CONCEPTUAL FRAMEWORK OF VALUATION
The term 'valuation' implies the task of estimating the
worth/value of an asset, a security or a business. The
price an investor or a firm (buyer) is willing to pay to
purchase a specific asset/ security would be related to
this value. Obviously, two different buyers may not
have the same valuation for an asset/business as their
perception regarding its worth/value may vary; one may
perceive the asset/business to be of higher worth (for
whatever reason) and hence may be willing to pay a
higher price than the other. A seller would consider the
negotiated selling price of the asset/business to be
greater than the value of the asset/business he is selling.
Evidently, there are unavoidable subjective
considerations involved in the task and process of
valuation. Inter-se, the task of business valuation is
more awesome than that of an asset or an individual
security. In the case of business valuation, the valuation
is required not only of tangible assets (such as plant and
machinery, land and buildings, office equipments, and
so on) but also of intangible assets (like, goodwill,
brands, patents, trademark and so on) as well as human
resources that run/manage the business. Likewise, there
is an imperative need to take into consideration
recorded liabilities as well as unrecorded/contingent
liabilities so that the buyer is aware of the total sums
payable, subsequent to the purchase of business. Thus,
the valuation process is affected by, subjective
considerations. In order to reduce the element of
subjectivity, to a marked extent, and help the finance
manager to carry out a more credible valuation exercise
in an objective manner, the following concepts of value
are explained in this Section: (i) book value, (ii) market
value, (iii) intrinsic value, (iv) liquidation value, (v)
replacement value, (vi) salvage value, (vii) value of
goodwill and (viii) fair value.
Book Value
The book value of an asset refers to the amount at
which an asset is shown in the balance sheet of a firm.
Generally, the sum is equal to the initial acquisition cost
of an asset less accumulated depreciation. Accordingly,
this mode of valuation of assets is as per the going
concern principle of accounting. In other words, book
value of an asset shown in balance does not reflect its
current sale value.
Book value of a business refers to total book value of
all valuable assets (excluding fictitious assets, such as
accumulated losses and deferred revenue expenditures,
like advertisement, preliminary expenses, cost of issue
of securities not written off) less all external liabilities
(including preference share capital). It is also referred to
as net worth.
Market Value
In contrast to book value, market value refers to the
price at which an asset can be sold in the market. The
market value can be applied with respect to tangible
assets only; intangible assets (in isolation), more often
than not, do not have any sale value. Market value of a
business refers to the aggregate market value (as per
stock market quotation) of all equity shares
"outstanding. The market value is relevant to listed
companies only.
Intrinsic/Economic Value
The intrinsic value of an asset is equal to the present
value of incremental future cash inflows likely to accrue
due to the acquisition of the asset, discounted at the
appropriate required rate of return (applicable to the
specific asset intended to be purchased). It represents
the maximum price the buyer would be willing to pay
for such an asset. The principle of valuation based on
the dis-counted cash flow approach (economic value) is
used in capital budgeting decisions.
In the case of business intended to be purchased, its
valuation is equivalent to the present value of
incremental future cash inflows after taxes, likely to.
accrue to the acquiring firm, discounted at the relevant
risk adjusted discount rate, as applicable to the acquired
business. The economic value indicates the maximum
price at which the business can be acquired.
Liquidation Value
As the name suggests, liquidation value represents the
price at which each individual asset can be sold if
business operations are discontinued in the wake of
liquidation of the firm. In operational terms, the
liquidation value of a business is equal to the sum of (i)
realisable value of assets and (ii) cash and bank
balances minus the payments required to discharge all
external liabilities. In general, among all measures of
value, the liquidation value of an asset/or business is
likely to be the least.
Replacement Value
The replacement value is the cost of acquiring a new
asset of equal utility and usefulness. It is normally
useful in valuing tangible assets such as office
equipment and furniture and fixtures, which do not
contribute towards the revenue of the business firm.
Salvage Value
Salvage value represents realisable/scrap value on the
disposal of assets after the expiry of their economic
useful life. It may be employed to value assets such as
plant and machinery. Salvage value should be
considered net of removal costs.
Value of Goodwill
The valuation of goodwill is conceptually the most
difficult. A business firm can be said to have 'real'
goodwill in case it earns a rate of return (ROR) on
invested funds higher than the ROR earned by similar
firms (with the same level of risk). In operational terms,
goodwill results when the firm earns excess ('super')
profits. Defined in this way, the value of goodwill is
equivalent to the present value of super profits (likely to
accrue, say for 'n' number of years in future), the
discount rate being the required rate of return applicable
to such business firms.
