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Determining Results
Cash Earning
Cash Flow Statement
Owners’ Equity
Financial Ratios
Insurance Companies’ Results
Values Per Share
Values Per Share
7.1. Introduction
Ratios per share are computed to estimate an investor’s potential claim on future earnings and net assets of a company. Ratios per share may be used for the following purposes:
to determine the relationship between the value per share and a share’s price (which is in itself a value per share);
to assess a company’s development over a period of time, specifically its earnings potential; and
to compare the relative value of different companies.
It is necessary to standardise the calculation of such ratios for these purposes with respect to the numerator and the denominator.
The standardisation of the numerator
is useful for determining a company’s earnings and cash earnings according to the procedures defined by ÖVFA.
The
standardisation of the denominator
involves defining the capital to which the corporate aggregates should be related when computing ratios per share. The theoretical and practical problems involve:
how to specify which equity instruments or equivalents should be used to compute the share capital of a company;
how to account for changes in owners’ equity, which is available to the company.
The following sections describe how the capital is determined that serves as the denominator for computing share ratios based on a number of differing assumptions regarding a company's capitalisation and business development. The procedures are presented using the example of earnings per share. However, the formulas may be applied analogously to other ratios as well.
7.2. Standard case
Where:
one class of shares
number of shares ............ A
earnings (in ATS millions) ............ G
earnings per share (ATS) ............ g
Based on these assumptions, earnings per share are computed as follows:
(1) g = G/A
All other values per share (cash earnings, etc.) are calculated in the same manner.
Example
Where
:
earnings according to ÖVFA (ATS m) ............ 46.28
share capital (ATS m) ............ 100.00
smallest par value (ATS) ............ 500.00
Calculation of earnings per share:
Number of shares:
100,000,000
= 200,000
500
Earnings per share according to ÖVFA: g =
46,280,000
=
231.4
200,000
ÖVFA reached the decision to round off values per share, with the exception of dividends, to whole numbers. In the example, earnings according to ÖVFA per share would therefore be ATS 231. If the original values are adjusted due to a change in the company's capital, the adjusted values must be rounded to one decimal place.
7.3. Several instruments representing owners’ equity
Where:
several equity capital instruments
number of shares ......... A1, A2, .. AT
par values of the different
classes of shares ......... n1, n2, ..., nT
To compute the total number of shares S used in calculating the values per share, the different classes of shares must be reduced to the smallest par value (e.g. n1):
(2) A = A1 + (n2/n1)*A2 + .... + (nT/n1) * AT
Earnings per share are then again computed as above:
(3) g = G/A
In calculating ratios in which the value per share is related to a share's price, earnings per share determined according to (3) must be multiplied by the applicable factor for those classes of shares whose par value is higher than the smallest par value; e.g.
(4) g2 = g * (n2/n1)
In calculating earnings per share for the entire company, ordinary and preferred shares, as well as participation certificates (issued by banks and insurance companies) must be included in the calculation. Profit-sharing capital should be included in the calculation of ratios per share if the securities entitle the holder to rights similar to those of preferred shares. For profit-sharing capital to qualify as share capital for the purpose of computing ratios per share, it must meet the following requirements:
distributions must be contingent on annual earnings;
the issuing terms and conditions of profit-sharing certificates must stipulate that in the event the minimum profit distribution for any financial year is not covered by the net profit for the year, such distribution shall be offset against future shares in the profit of the company, or that a shareholder’s right to a portion of liquidation proceeds shall be diminished correspondingly;
in the event of liquidation, profit-sharing capital must be subordinate in ranking to all of the company's liabilities even if it enjoy preferential treatment over ordinary shares and preferred shares.
