valuations (2nd edn) the late T A Hamilton Baynes at p 125 referred to this treatment:
'The problem was raised by Halmer Hudson FCA, in a public discussion with H Booth, a chief examiner (who was not necessarily expressing the view of the Shares Valuation Division). Halmer Hudson proposed a company which refused to pay a dividend and instead paid income tax on shortfall. The examiner accepted that there would be little that the holder of say 10% of the equity could do. The shares would have a value because the controlling share-holders would themselves have in mind a minimal value which they would be prepared to pay. He accepted the uncertainty of threatening action under section 210 (of the Companies Act 1948). Halmer Hudson suggested a method of valuing the shares by assuming that the company had paid a normal dividend. The valuation arising from such an assumed dividend would be discounted by 70%. The examiner preferred a discount of about 50%.'
Shares Valuation Division in commenting in an actual case on this concept stated:
'I think you will agree that the view expressed by Mr Booth during the course of the dialogue between himself and Halmer Hudson is his own personal view-point and is not binding upon the Revenue. However, the division does accept that a valuation has to be made of shares in a company trading very successfully but not paying dividends. To solve this problem, and as you wish to adopt the line advanced by Booth and Halmer Hudson also, I propose to fall in with your wishes in this particular valuation to produce an early settlement.'
And again later:
'I said that I would like the opportunity to consider the result of the dialogue which took place between Mr Booth (formerly of this office) and Mr Halmer Hudson. Having considered the results of such dialogue it is apparent to me that the process leading to a valuation in companies where no dividend is being paid is to assume the amount the company could afford to pay arrive at a value and then discount for non payment. I note this is the approach you have adopted and I have accepted the same.'
The Shares and Assets Valuation division Manual (at Chapter 17.5) describes the notional dividend method as 'not usually suitable' but provides a worked example to enable HMRC valuers to understand the method. The Manual suggests that the discount for lack of an actual dividend should be in the range of 30% to 50%.
The problem is to decide what would be the appropriate dividend in the circumstances and it might normally be appropriate for a trading company to distribute, say, one-third of its post-tax profits by way of dividend. This is very much a generalisation and what would be reasonable in the circumstances must be considered having regard to the company's cash flow and the requirement to use reinvested profits within the company. It may be that a reasonable board of directors in the circumstances of a particular case would recommend a distribution of the vast majority of the available profits, for example, if it were a property investment company, or declare a purely nominal dividend if the company is over-trading or likely to require retained profits for the maintenance and development of its business.
The notional dividend method received a measure of judicial approval in Whiteoak v Walker  4 BCC 122 at 129:
'Finally, on notional dividend assessment, Mr Sutherland's report criticised the defendant for deducting from the 1981 profit the difference between the valuation of certain factory property and its balance sheet value. The criticism was twofold. First, it assumed that the property was a fixed asset and it was therefore said that no deduction should have been made. Secondly, it presumed that the valuation was made by Mr Bentley and was therefore not to be relied upon. In fact, the property was trading stock and in 1981, when it could not be sold, it was let and turned into investment property, so that the loss on the notional realisation was a proper deduction, and the valuation was made by a firm of chartered surveyors. This valuation was disclosed on discovery months before Mr Sutherland's report and the nature of the asset was known to the plaintiff himself. Both criticisms were completely unjustified. Mr Sutherland had a valid criticism that the factory property was not shown at the reduced value in the 1982 accounts and the defendant as auditor did not qualify the accounts. However, the valuation was, as I have said, a professional valuation, and the criticism is one that lies against the defendant in his conduct of the audit, not in respect of his deduction when making his valuation.
It follows that in my judgment the defendant did not fall below the required standard, whether the specialist standard or the auditor standard, in applying the notional dividend method so as to arrive at a fair value of the relevant shares.'
It is important, however, not to disregard the general circumstances of the company and any other influences on value. In Re Charrington (Hong Kong Supreme Court 1975), the valuer for the estate proposed a notional dividend based value for a 10% shareholding which resulted in a figure of $250 per share, whereas net asset backing was $19,105 per share. The court imposed a value of $11,463 per share, taking account of the particular factors that affected the case.