The value of goodwill in terms of the present value of
super profits method can serve as a useful benchmark in
terms of the amount of .goodwill the firm would be
willing to pay for the acquired business. In the case of
mergers and acquisition decisions, the value of goodwill
paid is equal to the net difference between the purchase
price paid for the acquired business and the value of
assets acquired net of liabilities the acquiring firm has
undertaken to pay for.
Fair Value
The concept of 'fair' value draws heavily on the value
concepts discussed above, in particular, book value,
intrinsic value and market value. The fair value is
hybrid in nature and often is the average of these three
values. In India, the concept of fair value has evolved
from case laws (and hence is more statutory in nature)
and is applicable to certain specific transactions, like
payment to minority shareholders.
It may be noted that most of the concepts related to
value are 'stock' based in that they are guided by the
worth of assets at a point of time and not the likely
contribution they can make towards earnings/cash flows
of the business in the future. Ideally, business valuation
should be related to the cash flow generating ability of
acquired business. The intrinsic value reflects the firm's
capacity to generate cash flows over the long-run and,
hence, seems to be more aptly suited for business
valuation.
In fact, in general, business firms are not acquired with
the intent to sell their assets in the post-acquisition
period. They are to be deployed primarily for generating
more earnings. However, from the conservative point of
view, it will be useful to know the realisable value,
market value, liquidation value and other values, if the
acquiring firm has to resort to liquidation. In brief, the
finance manager will find it useful to know business
valuation from different perspectives. For instance, the
book value may be very relevant form accounting/tax
purposes; the market value may be useful in
determining share exchange ratio and liquidation value
may provide an insight into the maximum loss, if the
business is to be wound up.
APPROACHES/METHODS OF VALUATION
The various approaches to valuation of business with
focus on equity share valuation are examined in this
Section. These approaches should not be considered as
competing alternatives to the dividend valuation model.
Instead, they should be viewed as providing a range of
values, catering to varied needs, depending on the
circumstances. The major approaches, namely, the (i)
asset based approach to valuation, (ii) earnings based
approach to valuation, (iii) market value based approach
to valuation and (iv) the fair value method to valuation
are described below.
Asset-Based Approach to Valuation
Asset-based approach focuses on determining the value
of net assets from the perspective of equity share
valuation. What should the basis of assets valuation be,
is the central issue of this approach. It should be
determined whether the assets should be valued at book,
market, replacement or liquidation value. More often
than not, they are (and should be) valued at book value
that is, original acquisition cost minus accumulated
depreciation, as assets are normally acquired with the
intent to be used in business and not for resale. Thus,
the valuation of assets is based on the going concern
concept. Some other value measure may be used
depending on circumstances of the case. For instance, if
the plant and machinery has outlived its economic
useful life (earlier than its initial estimated period), and
is not in use for production, it will be in order to value
the machinery at liquidation value.
Apart from tangible assets, intangible assets, such as
goodwill, patents, trademark, brands, know how, and so
on, also need to be valued satisfactorily. It may be
useful to adopt the super profit method to value some of
these assets.
To arrive at the net assets value, total external liabilities
(including preference share capital) payable are
deducted from total assets (excluding fictitious assets).
The company's net assets are computed as per Equation
Net assets = Total assets - Total external liabilities
The value of net assets is also known as net worth or
equity/ordinary shareholders funds. Assuming the figure
of net assets to be positive, it implies the value available
to equity shareholders after the payment of all external
liabilities. Net assets per share can be obtained, dividing
net assets by the number of equity shares issued and
outstanding. Thus,
Net assets per share = Net assets/Number of equity
shares issued and outstanding
The value of net assets is contingent upon the measure
of value adopted for the purpose of valuation of assets
and liabilities. In the case of book value, assets and
liabilities are taken at their balance sheet values. In the
market value measure, assets shown in the balance
sheet are revalued at the current market prices. For the
purpose of valuing assets, and liabilities, it will be
useful for a finance manager/valuer to accord special
attention to the following points:
(i) While valuing tangible assets, such as plant and
machinery, he should consider aspects related to
technological obsolescence and capital improvements
made in the recent years. Depreciation adjustment may
also be needed in case the company is following
unsound depreciation policy in this regard.