Example:
Where:
earnings according to ÖVFA (ATS m) ........ 48.4
ordinary share capital (ATS m) ........ 42.0
par value of ordinary shares (ATS) ......... 500
preferred shares (ATS m) ......... 12.5
par value of preferred shares (ATS) ......... 100
Calculation of earnings per share:
Number of ordinary shares (at par value
of 100 each):
42,000,000
.* 5 = 420,000
500
Number of preferred shares: = 125,000
Total number of shares: = 545,000
Earnings per share according to ÖVFA: g =
48,400,000
= 88.8
545,000
When computing share ratios in which the share price is a factor (e.g. price/earnings ratio), earnings per share (prior to rounding) must be multiplied by a factor of 5 in the case of ordinary shares. Earnings per ordinary share according to ÖVFA are therefore ATS 444.
7.4. Adjustments in the event of capital increases
7.4.1 Old and new shares with equal dividend entitlements
In cases in which a change in the capital of a company results in an increase in the share capital, all other things being equal, the company's net worth increases along with other aggregates such as earnings, cash earnings, etc. To ensure the comparability of share prices and other values per share, both the share prices and the ratios per share must be adjusted for the impact of the capital increase.
Assumptions and definitions:
one class of shares
number of shares prior to capital increase ("old" shares) M
number of "new" shares N
subscription ratio z= M/N
share price prior to capital increase (ATS) k
_{m}
subscription price of new shares (ATS) e
(calculated) price after capital increase (ATS) k
_{ex}
(calculated) value of subscription right (ATS) e
adjustment (adjustment) factor for share prices and
other value per share f
unadjusted earnings per share according to ÖVFA for 20xx (ATS) g
_{xx}
adjusted earnings per share according to ÖVFA for 20xx g
_{xx.corr}
same par value of old and new shares
old and new shares with equal entitlement to dividends
Using the above assumptions and definitions, the adjustment factor f is calculated as follows:
(5) f=
z * km + e
(z+1) * km
This factor is used for the retrograde adjustment of historical share prices (prior to the capital increase). The theoretical share price Kex after the capital increase is:
(6) kex = f * km
Adjusted earnings per share for the year 20xx are calculated as follows:
(7) gxx,corr = f * g
Shareholders not participating in the capital increase who sell their subscription rights, should not suffer any loss in the value of their assets. Therefore:
(8) km = kex + B
The value of the subscription right is calculated as follows:
(9) B = km - kex = (1-f) * km =
km * e
z + 1
In practice, the adjustment factor f is rounded to four decimal places and the calculated value of the subscription right to two decimal places (i.e. to groschen). When several adjustment factors are applied, it is recommended to chain all values after rounding to four decimal places, and to apply this factor to the original values per share.
To ensure the comparability of values per share before and after changes in the capital of a company, the historical values per share must be multiplied by the adjustment factor f. Historical price/earnings ratios, price/cash earnings ratios, dividend yields, etc. will remain unchanged after adjusting share prices and value per share by the same factor.
The adjustment of the values per share by the same factor by which the historical prices are adjusted is based on the implicit assumption that there is no difference between old and new share capital. It is assumed that old and new shares will have the same price/earnings ratio or price/cash earnings ratio (relative to the share price pm of old shares and the issue price i of new shares). The assumption based on the principle of substance over form is that the inflow of (equity) capital will be used in a similar manner as existing (equity) capital as of the time it is received.
Capital increase during the year
Generally, changes in the capital of a company take place during the course of a year (i.e. during a company's business year). The procedure is as follows in such cases:
The values per share of previous years are adjusted by multiplying by the adjustment factor f as shown above.
The (projected) earnings of future years must be put into relation to the entire share capital; earnings are therefore divided by the total number of shares after the capital increase, i.e. M+N.
The earnings in the year of the capital increase must be related to the adjusted number of shares A of the current year, which is computed as follows:
(10) A=
b m *
M
+
b n * (M + N)
f
In this formula, b m is the annual fraction prior to the capital increase and b n is the one after the capital increase (therefore: b m + b n = 1). For practical purposes, ÖVFA defines b m and b n using the subscription period for new shares. In the month the subscription period ends, ÖVFA uses the number of shares before the capital increase and the increased number of shares for the subsequent month. Example: if the subscription period for new shares ends on 5 May, then b m = 5/12 and b n = 7/12.
