G.V. Semyashkin Determination of the market value of a closed joint-stock company by the WACC (weighted average cost of capital) index adjusted with band of investment method
Determination of the market value of a closed joint-stock company by the WACC (weighted average cost of capital) index adjusted with band of investment method
G.M. Semyashkin
Rector Advanced Training Institute, doctor of economics, professor (167003, Республика Коми, г. Сыктывкар, ул. Ручейная, 31; e-mail: insapk@parma.ru)
Аннотация. В статье поэтапно рассмотрен подход к определению рыночной стоимости закрытого предприятия с использованием показателя «средневзвешенная стоимость капитала» (WACC) скорректированного по методу инвестиционной группы.
Abstract. In article the approach is stage by stage considered to determination of the market value of a closed joint-stock company by the WACC (weighted average cost of capital) index adjusted with band of investment method.
Ключевые слова: рыночная стоимость, закрытая копания, средневзвешенная стоимость капитала
Keywords: market value, closed joint-stock company, weighted average cost of capital, WACC
In modern management of financial resources of an enterprise the indices of market cost of capital are undervalued. Partly, it can be explained by absence of traditions for its applying, or the fact that the majority of enterprises of the branch are unprofitable and in this case there are special approaches for management of the enterprises, but the main reason is that, as a rule, the methodology of market value is developed for valuation the results of activity of an open joint stock company, which sells its securities.
However, there are some examples of valuation of open joint-stock companies in the world and they are especially significant for agricultural and industrial complex, because of its low capitalization. The greatest authority on business enterprise valuation is Shannon P. Pratt. His researches published
is such books as «Cost of capital. Estimation and applications»1 and «Business valuation. Discounts and premiums»2 are devoted to closed joint-stock company valuation. In the given article we would like to use WACC (weighted average cost of capital) index for the valuation of market value of a closed joint-stock company. In fact WACC is a discount rate, being equal to the sum of weighted rates of return of equity and debt, where the weighted multiplier is a part of equity and the capital structure, it is estimated by the formula:
WACC = <e х We + Kp х Wp + i<d (1 -1) х Wd,
Ke - cost of common equity capital;
Kp - cost of preferred equity capital;
Kd - cost of debt prior tax effect;
We - weight of common equity in capital structure;
Wd - weight of debt in capital structure;
Wp - weight of preferred equity in capital structure;
t - tax rate.
Journal «Economy and Entrepreneurship», Vol. 3, Nom. 1 (January-February 2009)
Speaking about taxation, it should be mentioned that for market value valuation, net cash flows used. Business is not obliged to reinvest them in order to keep the rate of return in return, i.e. free from Liabilities and also tax Liabilities.
WACC index can be used in various cases, for example, when a company is prepared for acquisition for sale and when the purpose of estimation is to value all the capital structure of the company, for example when a buyer payment to the owners of equity and debt. In this case, first all the capital structure is valued, then market value of the debt is subtracted and the remaining sum is the cost of equity. The most important moment of WACC estimation is that relative weights of equity and debt are based not on book value, but market value of each component. We would like to value market cost of equity of the State Unitary Enterprise, which has been made a joint-stock company. The enterprise is ready for sale, but it lacks in market value of shares. Here, we can use the methodology of closed joint-stock company valuation, suggested by Shannon P. Pratt.
The methodology is based on the principle of the repetition of the process, which takes several steps:
1) Valuation of debt securities at a fixed
price.
2) The first estimation of the market value of debt securities and stocks, the coast of stocks is valued by the total income.
3) The first approximate estimation of WACC.
4) The first estimation of market value by using the results of WACC, obtained in p. 3, by the formula of capitalization:
PV--
NCF1 K - g
PV - present market value; NCF1 - net cash flow, expected during the first period after valuation date;
K - discount rate (cost of capital); g - expected long - term rate of increment of net cash flow of the investor.
5) Estimation of market value of stocks by subtraction from market value (p. 4) the cost debt securities (p. 1).
6) Estimation of parts of capital structure by using the equity value from p. 5.
7) Repetition of the process, starting with p. 3, till the parts of the market value are enough equal for WACC estimation.
In our opinion the given methodology has a drawback. The use of total rate of return for estimation of stocks value in p. 2 is not altogether correct, because the amount of total rate of return is influenced by debt. We can suppose that is could be better to use the methodology of band of investment during the given period and the residual return technique3 for estimation of stocks value due to its profitability, not due to total of return. If we did so, the estimation would be more accurate and correct.
For example, let us estimate the market value of equity of an enterprise. The capital structure, book value. Amount of net cash flow (NCFi), tax rate and average annual rate of income increment are given.