(ii) Is the valuation of goodwill satisfactory, given the
amount of profits, capital employed and average rate of
return available on such businesses?
(iii) With respect to current assets, are additional
provisions required for "unrealisability" of debtors?
Likewise, are adjustments required for "unsaleable"
stores and stock?
(iv) With respect to liabilities, there is a need for careful
examination of 'contingent liabilities', in particular
when there is mention of them in the auditor's report,
with a view to assess what portion of such liabilities
may fructify. Similarly, adjustments may be required on
account of guarantees invoked, income tax, sales tax
and other tax liabilities that may arise.
The net assets valuation based on book value is in
tune with the going concern principle of. accounting. In
contrast, liquidation value measure is guided by the
realisable value available on the winding up/liquidation
of a corporate firm.
Liquidation value is the final net asset value (if
any) per share available to the equity shareholder. The
value is given as per Equation.
Net assets per share = (Liquidation value of assets -
Liquidation expenses - Total external
liabilities)/Number of equity shares issued and
outstanding.
In the case of liquidation, assets are likely to be sold
through an auction. In general, they are likely to realise
much less than their market values. This apart, sale
proceeds from assets are further dependent on whether
the company has been forced to go into liquidation or
has voluntarily liquidated. In the case of the 'former'
type of liquidation, the realisable value is likely to be
still lower.
The net asset value (NAV) per share will be the lowest
under the liquidation value measure (Example).
(Example Following is the balance sheet of
Hypothetical Company Limited as on March 31, current
year:
(Rs lakh)
Liabilities Amount Assets Amo
unt
Share capital Fixed
assets
Rs
150
40,000 11%
Preference shares of
Rs 100 each, fully
paid-up
40 Less:
Depreciati
on
30 120
1,20,000 Equity shares
of Rs 100 each, fully
paid-up
120 Current
assets:
Profit and loss account 23 Stocks 100
10% Debentures 20 Debtors 50
Trade creditors 71 Cash and
bank
10 160
Provision for income
tax
8 Preliminar
y
expenses
2
282 282
Additional Information:
(i) A firm of professional valuers has provided the
following market estimates of its various assets: fixed
assets Rs 130 lakh, stocks Rs 102 lakh, debtors Rs 45
lakh. All other assets are to be taken at their balance
sheet values.
(ii) The company is yet to declare and pay dividend on
preference shares.
(iii) The valuers also estimate the current sale proceeds
of the firm's assets, in the event of its liquidation: fixed
assets Rs 105 lakh, stock Rs 90 lakh, debtors Rs 40
lakh. Besides, the firm is to incur Rs 15 lakh as
liquidation costs.
You are required to compute the net asset value per
share as per book value, market value and liquidation
value bases.
Solution
Determination of Net Asset Value per Share
(Rs. Lakh)
(i) Book value basis Rs.
120
Fixed assets (net)
Current assets:
Stock 100
Debtors 50
Cash and Bank 10 160
Total assets 280
Less : External liabilities:
10% Debentures 20
Trade Creditors 71
Provision for taxation 8
11% Preference Share capital 40
Dividend on preference shares (0.11 x
Rs. 40 Lakh)
4.4 143.4
Net assets available for equityholders 136.6
Divided by the number of equity
shares (in lakh)
1.2
Net assets value per share (Rs.) 113.83
(ii) Market value basis
Fixed assets (net) 130
Current assets:
Stock 102
Debtors 45
Cash and Bank 10 157
Total assets 287
Less: External liabilities (as per
details given above)
143.4
Net assets available for equityholders 143.6
Divided by the number of equity
shares (in lakh)
1.2
Net assets value per equity share (Rs.) 119.67
(iii) Liquidation value basis
Fixed assets (net) 105
Current Assets:
Stock 90
Debtors 40
Cash and Bank 10 140
Total assets 245
Less : external liabilities (listed
above);
143.4
Less : Liquidation costs 15.0
Net assets available for equityholders 86.6
Divided by the number of equity 1.2
shares (in lakh)
Net assets value per equity share (in
Rs.)
72.17
The asset based approach is intuitively appealing in that
it indicates the net assets backing per equity share.
However, the approach ignores the future earnings/cash
flow generating ability of the company's assets. In fact,
the assets acquisition by business firms are not an end
in themselves; they are means to an end. The end is
value maximization and firms acquire assets for the
purpose of creating value. The earning based approach
reckons this perspective.