Example:
Where:
share capital prior to capital increase (ATS m) ............ 100
capital increase by (ATS m) ............ 40
subscription period ............ 14 – 27 Oct. 1990
markdown ............ 14 Oct. 1990
dividend entitlement of new shares ............ from 1 Jan. 1990
subscription price of new shares (ATS) ............ 120
last price quoted prior to capital increase (ATS) ............ 265
(ex-1989 dividend)
smallest par value (ATS) ............ 100
1989 earnings per share (ATS) ............ 26.5
1990 profit (ATS m) ............ 27.3
1991 profit (ATS m) ............ 31.3
dividends per share 1989, 1990, 1991 (ATS) ............ 12
Calculation of adjustment factor, subscription right and adjusted value per share:
f =
265 * 2.5 + 120
= 0.8437
265 * 3.5
B =
265 * 120
= 41.43
3.5
A =
10 *
1,000,000
+
2 *
1,400,000 = 1,221,046
12 0.8437 12
Thus:
g89,corr = 0.8437 * 26.5 = 22.4
g90,corr =
27,300,000
=
22.4
1,221,046
g91,corr = 22.4
The development of earnings assumed shows that the company's operating earnings power remains unchanged in the period of observation. By contrast, an analysis of unadjusted earnings per share could lead to the conclusion of fluctuating or declining earnings depending on the mode of calculation. This is presented in the table below.
Year Adjusted earnings Unadjusted earnings
per share, in ATS per share, in ATS
1989... 22.4 26.5
1990... 22.4 ..19.51)/25.62)
1991... 22.4 22.4
1) Based on entire share capital after the capital increase
(= capital entitled to 1990 dividends).
2) Based on 1990 average share capital.
Adjustment of the dividend results in the following values:
Adjusted 1989 dividend = 0.8437 * 12 = 10.12
Adjusted 1990 dividend =
12 * 1,400,000
=
13.76
1,221,046
The company's dividend shows the following development over time:
Year Adjusted dividend Unadjusted dividend
in ATS in ATS
1989..... 10.12 12.00
1990..... 13.76 12.00
1991..... 12.00 12.00
Surprisingly, in the year of the capital increase the adjusted dividend is higher than the nominal dividend per share. This reflects the fact that in this example the company pays dividends already on the entire increased share capital in the year of the capital increase even though the capital becomes available to the company only in the 4th quarter. In order to determine the correct dividend payout ratio (dividend cover) on the basis of values per share, as well as the dividend yield in the year of the capital increase, the calculation must be based on the adjusted dividend, as shown below:
Calculation of dividend payout ratio (DPR) in 1990:
DPR90 =
12 * 1,400,000
= 61% =
13.76
27,300.000 22.4
Had the dividend payout ratio been computed on the basis of the unadjusted dividend, the result would have been 54%.
Calculation of the dividend yield:
On the assumption of constant share prices prior to and after the capital increase, the dividend yield r of a shareholder who had acquired 5 shares (at a price of 265) at the beginning of the year and exercised subscription rights in October would be as follows:
r =
7 * 12
= 6.2%
5 * 265 + (2/12)* 2* 120
The same value is obtained when the adjusted dividend is related to the share price after the capital increase:
r =
13.76
= 6.2%
223.6
However, on the basis of the unadjusted dividend per share, the yield would only be 5.4%
7.4.2 Old and new shares with different dividend entitlements
Where:
Analogous to section 4.1 except for the assumption of equal dividend entitlements
dividend of old shares (ATS) ............ dm
dividend of new shares (ATS) ............ dn
dividend disadvantage (ATS) ............ d = dm - dn
When old and new shares have different dividend entitlements, which is frequently the case when a change in capital takes place during the year, the formula for the adjustment factor f is as follows:
(11) f =
z * km + e + d
z + 1) ÷ km
The subscription right B is therefore:
(12) B =
km - e - d
z + 1
In practice, the dividend disadvantage d is calculated on the last paid dividend and the dividend entitlement of the new shares. If due to current the business development of the enterprise, the previous dividend payment would not be a valid assumption, ÖVFA proceeds on the dividend disadvantage agreed on between the company and Wiener Börse, the exchange operating company, to determine the subscription right markdown.