If the earnings yield is divided by the dividend yield this gives the cover for the dividend, that is, the number of times the net dividend could be paid out of the current net profit. The identical figure is of course given by dividing the earnings per share by the dividend per share.
Tornado Ltd for the year ended 31 December has an earnings yield of 32% and a dividend yield of 12%.
The dividend cover is:
Alternatively, on the basis of earnings per share of 24p and a dividend per share of 9p:
The dividend cover is:
24/9 = 22⁄3 times
It will be noted that if the average capital is used to calculate the earnings per share, 26.7p as previously calculated, it would be necessary to recalculate the dividend per share on the basis of the average capital.
It will be appreciated that the greater the dividend cover the more secure the dividend is and therefore if all other factors are equal a company with a greater dividend security is likely to be more valuable as being less speculative than one with a lower dividend cover. However it is extremely rare that all other things are equal.
When considering dividend yields and cover it should be noted that at various times the government has restricted the amount that can be paid by way of dividend which means that the past dividend record may be a poor guide to the prospective future dividends once those restrictions have been removed.
Prior to accounting periods beginning after 31 March 1989, close companies had to distribute their investment income unless they could show that profits could be retained for the maintenance and development of the business within the provisions of TA 1988, Sch 19, paras 8 and 9. Similarly, closely held property companies had to distribute 50% of their estate income under TA 1988, Sch 19, para 2(1), again subject to the requirements of the company's business which did not include the acquisition of further investments. Consequently, when considering the significance of dividends in relation to a valuation as at 31 March 1982, these factors meant that unquoted investment companies and property companies were likely to distribute a substantial proportion of their profits. Trading companies, on the other hand, might normally wish to retain their profits in the company, so far as possible, and therefore the dividends might be small or non existent, with the proprietors being rewarded by remuneration which would be taxed in their hands as earned income.
With the present National Insurance contribution regime, companies may sometimes choose to distribute income by way of dividend, rather than in the form of directors' remuneration. The effect on value of a distribution policy inspired by a desire to mitigate National Insurance contributions will depend on the circumstances. A purchaser of a 40% interest in an unquoted company paying dividends in these circumstances would not be prudent to expect a reasonable future dividend stream as the controlling shareholders could simply reduce dividends or cease to pay them entirely. There would possibly be grounds to bring a CA 2006, s 996 action for unfairly prejudicial conduct but it would not be safe to rely on such a remedy. If a smaller shareholding, say 10%, was the subject of the valuation, it may be more feasible to assume that the majority shareholders would continue their distribution policy. Nevertheless, if the dividend is well covered by earnings, a valuation based solely on dividend yield could produce a value lower than one based solely on earnings.
It will be appreciated that under the classical system of corporation tax the earnings after tax represented the maximum gross dividend that could be paid to a shareholder. However, while advance corporation tax existed, the situation was slightly more complicated because the payment of a dividend itself affected the amount of corporation tax, as the mainstream liability was reduced by the advance corporation tax in respect of the dividends. Advance corporation tax was abolished after 5 April 1999.
There are therefore three ways of calculating earnings in respect of periods for which advance corporation tax applied.
The gross basis – also known as the full distribution or maximum distribution basis – is the maximum gross equivalent dividend which the company could pay from its current profits. This is calculated on the assumption that the whole of the earnings after tax are distributed by way of dividend and is based on the post-tax profits grossed up at the current rate of advance corporation tax. If the rate of advance corporation tax was 1/4 and the profits after corporation tax £80,000, the earnings on a gross basis would be £100,000, and this would be compared with the total of the dividend and tax credit to give the dividend cover. It will be appreciated that where there is a change in the rate of tax at which relief is given, so that there is a change in the rate of corporation tax, the figure for gross earnings would alter on the same net profit after corporation tax.