Earnings Based Approach to Valuation
The earnings approach is essentially guided by the
economic proposition that business valuation should be
related to the firm's potential of future earnings or cash
flow generating capacity. This approach overcomes the
limitation of assets-based approach, which ignores the
firm's prospects of future earnings and ability to
generate cash in business valuation. Earnings can be
expressed in the sense of accounting as well as financial
management. Accordingly, there are two major variants
of this approach: (i) earnings measure on accounting
basis and (ii) earnings measure on cash flow (financial
management) basis.
Earnings Measure Based on Accounting—
Capitalisation Method As per this method, the earnings
approach of business valuation is based on two major
parameters, that is, the earnings of the firm and the
capatilisation rate applicable to such earnings (given the
level of risk) in the market. Earnings, in the context of
this method, are the normal expected annual profits.
Normally to smoothen out the fluctuations in earnings,
the average of past earnings (say, of the last three to five
years) is computed.
Apart from averaging, there is an explicit need for
making adjustments, to the profits of the past years, in
extraordinary items (which are not likely to occur in the
future), with a view to arriving at credible future
maintainable profits. The notable examples of
extraordinary/non-recurring items - include profits from
the sale of land, losses due to sale of plant and
machinery, abnormal loss due to major fire, theft or
natural calamities, substantial expenditure incurred on
the voluntury retirement scheme (not to be repeated)
and abnormal results due to strikes and lock-outs of
major competing firm(s). Obviously, their non-
exclusion will cause distortion in determining
sustainable future earnings.
Above all, it will be useful to understand the profile of
the business, focussing on identifying the major growth
and income drivers. Are such drivers likely to continue
in future years? If not, projected profits need to be
discounted. Finally, additional income expected in the
coming years— say, due to launch of a new product—
should also be considered. In brief, the valuer should try
to familiarise himself or herself with all major
factors/events that had affected the profits of the
business in the past year(s) and are likely to affect them
in the future years too.
Determination of appropriate capitalisation rate is
another major requirement of this approach.
Capitalisation rate, normally expressed in percentages,
refers to the investment sum, that an investor is willing
to make to earn a specified income. For instance, 12.5
per cent capitalisation rate implies that an investor is
prepared to invest Rs 100 to earn an income of Rs 12.5
or an acquiring firm is prepared to invest Rs 100 to buy
the expected profits of Rs 12.5 of another business.
Given the risk return framework of financial decision
making, businesses that exhibit (or are exposed to)
higher business and financial risks obviously warrant a
higher capitalisation factor. Conversely, businesses
carrying a low degree of risk are subject to lower
capitalisation factor. There are a host of factors that
affect the risk complexion including fluctuation in
sales/earnings, degree of operating leverage, degree of
financial leverage, nature of competition, availability of
substitute products and their prices, pace of change in
technology and the level of governmental regulations.
Thus, there are a number of internal and external factors
associated with a business that can influence the risk
and, hence, the capitalisation factor.
The determination of the capitalisation factor is not an
easy task in practice. A few guidelines/ principles may,
however, be helpful to the valuer in its quantification.
First, the capitalisation factor for a business firm should
be higher than that of a government security (normally
considered riskless). Secondly, the capitalisation factor
should match/hover around the one that is used for
other firms operating in similar type of businesses. In
case the valuer wants to apply different capitalisation
rate, there should be weighty and convincing reasons to
do so. For instance, firms having the potential and
prospects of achieving abnormal growth rates (for
reasons that are firm specific), vis-a-vis other firms in
the industry, managed by a well known management
team (having a good track record), may have low
capitalisation factor and vice versa.
Having determined the two major inputs, Equation, can
be used to compute the value of business ,VB, (from the
perspective of share owners).
VB = Future maintainable profits / Relevant
capitalisation factor
Example. In the current year, a firm has reported a
profit of Rs 65 lakh, after paying taxes @ 35 per cent.
On close examination, the analyst ascertains that the
current year's income includes: (i) extraordinary income
of Rs 10 lakh and (ii) extraordinary loss of Rs 3 lakh.
Apart from existing operations, which arc-normal in
nature and are likely to continue in the future, the
company expects to launch a new product in the coming
year.
Revenue and cost estimates in respect of the new
product are as follows: (Rs lakh)
Sales 60
Material Cost 15
Labour Cost (additional) 10
Allocated fixed costs 5
Additional fixed costs 8
From the given information, compute the value of the
business, given that capitalisation rate applicable to
such business in the market is 15 per cent.