Example
Assumptions:
same assumptions as in previous example
except for the dividend entitlement of new shares
dividend entitlement of new shares ............ from 1 Nov. 1990
Calculation of dividend disadvantage, adjustment factor, and subscription right:
d = 12 -
2
* 12 = 10
12
f =
265 * 2.5 + 120 +10
= 0.8544
265 * 3.5
ù
B =
265 - 120 - 10
= 38.57
3.5
7.5 Adjustment procedure in the event of a capital adjustment (bonus shares)
When a company conducts a capital adjustment, the number of shares is increased without new capital flowing into the company. If old and new shares have the same dividend entitlements, the adjustment factor f reflects the ratio between the share capital prior to the adjustment and the share capital after the adjustment:
(13) f =
z
z + 1
(13) derives directly from (5) if the subscription price in this formula is defined as zero, because the shares are obtained free in the case of capital adjustments. In the more general case of different dividend entitlements, the following formula applies:
(14) f =
z * km + d
(z + 1)*km
(14) derives from (11) if e = 0.
Example
Where:
share capital prior to capital adjustment
(ATS m) on 1 July 1991 ............ 84.0
subscription ratio ............ 2:1
dividend entitlement of new shares ............ from 1 Jan. 1991
earnings per share according to ÖVFA 1990 (ATS) ............ 50.0
earnings according to ÖVFA 1991 (ATS m) ............ 42.0
earnings according to ÖVFA 1992 (ATS m) ............ 42.0
smallest par value (ATS) ............ 100
Calculation of adjustment factor and adjusted value per share:
f =
2
3
g90,corr = 0.6667 * 50 = 33.3
g91,corr = g92,corr =
42,000,000
= 33.3
1,260,000
7.6 Capital increase at current market price
If the issue price is equal to the current market price and old and new shares enjoy the same dividend entitlement, there is no difference between old and new capital from the standpoint of the principle of substance over form. Consequently, in such cases an adjustment of share prices and values per share is not necessary.
This is the direct result of (5) if e = km.
(15) f =
z÷ km + km
= 1
(z+1)÷ km
7.7 Adjustment in the event of share splits
A share split changes only a share's par value and the number of shares. If the par value before the split is x times the par value after the split, the historical value per share must be divided by the factor x to ensure comparability.
7.8. Adjustment in the event of capital reductions
In the event of a capital reduction in which only the nominal share capital—and thus the number of shares—are reduced without any funds flowing from the company to shareholders, the adjustment factor f is calculated as follows:
Where:
one class of shares
number of shares prior to capital adjustment ............ M
number of shares after capital adjustment ............ H
same par value before and after capital adjustment
(16) f =
M
H
This formula can also be applied in cases in which the capital is reduced by lowering the shares' par value while leaving the number of shares unchanged. In this case, the number of shares before the capital reduction (M) must be converted to the par value after the capital reduction.
7.9 Capital increase in the case of several classes of shares
7.9.1 Standard case
Where:
two classes of shares (e.g. ordinary/preferred shares)
number of ordinary shares prior to capital increase ............ Mo
number of new ordinary shares ............ No
number of preferred shares before capital increase ............ Mp
number of new preferred shares ............ Np
prices of ordinary and preferred shares prior to capital increase (ATS) ............ kmo, kmp
subscription prices of new ordinary and preferred shares (ATS) ............ eo, ep
dividend disadvantages of new ordinary and preferred shares (ATS) ............ do, dp
shares of ordinary and preferred share capital (before capital increase) ............ a o, a p
same par value of ordinary and preferred shares
same par value of old and new shares
If several classes of shares are listed on the stock exchange, two different types of adjustments are required in the event of capital increases:
adjustment of market prices to account for the fact that share prices are marked down by the value of the subscription right, and
adjustment of the value per share for the entire company to account for the fact that the value of owners’ equity increases less in percent than the number of shares (if the issuing prices are below the current market price).