The second normal method of computing earnings under the imputation system would be on a nil distribution basis, usually known as the nil basis, under which the earnings after tax would be the figure for the profits for the year less the corporation tax provided thereon.
The third basis is known as the net basis and from earnings would be deducted not only the provision for corporation tax, as shown by the accounts, but also any unrelieved advance corporation tax on actual distributions.
This figure is obviously affected by any actual distributions and whether or not the company has taxable profits in the UK. If the company paid full corporation tax on its profits then there is unlikely to be any irrecoverable ACT and the net earnings would be the same as the earnings on a nil distribution basis. On the other hand, if the company had a very small or non existent UK tax charge because of, for example, capital allowances or because a large proportion of its earnings were from overseas, there is likely to be unrecovered advance corporation tax on the dividends actually paid and therefore the net earnings would be less than those on a nil distribution basis. As from 1 July 1994, companies operating the optional Foreign Income Dividend Scheme obtained repayment of surplus ACT when dividends were paid out of foreign source profits in certain circumstances.
It is important when comparing earnings of different historical periods or of different companies that the earnings are calculated on a comparable basis.
The price/earnings ratio is merely the reciprocal of the earnings yield per cent, ie 100 divided by the earnings yield per cent. It may also be regarded as the number of year's purchase of the post-tax earnings per share which is represented by the price per share. The only advantage of the price/earnings ratio compared with the earnings yield is that it is applicable where, as in America, shares are issued with no par value. The price/earnings ratio can also be calculated on the price per share in pence divided by the earnings per share in pence and for valuation purposes the price per share can be arrived at by multiplying the earnings per share by the price/earnings ratio.
For the year ended 31 December 2007 Tornado Ltd had earnings of £48,000, an earnings yield of 32%, and earnings per 25p share of 24p and a price per share of 75p.
The price/earnings ratio is:
100/32 = 3.125 (yield reciprocal)
or 75/24 = 3.125 (earnings per share reciprocal)
On the basis of the average share capital outstanding of 180,000 shares the earnings yield becomes:
and the earnings per share, as previously calculated 26.7p.
The price/earnings ratio then becomes:
100/35.55 = 2.81 (yield reciprocal)
or 75/26.7 = 2.81 (earnings per share reciprocal)
Conversely, the value becomes
26.7 × 2.81 = 75p per share
It is usually better for the purposes of comparisons to calculate earnings per share on the basis of the average capital during the year.
As with the earnings yield there are different ways of calculating the earnings for the price/earnings ratio. These are usually calculated on the nil basis, assuming no distributions, which is therefore merely the profits after corporation tax.
The price/earnings ratio was introduced into the Financial Times Actuaries Share Index on the 9 August 1965.
The Investors Chronicle uses a method of a calculating a price/earnings ratio in which pre-tax profit is reduced by corporation tax at the standard rate (30% at the time of writing). The difference between the price/earnings ratio published in the Investors Chronicle and that published in the Financial Times can be quite marked at times when the corporation tax regime permits significant allowances against tax (see 18.21 on valuation at 31 March 1982).
When calculating earnings with a view to arriving at an earnings yield or price/earnings ratio it is desirable to base the calculation on the anticipated future earnings of the company, as a purchaser of the company's shares is interested in what he is likely to participate in the future rather than what has happened in the past. The problem is to gaze into the crystal ball to arrive at some meaningful figure for future profits. A common method, which has little to recommend it except convenience, is to take the average earnings for the past three or five years depending on the extent to which profits fluctuate and to take the arithmetic mean of these figures, but if there is a marked trend in the earnings, be it upwards or downwards, the average earnings are not only incorrect as future potential earnings, but positively misleading. It is necessary to continue the trend into the future, that is, if the trend is upwards, future earnings are likely to be higher than those of the current year. If the profits fluctuate wildly or go in cycles it may be sensible to average over a longer period. The trouble with any substantial period of averaging is that inflation can mean that results of several years ago are unlikely to be a valid indication of current figures. One practice which tries to cater for this is by applying a 'sum of the years' digits' average to the earnings of the past three or five years.