Solution
TABLE 1 Valuation of Business
(Rs lakh)
Profit before tax (Rs. 65 lakh / (1-
0.35)
Rs.
100
Less : Extraordinary income (not
likely to accrue in future)
(10)
Add: extraordinary loss (non-
recurring in nature)
3
Sales Rs. 60
Less: Incremental costs
Material Costs Rs. 15
Labour Costs 10
Fixed costs (additional) 8 33 27
Expected profits before taxes 120
Less: Taxes (0.35) 42
Future maintainable profits after
taxes
78
Relevant capitalization factor 0.15
Value of business (Rs 78 lakh /
0.15)
520
Some useful insights into estimate of capitalisation rate
can be made by referring to the Price earnings (P/E)
ratio. The reciprocal of the P/E ratio is indicative of the
capitalisation factor employed for the business by the
market. In Example 32.2, the P/E ratio is approximately
6.67 (1/0.15). The product of future maintainable
profits, after taxes, Rs 78 lakh and the P/E multiple of
6.67 times, yield Rs 520 lakh. Given the fact that P/E
ratio is a widely used measure, it is elaborated below.
Price Earnings (P/E) Ratio The P/E ratio (also known as
the P/E multiple) is the method most widely used by
finance managers, investment analysts and equity
shareholders to arrive at the market price of an equity
share. The application of this method primarily requires
the determination of earnings per equity share (EPS).
The EPS is computed as per Equation.
EPS = Net earnings available to equity shareholders
during the period
Number of equity shares outstanding during the period.
The net earnings/profits are after deducting taxes,
preference dividend, and after adjusting for exceptional
and extraordinary items (related to both incomes and
expenses/losses) and minority interest. Likewise,
appropriate adjustments should be made for new equity
issues or buybacks of equity shares made during the
period to determine the number of equity shares.
The EPS is to be multiplied by the P/E ratio to arrive at
the market price of equity share (MPS).
MPS = EPS x P/E ratio ($2.6)
A high P/E multiple is suggested when the investors are
confident about the company's future
performance/prospects and have high expectations of
future returns; high P/E ratios reflect optimism. On the
contrary, a low P/E multiple is suggested for shares of
firms in which investors have low confidence as well as
expectations of low returns in future years; low P/E
ratios reflect pessimism.
The P/E ratio may be derived given the MPS and EPS.
P/E ratio = MPS/EPS
The future maintainable earnings/projected future
earnings should also be used to determine UPS. It
makes economic sense in that investors have access to
future earnings only. There is a financial and economic
justification to compute forward or projected P/E ratios
with reference to projected future earnings, apart from
historic P/E ratios. This is all the more true of present
businesses-that operate in a highly turbulent business
environment. Witness in this context, the following: "In
a dynamic business world, a firm's past earnings record
may not be an appropriate guide to its future earnings.
For example, past earnings may have been exceptional
due to a period of rapid growth. This may not be
sustainable in the future.
The P/E ratios should, however, be used with caution as
the published P/E multiples are normally based on the
published financial statements of corporate enterprises.
Obviously, earnings are not adjusted for extraordinary
items and, therefore, to that extent, may be distorted.
Besides, all financial fundamentals are often ignored in
published data. Finally, they reflect market sentiments,
moods and perceptions. For instance, if investors are
upbeat about retail stocks, the P/E ratios of these stocks
will be higher to reflect this optimism. This can be
viewed as a weakness as well, in particular when
markets make systematic errors in valuing entire sector.
Assuming retail stocks have been overvalued, this error
has to be built into die valuation also.
In spite of these limitations attributed to the P/E ratio, it
is the most widely used measure of valuation.- The
major plausible reasons are: (i) It is intuitively
appealing in that it relates price to earnings, (ii) It is
simple to compute and is conveniently available in
terms of published data. (iii) It can be a proxy for a
number of other characteristics of the. firm, including
risk and growth.
Example For facts in Example, determine the
market price per equity share (based on future
earnings). Assuming:
(i) The company has 1,00,000 11% Preference shares
of Rs 100 each, fully paid-up.
(ii) The company has 4,00,000 Equity shares of Rs
100 each, fully paid-up.
(iii) P/EE ratio is 8 times.