The first adjustment is carried out by deducting the subscription right from the last market price before the capital increase and by correcting historical prices by the adjustment factors arrived at in section 4. The adjustment factors for the prices of ordinary and preferred shares are therefore as follows:
(17) fi =
z*
kmi + ei + di
i = o, p
(z + 1)* kmi
The company-specific values per share that relate to the whole company and are independent of the number and nature of the equity instruments are adjusted by the following factor:
kmo*Mo+eo*No+do*No+kmp*Mp+ep*Np+dp*Np
Mo+No+Mp+Np
(18) f = ------------------------------------------
kmo*Mo+kmp*Mp
Mo+Mp
The adjustment factor thus determined is formally identical to the factor defined in formula (11) for a single class of shares. In the present case, however, the corresponding averages of all classes of shares are used instead of the share price, the issue price and the dividend disadvantage of a single class of shares. (18) may also be expressed as:
(19) f =
Z * Km + E + D
(Z + 1) * Km
In this formula,
K is the average price of equity capital:
(20) Km =
a o * kmo + a p * kmp
E is the average issue price:
(21) E =
No
* eo +
Np
* ep
No + Np No + Np
D is the average dividend disadvantage:
(22) D =
No
* do +
Np
* dp
No + Np No + Np
Z is the ratio between the total number of shares prior to and after the capital increase:
(23) Z =
Mo + Mp
No + Np
The formulas (18) and (19) are generally applicable to capital increases, even in cases in which the number of ordinary and preferred shares is increased by different percentages and the proportion of the different classes of shares changes as a result of the capital increase.
Frequently, however, capital increases are conducted in such a way that the ratio between ordinary and preferred shares remains unchanged. (Please note that the different classes of shares may be subject to different dilution effects depending on the subscription terms). In such cases the adjustment factor is calculated as follows:
(24) f =
a o * kmo
* fo +
a o * kmp
* fp
a o *kmo + a p * kmp a o * kmo + a p * kmp
Example
Where:
two classes of shares: ordinary, preferred
number of ordinary shares prior to capital increase ............ 100,000
price of ordinary share before capital increase (ATS) ............ 1,000
subscription price of new ordinary shares (ATS) ............ 100
subscription ratio of ordinary shares .......... 10 : 1
dividend disadvantage of ordinary shares (ATS) ............ 10.0
number of preferred shares before capital increase ............ 50,000
price of preferred shares before capital increase ............ 500
subscription price of new preferred shares (ATS): ............ 100
subscription ratio preferred shares ............ 10:1
dividend disadvantage of preferred shares (ATS) ............ 10.0
same par value of ordinary and preferred shares
same par value of old and new shares
Calculation of the adjustment factors for the two classes of shares and of the average adjustment factor for the values per share of the entire company:
fo =
1,000*10+100+10
= 0.9191, fp =
500*10+100+10
=
0.9291
1,000*11 500*11
f=
0.6667*1.000
= 0.9191+
0.3333*500
* 0.9291 = 0.9211
0.6667*1,000+0.3333*500 0.6667*1,000+0.3333*500
The adjustment factor thus determined allows an analysis of the development of the values per share
for the entire company
over time. However, the subscription terms usually have different effects on the different classes of shares, as shown in the example, which is based on extreme assumptions:
Example
Where:
capital increase on 1 Jan. 1992
number of ordinary shares before capital increase ............ 100,000
price of ordinary shares before capital increase (ATS) ........... 1,000
subscription price of new ordinary shares (ATS) ............ 1,000
subscription ratio of ordinary shares ............ 10 : 1
number of preferred shares before capital increase ............ 50,000
price of preferred shares prior to capital increase ............ 500
subscription price of new preferred shares (ATS) ............ 100
subscription ratio of new preferred shares ............ 10 : 1
same dividend entitlement of old and new shares
same par value of ordinary and preferred shares
same par value of old and new shares
earnings according to ÖVFA 1991 (ATS m) ............ 12.50
earnings according to ÖVFA 1992 (ATS m) ............ 13.55
price/earnings ratio ordinary and pref. shares 20xx ............ PERxx,o,PERxx,p
average price/earnings ratio of company 20xx ............ PERxx
calculated prices of ordinary and preferred shares after
capital increase ........... kex,o, kex,p
The information above shows that shareholders owning ordinary shares purchase new shares at the current market price, whereas owners of preferred shares buy at the lower price of ATS 100. This implies a dilution of share capital.