Table 1
Information for WACC estimation
№ Index Amount, mln. roubles Percentage
1. Equity 120 60
2. Long-term debt 80 40
3. Book value, total 200 100
4. Net cash flow 40 -
5. Increment of net cash flow, % 6 -
6. Percentage rate for debt 12 -
7. Tax rate 24 -
The sequence of estimation in the given approach is the following.
1) Cost debt is fixed at 12 % according to credit contract.
2) Knowing annual return, lets estimate total rate of return:
K = -
NCF
bookvalue 40m In.roubles
-x 100 % =
x 100 % = 20 %
200m In.roubles We can estimate rate of return of equity by method of band of investment according to residual technique.
In the above mentioned methodology, suggested by Shannon P. Pratt, total rate of return is used as a rate of return of equity during the third step of the procedure and in this case WACC is
0,2 x 0,6 + (0,1 - (1 - 024) x 0,4) = = 0,12 + 0,03 = 0,15.
Table 2
Estimation of rate return by method of band of investment with residual return for equity
Index Capital share, % Rate of return Weighted rate
1. Book 100 x 0,20:100 = 0,20
value, total
2. Long- 40 x 0,10:100 = 0,04
term debt
3. Equity 60 ? 0,16
4. Rate of 0,16:0,6 = 27 %
return of
equity estimation
So, the estimation of coast of equity would be
40mIn.roubIes ... ,
-= 444mIn.roubIes
0,15 - 0,06
i.e. the WACC difference would be 4,2 points (19,2 - 15), the difference in cost of equity would be
46 % (444 - 303 : 303 x 100).
To estimate the weighted rate of return of equity, lets subtract the weighted rate of return of debt from the total weighted rate of return and the obtained value is divided by the share of equity
(0,20 - °,°4 x i00 = 27). We well get the rate of
v 0,6 /a
return equity, which is 26,7 % or 27 %.
3) The first WACC estimation is made by equity return
5) Let us estimate the coast of equity in the first estimation by subtraction of the cost of debt from the market cost of capital, obtained in p. 4.
303 mln. - 80 mln. = 223 mln. roubles
6) Then we estimate parts of capital structure, using the cost of equity.
Table 3
Estimation of a part in capital structure
WACC1 = 0,27x 0,6 + (0,10x (1- 0,24) x 0,40) = 0,162 + (0,076 x 0,40) = 0,16 + 0,03 = 0,192.
4) Using the formula of capitalization we can estimate market value using WACC, obtained in p. 3
P^ = NCFi
K - g
40 mln. rub.
40
0,192 - 0,06 0,132
= 303mIn.roubIes
Index Amount, mln. roubles Percentage
1. Equity 223 73,6
2. Long-term debt 80 26,4
3. Market cost of 303 100
capital, total
7) Then we estimate WACC at the final stage, using the data of share in capital structure from p. 6
WACC = 0,27 x 0,736 + (0,1 (1 - 0,24) x 0,264) = = 0,199 + 0,02 = 0,219.
Journal «Economy and Entrepreneurship», Vol. 3, Nom. 1 (January-February 2009)
8) We estimate market cost of capital using the formula of capitalization at the final stage:
PV--
NCF1 40mln.roubes 40
K - g 0,219- 0,06 0,159
= 251,57mlnroubles
9) Let us estimate the coast of equity at the final stage, by subtraction of cost of debt from market cost of capital, estimated in p. 8
251,57 mln. roubles - 80 mln. roubles = = 171,57 mln. roubles
L i t e r a t u r e:
1. Shannon P. Pratt «Cost of capital. Estimation and Applications». Kwinto-Consulting, 2006.
2. Shannon P. Pratt «Business valuation. Discounts and premiums». Kwinto-Management, 2006.
3. Jack P. Friedman, Nicholas Ordway «In-come property appraisal and analysis», M. «Delo-LTD», 1995, h. 185.
Table 4
Capital structure of a firm at the final stage
Index Value, mln. roubles Percentage
1. Equity 171,57 68
2. Long-term debt 80 32
3. Market cost of 251,57 100
capital, total
The difference between market cost of equity and its book value is 43 %, the difference between market cost a firm and its book value is 26 %. So we can say, that the corrections are rather important. Then, knowing the total number of stocks we can estimate market value of a stock. If the given firm has issued 200 000 stocks, then market value of every stock is 858 roubles
(171,57 mln. roubles : 200 000 stocks).
The given methodology is vital and has practical significance for enterprises of any branch and form of proprietorship. The methodology is especially significant for
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