Solution
Determination of Market Price of Equity Share
Future maintainable profits after taxes
Less: Preference dividends (1,00,000 x Rs
11)
Earnings available to equity-holders
Divided by number of equity shares
Earnings per share (Rs 67 lakh/4 lakh)
Multiplied by P/E ratio (times)
Market price per share (Rs 16.75 x 8)
Rs.
78,00,000
11,00,000
67,00,000
4,00,000
16.75
8
134
To conclude, the P/E ratios should be used/interpreted
with caution and care. In particular, die investors should
focus on prospective/future P/E ratios, risk and growth
attributes of business and comprehensive company
analysis with a view to have more authentic and
credible valuation.
Earnings Measure on Cash Flow Basis (DCF Approach)
The P/E ratio approach, as a measure of valuation of
equity shareholders wealth, is essentially based on
accounting profits/earnings. Normally, such earnings
are either of the current year or prospective earnings of
the next year! Tin-single year earnings can be
camouflaged by either recording revenues earlier or by
postponing expenses. Ideally, valuation should be based
on the likely earnings of all the future years. The cash
flow approach is superior to the accounting profit
approach. The discounted cash flow method is also
driven by the firm's cash flow generating ability in
future years.
Discounted cash flow approach is used to evaluate
capital expenditure proposals in terms of their potential
for creating net present value for the firm. The DCF
approach is applied to the entire business, which may
consist of individual capital budgeting projects.
Accordingly, the value of business/firm is equal to the
present value of expected future cash flows (CF) to the
firm, discounted at a rate that reflects the riskiness of
the cash flows (k0). In equation terms:
To use the DCF approach, accounting earnings (as
shown by the firm's income statement) are to be
converted to cash flow figures as shown in Format 1.
FORMAT Computation of Cash Flows
After tax operating earnings*
Plus: Depreciation
Plus: Other non-cash items (say, amortisation of non-
tangible
asset, such as patents, trade marks, etc and loss on sale
of long-term assets)
* The interest costs are included as a part of the
discount rate (Ko).
However, analysts/valuers prefer to discount expected
future free cashflows (FCFF) to operating cash flows
(as per Format) for the purpose of firm valuation. The
reason is that firms, in general, are required to make
investments in long-term assets as well as in working
capital to generate/earn future cash flows; hence, the
need for adjusting operating cash flows to free cash
flows.
Format shows computation of operating free cash flows
(OFCF) for the purpose of valuation of a business.
FORMAT 1 Determination of Operating Free Cash
Flows (OFCFF)
After tax operating earnings*
Plus: Depreciation, amortisation and other non-cash
items
Less: Investments in long-term assets
Less: Investments in operating net working capital**
Operating free cash flows (OFCFF)
*Exclusive of income from (i) marketable securities and
non-operating investments and (ii) extraordinary
incomes or losses.
**Addition is to be made in the event of decrease of net
working capital.
The free cash flow (FCFF) is the legitimate cash flow
for the purpose of business valuation in that it reflects
the cash flows generated by a company's operations for
all the providers (debt and equity) of its 'capital'6. The
FCFF is a more comprehensive term as it includes cash
flows due to after tax non-operating income as well as
adjustments for non-operating assets. Format 3 exhibits
the procedure of determining FCFF.
FORMAT 2 Determination of Free Cash Flows (FCFF)
Operating free cash flows (as per Format 2)
Plus: After tax non-operating income/cash flows
Plus: Decrease (minus increase) in non-operating
Assets, say marketable securities
Free cash flows to Firm (FCFF)
*Non-operating income (1 - tax rate)
Since the FCFFs are available to all the capital
providers of a corporate enterprise, the discount rate to
be applied to such cash flows should be indicative of
the opportunity cost of the funds made available by
them, weighted by their relative contribution to the total
capital of a corporate enterprise. The opportunity cost is
equivalent to the rate of return the investors expect to
earn on other investments of equivalent risk. The cost to
the firm equals the investors' cost less any tax benefits
received by the company itself (say, tax advantage on
the payment of interest) plus any tax payments required
to be made (say, dividend payment tax).
The value of the firm is given by Equation
Thus, the value of a firm is the present value of FCFF
through infinity. The equity valuation can be deduced
by subtracting the total external liabilities (debtholders
and preference shareholders) from the value of the firm.