An estimate of the average profits of Dewoitine Productions Ltd is required for the years 2003–2007.
A more precise calculation might possibly be to adjust the profits for earlier years for inflation in accordance with, for example, the general index of retail prices, and to take the average of these profits. This could be a reasonable means of arriving at the anticipated future profits of a static business but is unlikely to take account of one where a considerable degree of growth is apparent. The combination of the sum of the years' digits with inflation adjusted profits would give more weight to the most recent profits and therefore take account of the profit trend to some extent.
Another method might be to see whether there is a trend in profits which may be extrapolated using linear regression techniques. In all such cases it is necessary to consider the end result carefully as it is very easy to manipulate figures mathematically with great accuracy and still end up with a result which bears little resemblance to any reasonable future profits that are likely to be achievable.
It may be worth looking at the earnings of a company to see whether there is a predictable trend in the results, although any such statistical exercise must be viewed with a good deal of caution. It would be unusual to find a company where mere extrapolation of a trend line based on past results gave an accurate estimate of the future profit level.
The mathematics in the operation is very simple and it is usual to set down the data in tabular fashion as follows:
John Holt & Company (Liverpool) Ltd
The figures in the end column are arrived at by solving the simultaneous equations. (S = the sum of, a and b the unknown factors to be found).
(i) S y = na + b S x
(ii) S xy = aSx + b S x2
(i) 3,715,901 = 5a + 15b
(ii) 11,698,843 = 15a + 55b
multiplying equation (1) by 3
(iii) 11,147,703 = 15a + 45b
by subtraction of (ii)–(iii)
551,140 = 10b
b = 55,114
by substitution into (i)
3,715,901 = 5a + 15b
3,715,901 = 5a + 15 × 55,114
3,715,901 = 5a + 826,710
3,715,901 – 826,710 = 5a
2,889,191 = 5a
a = 577,838
y1 = 577,838 + 55,114 = 632,952
577,838 + 2(55,114) = 688,066
577,838 + 3(55,114) = 743,180
577,838 + 4(55,114) = 798,294
577,838 + 5(55,114) = 853,408
by extrapolation, year six becomes:
577,838 × 6(55,114) = 908,522
Column one consists of the last say, five years, for which results are available in date order.
Column two represents the adjusted pre-tax earnings of the company for each of those years, the dependent variable y.
Column three represents the plot along the abscissa (the horizontal access of the graph) and is numbered from one to five inclusive. x is the independent variable.
Column four is the product of the independent variable x and the dependent variable y.
In column five the square of the independent variable x is calculated. Columns two to five are totalled and substituted in the simultaneous equations needed to calculate the trend lines.
In column six the trend line of y (y1) is calculated from the solution of the simultaneous equations.
If the trend line is extending forwards the projected future earnings may be estimated and if the correlation is high between the earnings and the time scale, the calculated earnings might be sufficiently accurate to assist in the valuation of the shares.
The projected profit in this example for year six (2008) using this method is £908,522. The actual profit was £1,142,750.
This method, in this particular example gives a more accurate projection for the 2008 profit than a mere weighted average, see the capitalisation of earnings calculation in Division B, Example 2.
Most spreadsheets have statistical and financial functions which can automatically produce a trend line and calculate the correlation coefficient.
If shares are entitled to dividends but not to votes and the company has a history of paying regular dividends it may be reasonable to value the shares on the basis of an appropriate dividend yield, with a discount of, say, 15% for lack of voting rights. Experience of non-voting shares on the Stock Exchange where shares which are otherwise identical but carry votes are also quoted would suggest that a discount of this order is reasonable.
If, however, shares are entitled to dividends, but the company does not pay dividends, the shares might be valued on the basis of a hypothetical reasonable dividend discounted by say 50% for non payment with a further discount of 15% for lack of voting power.