Calculation of earnings per share, price/earnings ratios, and adjustment factors:
g91 = 83.33 (unadjusted)
PER91,o = 12
PER91,p = 6
g91 = 82.12
fo = 1.0000
fp = 0,9273
f = 0.8 * 1 + 0.2 * 0.9273 = 0.9855
It follows that:
g91,corr = 83.33 * 0.9855 = 82.12
A comparison of earnings per share in the two years shows that the company's earnings from operations cannot be expected to grow, which means that any increase in earnings is attributable solely to the capital increase. The company's average price/earnings ratio remains unchanged:
PER91 =
2*
12+
1*
6 = 10 =
2*
12.18 +
1*
5.65 = PER92
3 3 3 3
Share prices, on the other hand, are adjusted by the share’s class-specific factors as follows:
kex,o = 1,000 * 1.0 = 1,000
kex,p = 500 * 0.9273 = 463.6
The following price/earnings ratios are calculated on this result:
PER91,o =
1.000
= 12.18 = PER92,o
82.12
PER91,p =
463.65
= 5.65 = PER92,p
82.12
According to this calculation, the valuation of the two classes of shares has changed, as shown in the comparison of the price/earnings ratios before and after the capital adjustment. In 1991, the shareholders of ordinary shares paid, on the basis of unadjusted values, 12 times the earnings per share; after the capital increase, however, 12.18 times the earnings. For the holders of preferred shares, however, the share price declined from 6 times the (unadjusted) earnings per share to 5.7 times.
7.9.2 Cross subscription rights
The formulas (18) and (19) are also applicable to capital increases with cross subscription rights as conducted in Austria in recent years, for example, by EA Generali. Since a shareholder under such a scheme also has the right to subscribe to the respective other class of shares, the adjustment factors and the calculated value of the subscription right depend on the old prices of the two classes of shares. f is calculated as follows:
(25) fo =
Z÷ kmo+a p(kmo-kmp)+e+d
(Z+1)÷ kmo
(26) fp =
Z÷ kmp+a o÷ (kmp-kmo)+e+d
(Z+1)÷ kmp
Z is the average subscription ratio as defined in formula (23). The special feature of this form of capital increase is that the absolute markdown from the old prices is the same for both classes of shares. Therefore:
(27) (1-fo) * kmo = (1-fp) * kmp
and
(28) kmo - kex,o = kmp - kex,p = B
Example
Where:
number of ordinary shares before capital increase ............ 6,000,000
price of ordinary share before capital increase (ATS) ........... 4,000
subscription price of new ordinary shares (ATS) ............ 550
number of preferred shares before capital increase ............ 600,000
price of preferred shares before capital increase ............ 3,270
subscription price of new preferred shares (ATS) ............ 550
last dividend (ATS) ............ 15.0
dividend entitlement of new shares ............ 3 months
same par value of ordinary and preferred shares
same par value of old and new shares
subscription ratios:
Coupon A of ordinary/preferred shares: right to subscribe to ordinary shares at a ratio of 66:10
Coupon B of ordinary/preferred shares: right to subscribe to preferred shares at a ratio of 66:1
Calculation of adjustment factors and subscription right:
Average subscription ratio: Z = 6:1
Average share price: Km =
10
÷
4,000+
1*
3,270 = 3,933.64
11 11
Average subscription price: E = 550
Average dividend disadvantage: D = 11.25
Using these values in (19) results in:
f =
3,933.64
÷
6+561.25
= 0.8775
3,933.64
÷
7
B = 3,933.64 - 0.8775 * 3,933.64 = 481.77
Thus:
fo =
4,000-481.77
= 0.8796
4,000
fp =
3,270-481.77
= 0.8527
3,270
7.10. Adjustments in the event of new issues
7.10.1 New issues of an additional class of shares
Whenever shareholders are invited to subscribe to a newly created class of shares, it is not possible to determine the theoretical value of the subscription right and the resulting adjustment of the market price of the already existing class of shares, and values per share. The adjustment factor is therefore calculated on the basis of the actual price quoted for the subscription right. The calculation of B is based on the average price of the three days on which the subscription right is traded. The adjustment factor is therefore:
(29) f = 1 -
B
km
However, this adjustment is only possible after the end of the subscription period. Analysts who wish to quote a value per share in the case of new issues are therefore confronted with the problem of having to anticipate the markdown for shares already quoted on the basis of an assumed subscription price for the new class of shares. In this case, ÖVFA recommends using a hypothetical spread between the different classes of shares. Based on empirical evidence regarding spreads observed in the market between ordinary and preferred shares and/or between ordinary shares and participation certificates it seems justified to assume the following spreads:
Spread between ordinary and preferred shares (preferred shares = 100): 25%
Spread between ordinary shares and participation certificates (participation certificates = 100): 66%
Spread between preferred shares and participation certificates (participation certificates = 100): 33%
The assumption is a price ratio between the above classes of securities of 3 : 4 : 5.
7.10.2 Initial public offerings
In cases in which the capital of a company changes in the course of a public offering, the problem arises of which number of shares can be used to determine the value per share for the current year and previous years, as the market value of the shares, of course, not available before company goes public.
Assuming that the offer price that needs to be determined for the public offering is the best available approximation of the share’s market value, an adjustment of historical values is not necessary. (It is assumed that new issues are neither under-priced nor over-priced
on purpose
).
A difficult problem that cannot be solved satisfactorily either in theory nor in practice arises when capital increases are conducted before a company goes public, as it cannot be assumed that such capital increases are always made at the "right" market value. In cases in which a company's share capital has undergone significant changes in the phase prior to the public offering, the value per share must be interpreted with extreme caution taking into account the development of earnings in absolute terms.
The procedure for calculating the value per share in the case of an initial public offering is as follows:
The (projected) earnings of future years is to be related to the entire share capital.
Absolute earnings for the current year must be divided by the average number of shares in the year of the initial public offering. The weighting of the number of shares before and after the issue, and of the resulting capital increase is based—the same as in the case of regular capital increases—on the applicable fractions of the year. The month in which the subscription period ends is calculated with the number of shares prior to the capital increase; from the subsequent month onwards, the increased number of shares is used as the basis.
The earnings of previous years in absolute terms must be related to the average number of shares of the respective year, with the average weighting used being based on the applicable fractions of the year. In the case of capital increases from a company's own funds, the value per share must be adjusted using the formula arrived at in section 5.
7.11 Fully diluted result
A company may have securities in circulation that do not grant holders any claims on earnings at present, but do entitle the holders to a share in the earnings at a future point in time. Such securities include convertibles bonds and warrants. These financing instruments may lead to an increase in capital entitled to profit distributions in the future. This could result in a dilution of owners’ equity, which is an effect of interest to investors. The examples below illustrate only the effects of a dilution on earnings per share.