Alternatively, the value of equity can be obtained,
straight way, by discounting future free cash flows
available to equity-holders, (FCFE), after meeting
interest, preference dividends and principal payments,
the discount rate being rate of return required by equity
investors, that is, cost of equity (ke)
Thus, there are varying connotations of FCFF to serve
different needs. However, while the valuation of a firm
and equity use different definitions of FCFF as well as
of discount rates, they provide identical answers as long
as the same set of assumptions is used in both the
equations. Example 4 illustrates it.
Example 4 Suppose a firm has employed a total capital
of Rs 1,000 lakh (provided equally by 10 per cent debt
and 5 lakh equity shares of Rs 100 each), its cost of
equity is 14 per cent and it is subject to corporate tax
rate of 40 per cent. The projected free cash flows to all
investors of the firm for 5 years are given in the table:
(Rs. Lakh)
Year-end 1 Rs. 300
2 200
3 500
4 150
5 600
Compute (i) valuation of firm and (ii) valuation from
the perspective of equityholders. Assume 10 percent
debt is rapayable at the year-end 5 and interest is paid at
each year-end.
Solution
(i) Computation of Overall Cost of Capital
Source of capital After tax
cost (%)
Weights Total
cost (%)
Equity 14 0.5 7
Debt 6* 0.5 3
Weighted average cost
of capital (ko)
10
*10% (1-0.4 tax rate) = 6 percent
(ii) Valuation of Firm, Based on Ko
(Rs. Lakh)
Year-end FCFF PV factor
(0.10)
Total present
value
1 Rs.300 0.909 Rs.272.70
2 200 0.826 165.20
3 500 0.751 375.50
4 150 0.683 102.45
5 600 0.621 372.60
Total present value / Valuation of Firm 1288.45
Less : Value of debt 500.00
Value of Equity 788.45
(iii) Valuation of Equity, Based on Ke
(Rs. Lakh)
Year-
end
FCFF to
all
investor
s
After
tax
payment
to
debthol
ders
FCFE to
equityh
olders
PV
factor
(0.14)
Total
present
value
1 300 30 270 0.877 236.79
2 200 30 170 0.769 130.73
3 500 30 470 0.675 317.25
4 150 30 120 0.592 71.04
5 600 530 70 0.519 36.33*Interest on Rs 500 lakh @ 10% = Rs 50 lakh; Rs 50
lakh (1 - 0.4) = Rs 30 lakh
**Inclusive of debt repayment of Rs 500 lakh at year-
end 5.
Thus, the valuation of equity by both the methods is
virtually the same (Rs 788.45 lakh and Rs 792.14 lakh).
The minor difference of Rs 3.69 lakh can be attributed
primarily to rounding-off the present value figures.
Total present value of the projected free cash flows to
equityholder can be used to compute free cash flows per
equity share FCFE as per Equation 11.
FCFE per equity share = PV of FCFE to equityholders
Number of equity shares outstanding
In Example 4, FCFE per equity share is =
Rs 792.14 lakh = Rs 158.428
5 lakh
In Example 4, for the sake of simplicity, we have
assumed the life of the corporate firm as 5 years. In
practice, firms have perpetual long-term
existence/indefinite life. Evidently, the indefinite life of
business/corporate firms, in general, is an additional
aspect to be reckoned in a firm's valuation. Ideally, one
approach is to forecast future FCFF for a very long
period of time, say 30-40 years and ignore all
subsequent year's FCFF. The reason is the discounted
value of such FCFF in such distant years will be
insignificant. However, there are genuine difficulties in
explicitly forecasting decades of performance. In fact, it
is virtually impossible to make reasonably accurate
forecasts of profits/cash flows beyond a certain period
(say 7—10 years) in most of the businesses.
To overcome the problem Copeland et al suggest that
the exercise related to valuation of business can be
segregated into two periods, during and after an explicit
forecast period. The value of a business/firm is:
Present value of cash flows during explicit forecast
period + Present value of cash flows after explicit
forecast period. (12)
What constitutes an ideal explicit forecast period? This
question is not easy to answer. The following guidelines
may be relevant and useful in selecting such a period.
Whereas in cyclical businesses, the period can
correspond to one full business cycle, in other
businesses, the period can match with the number of
years during which they are likely to perform well. In
operational terms, the period should not be very short,
say 2—3 years, and given the current turbulent dynamic
business world, the period, in general, should not be
very long also, say 10-15 years.