If shares are entitled to votes, but not to participate in dividends, it is suggested that a valuation on the normal basis of ordinary shares should be made subject to a further discount for lack of dividend rights. In the case of a controlling interest the lack of dividend rights would not be so important, as the profits could within reason be extracted by way of remuneration and a discount of say 15% might be reasonable. In the case of a minority interest however the shareholder who was not on the board of directors and who had no rights to obtain a seat on the board, and had no rights to a dividend could well expect a discount of a further 40% or thereabouts compared with similar shares with dividend rights.
If the shares only have rights to participate in a liquidation surplus with no voting or dividend rights it would be necessary to consider whether there was any likelihood of a liquidation taking place. In most such cases there would be little or no likelihood and it is suggested that a method of valuation would be to calculate the asset value per share, assuming an immediate liquidation, and to discount that figure for say 20 years at a market rate of interest of currently, say, 5% per annum in order to arrive at a realistic value. Such a discount would very heavily reduce the value of such shares but then the real value in such circumstances would be very low. £100 discounted for 20 years at 15% per annum amounts to just over £6.
The lack of right to participate in a surplus however, as far as the other shares are concerned, would justify a further discount of say 15%. It will be appreciated that by structuring a company in this way it may possible to depreciate substantially the overall value of the shares. However, in respect of employee shares, the Income Tax (Earnings and Pensions) 2003 introduced the concept of 'actual market value' ie considering the value of the shares including any restrictions placed upon them, as well as 'unrestricted market value', which ignores restrictions. When considering a valuation for taxation purposes, the valuer now has to consider which value he or she is attempting to calculate. Shares and Assets Valuation Division have not attributed a specific discount to any of the main restrictions eg bad leaver provisions, lack of voting rights etc. which may be seen in relation to employee shares, but the current trend is for a differential of between 10% and 12% between unrestricted and actual market value to be agreed in respect of 'standard' restrictions. Both the unrestricted and actual market values are required to be shown on Form 42.
The valuer has:
(a) calculated the net assets' value per share, the earnings yield, the dividend yield, the cover, the earnings per share, the trend of profits, the price/earnings ratio, etc;
(b) made all the same calculations for any company he considers comparable, noted the differences between the companies and estimated the effect of those differences on 'price';
(c) looked in detail at the particular company and ascertained every available fact, including the tenure of premises, the liquidity ratio, the adequacy of working capital, the quality of the management and so on;
(d) considered whether any special method of valuation is appropriate eg for property companies, investment companies, companies making no profit and/or without any prospect of doing so in the future, control holdings.
With their mind full of this relevant information, the valuer should then ask themselves two questions:
(1) Would I recommend that a client sell a holding of shares in this company for x pence per share? If not, continue asking that question at different prices until there is a positive answer.
(2) Would I advise a client to buy a holding of shares in this company at y pence per share? Again, if not, continue asking that question at different prices until there is a positive answer.
It is improbable that x and y will be the same figure but, if the valuer has ascertained every relevant fact, then the open market value will fall somewhere between the two. Where within the range, the precise value falls is a matter of choice and experience.
Of course the valuer may well have to defend the valuation either in correspondence or at discussions. It is suggested that when asking the two questions above, any negative answer, should be accompanied by a written summary of the factors which resulted in that answer. In this way, what are considered to be the crucial factors in the valuation have been identified, the weight attached to them crystallised and the valuer has prepared cogent evidence in support of the valuation.
It must be emphasised that valuation is not a precise art; it is impossible to calculate the price with certainty. It is a matter of opinion backed by experience and research. Very few valuers will have the benefit of the background information available to HMRC's Shares and Assets Valuation division. Nevertheless the valuer should have one important advantage – a familiarity with the company and an opportunity to talk to the directors.
Preference shares are normally much easier to value than ordinary shares, as it is reasonably simple to obtain the yield on quoted preference shares in a broadly comparable industry. Average yields for quoted preference shares were also included in the fixed interest section of the Financial Times Actuaries Share Index until the end of 1990 and therefore this information might be useful if a March 1982 valuation is required. An uplift of, perhaps, 20% would be given to allow for non-marketability, although it may be possible to agree a higher non-marketability discount of up to one-third, with Shares and Assets Valuation division. A greater uplift might also be necessary if there was some doubt as to the financial viability of the company and its ability to continue preference dividend payments.