7.11.1 Convertible bonds
Where:
one class of shares
number of shares ............ M
number of convertible bonds outstanding ............ X
par value of convertible bond (ATS) ........... c
total volume of convertible bonds outstanding (ATS) ............ Q = c ÷ X
conversion ratio: x convertible bonds grant
subscription rights to y shares ............ w =
y
x
interest rate of convertible bond (%) ............ r
income tax rate (%) ............ t
company’s earnings (ATS m) ............ G
fully diluted earnings per share (ATS) ............ gdil
At the time the bonds are converted into shares, the company is relieved of the obligation to pay interest, but must issue new shares. The interest savings (R) upon conversion are calculated as follows:
(30) R = (1-t) * r * Q
The number of additional shares (N) resulting from the conversion is
(31) N = X* w
Thus:
(32) gdil =
G + R
M + N
Example:
Where:
share capital (ATS m) ............ 100.0
smallest par value of share (ATS) ............ 100
number of convertible bonds ............ 40,000
par value of convertible bond (ATS) ............ 10,000
conversion date two years from now
conversion ratio (shares:bonds) ............ 17 : 2
bond interest rate (%) ............ 4.5
tax rate (%) ............ 40.0
earnings according to ÖVFA (ATS m) ............ 48.0
Calculation of diluted earnings per share:
Interest savings upon conversion: Z = 400,000,000ù
0.045*0.6 = 10,800,000
New shares upon conversion: N = 40,000 *
17
= 340,000
2
Fully diluted result: gdil =
58,800,000
=
43.88
1,340,000
Dilution effect: gdil - g = 43.88 - 48.00 = - 4.12
7.11.2 Warrants
Where:
one class of shares
number of shares ............ M
share price (ATS) ............. k
number of additional shares upon exercise ............ X
exercise price ............ p
corporate profit (ATS m) ............ G
fully diluted earnings per share (ATS) ............ gdil
According to the treasury stock method, the number of additional shares (N) used in calculating the fully diluted result is computed as follows:
(33) N =
k - p
* X
k
This calculation assumes that the company will use the proceeds from the exercise of the warrants to buy additional treasury stocks in the market. However, as the market price is above the exercise price (otherwise the warrants would not be exercised), the company is only able to buy fewer shares than are in circulation due to the exercise of the warrants. Thus, the total number of shares in circulation is effectively increased.
The fully diluted result is therefore expressed as follows:
(34) gdil =
G
M+ N
It is recommended to determine the fully diluted result only if market conditions indicate that it is likely that the warrants will be exercised. This is the case whenever the share price rises above the exercise price for an extended period of time, about three months.
Example
Where:
number of shares ............ 1,000,000
number of shares created by exercise of warrants ............ 500,000
share price (ATS) ............ 550
exercise price (ATS) ............ 450
company’s earnings (ATS m) ............ 28.0
Calculation of the fully diluted result:
Additional shares: N =
550-450*
500,000 = 90.909
550
Fully diluted result: gdil =
28,000,000
= 25.67
1,000,000+90.909
Dilution effect: gdil-g = 25.67-28.00 = -2.33
Authors:
Chapter 1 (Calculation of earnings according to the ÖVFA method), Chapter 2 (ÖVFA cash earnings), Chapter 4 (ÖVFA owners’ equity /adjusted total capital), as well as Chapter 5 (ÖVFA financial ratios) were written by Friedrich Spandl with the assistance of Thomas Hammer using the contributions and comments provided by the experts on the ÖVFA Accounting Policy Advisory Committee.
The following ÖVFA members made valuable contributions to this publication series:
Michael Buchbauer
Gerhard Edelmann
Michaela Fiala
Thomas Hammer
Birgit Kuras
Andreas Mäutner
Friedrich Mostböck
Wolfgang Pinner
Manfred Radinger
Andreas Riegler
Karl Schaffer
Josef Schwarzecker
Claudia Schwarz-Vartok
Paul Severin
Friedrich Spandl
Peter Szopo
Claudio Vince-Bsteh
Heidemarie Wiederwald
Chapter 3 (Cash flow statement and definition of derived ÖVFA cash flow) was written by Josef Schwarzecker using valuable contributions by Thomas Hammer and Friedrich Spandl. Parts of Chapter 3 were taken from the book "
Cash-flow, Gewinn und Eigenkapital
" by Josef Schwarzecker, published by Ueberreuter, 1992. We thank Ueberreuter for their permission to use these passages.
Chapter 6 (Insurance companies’ results according to the ÖVFA method) and Chapter 7 (Values per share) were written by Peter Szopo.