Not all shares described as 'preference' shares will have the characteristics normally associated with such shares, ie a right to a fixed dividend, no voting rights in normal circumstances and no right to participate in any surplus on a winding up. The company's articles of association should be read carefully to ascertain the precise class rights. If the articles do not say that 'preference' shares carry no votes, the shares will carry one vote each. It should also be remembered that preference shares no longer shown as equity on the balance sheet and will be included in the account notes for creditors.
Debentures and loan stock may similarly be compared with the yield available on similar quoted securities. Again, however, it will be necessary to consider an increase in yield not only to account for non-marketability, but also lack of security compared with debentures issued by large quoted public companies.
For fixed interest securities with a fixed redemption date, it will first be necessary to calculate the yield to redemption. However, if the debentures are redeemable at a variable date (such as on the death of the debenture holder) it would be necessary to estimate this actuarially in order to ascertain the probable redemption date. Similarly, if the redemption period is within a period of time at the borrower's option it would be necessary, having regard to current interest rates, to estimate whether the company would be likely to redeem the debentures at the earliest or latest available date under the debenture deed.
The flat or running yield of a debenture is merely the nominal price divided by the market price multiplied by the percentage rate of interest to give the interest yield per cent. It is clearly necessary to know the coupon rate of the debenture or loan stock and whether interest is paid yearly, half-yearly or at other intervals. The redemption terms will also be required as it is possible that the debenture may be repaid at a discount or premium rather than at par. Yields of debentures and loan stock are always quoted as gross yields.
Leading firms of stockbrokers publish lists of corporation stocks showing the values of quoted debentures. HMRC would normally accept a relatively small discount of, say, £5 per £100 stock of the nearest comparable quoted stock as appropriate for valuation purposes. In most cases, the list of redemption yields is compiled on the basis of the annual coupon rate of interest which, because the interest is in fact paid half-yearly, is rather less than the true annual equivalent. For example, a redemption yield of 16% is in reality 8% per half year which on a true annual basis is equivalent to a rate of interest in excess of 16.6%.
The yield to redemption can also be found from compound interest tables such as Parry's valuation tables applying the formula:
Mr Lancaster, at his death on 1 January 2008, held £10,000 £1 debentures in Lancaster Ltd. These paid interest at 8% per annum, half-yearly, and were due for redemption in 2032 at a premium of 3%.
The required yield is agreed at 18%, per annum. The value is required for capital transfer tax purposes.
The required yield is taken as 9% per half year for 25 years, 50 half-yearly periods
The majority of computer spreadsheet programmes have financial functions which readily compute the present value of a bond. For example, if the applicable rate is 18% payable half-yearly and the debenture stock matures in 25 years time, it is necessary to enter the number of half-yearly periods ie 50, and the half-yearly required yield, ie 9% and the redemption value, say £10,300, and then calculate the present value of the capital repayment at the chosen rate of interest ie £138.52. To this figure must be added the present value of the half-yearly payments at the chosen rate of interest. If the stock carries an 8% coupon this would be £4 per half year per £10,000 stock ie £400 per half year for 50 periods, discounted, which would amount, at a present value at 9% per half year, to £4,384.67. The total value is therefore £4,523.19 or, say, £4,500 as in the previous example.
Various formulae are sometimes used, for example Dymonds Capital Taxes para 23.384 quotes the formula:
100 + rt
100 + ty
where r% is the rate of interest on the security, t years the number of years to redemption and y% the yield required.
It is pointed out in the Shares and Assets Valuation division Manual (at 13.7), however, that this formula produces an error which increases with t and the difference between r and y. The Manual warns HMRC valuers that this formula must not be used.
A better formula is that of P = r/y + I – r/y
(I + y/2)2t
Where r% is the rate of interest on the security, t years the number of years to redemption; y% is the required yield. This is basically an algebraic expression of the A + Ani formula.