The explicit forecast period is die period in which the
firm grows at a rapid pace; it is said to be at saturation
point at the end of the explicit forecast period, so far as
growth rate is concerned (the economic premise is that
firms, in general cannot sustain abnormal rates of
growth for an indefinite period). The firm is expected to
have attained a steady rate (at the end of explicit
forecast period) and starts growing at a stable growth
rate, which is likely to continue in future years. The
value determined after the explicit forecast period is
referred to as the continuing value. According to
Copeland et al the continuing value can be estimated as
per Equation 13-
Continuing value = NOPLATT+1 (1-g/ROICI)
k0 - g
Where NOPLATT+1 = The normalised level of net
operating profits less adjusted taxes in the first year
after the explicit forecast period.
g= The expected growth rate in NOPLAT in perpetuity.
ROICI = The expected rate of return on the net new
investment.
The derivation of the formula as per Equation 13 to
compute continuing value is as follows:
Continuing value = FCFFT+1
k0-g (13.1)
Where FCFFT+1 refers to the normalised level of free
cash flow in the first year after the explicit forecast
period.
Free cash flows (FCFF) can be defined in terms of
NOPLAT and investment rate, IR (that is, the
percentage of NOPLAT reinvested in the business each
year).
FCFF= NOPLAT (1-IR) (13.2)
We know, growth rate, g is the product of return on
invested capital, ROICI and IR, ie,
g=ROICIxIR (13.3)
or IR=g/ROICI (13.4)
Incorporating value of IR in FCFF definition
FCFF= NOPLAT (l-g/ ROICI) (13.5)
Continuing value = NOPLAT(1-g/ ROICI)
k0-g
Equation 13 is termed as a value driven formula. Since
Equations 13 and 13.1 provide the same answer of
continuing value, it is logistically more convenient to
compute continuing
value based on Equation 13.1.
The major simplifying assumptions made in
determining continuing value are: (i) the firm earns a
constant return on the existing invested capital; (ii) the
firm's NOPLAT grows at a constant rate and it invests
the same proportion of its gross cash flow in business
each year and (iii) the firm earns a constant return on all
new investments.
All the items in equation 13 are self explanatory, except
the term adjusted taxes. Adjusted taxes is the increase in
the estimated tax liability due to the exclusion of the tax
shield provided by interest charges. This is illustrated in
Example 5.
Example 5 Following is the summarised income
statement of Hypothetical Ltd:
(Rs lakh)
Sales revenues
Less: Cost of goods sold
Less: Administrative expenses
Less: Selling and distribution expenses
Earnings before interest and taxes
(EBIT)
Less: Interest
Earnings before taxes
Less: Taxes (0.40)
Earnings after taxes
Rs 100
42
8
20
30
10
20
8
12
Solution
Determination of NOPLAT
(Rs lakh)
Net operating profit or EBIT
Less: Taxes as per income statement
Less: Adjusted taxes (interest, Rs 10
lakh x 0.4, tax rate)
Net operating profit less adjusted taxes*
Alternatively, it can be determined as
EBIT less taxes
EBIT
Less: Taxes (0.40 x Rs 30 lakh, EBIT)
NOPLAT
30
8
4
18
30
12
18
Adjusted taxes = (Taxes as per income statement, Rs 8
lakh + Tax shield on interest, ie, Rs 10 lakh x 0.4 = Rs 4
lakh). The rationale for enhancing tax liability is that
the weighted average cost of capital uses the after tax
cost of debt. Advantage of tax savings on interest
should not be counted twice.
According to Copeland, the finn's value is the aggregate
of (i) the present value (PV) of FCFF during the explicit
forecast period, (ii) PV of continuing value (of
FCFF/NOPLAT) and (iii) value of non-operating assets
(if any) at the end of explicit forecast period (say,
marketable securities).
Among the various variants of the earnings approach,
the DCF approach (that is, free cash flows) seems to be
conceptually superior for business valuation as well as
equity valuation.. The computation of FCFF and
continuing value is illustrated in Example 6.
Example 6 Sagar Industries deals in production and
sales of consumer durables. Its expected sales revenues
for the next 8 years (in Rs million) are given in the
table:
Years Sales Revenue
1 Rs. 80
2 100
3 150
4 220
5 300
6 260
7 230
8 200
Its condensed balance sheet as on March 31, current
year is as follows: (Rs million)
Liabilities Amount Assets Amount
Equity Funds 120 Current Assets 30
12% Debt 80 Long-Term Assets
(net)
170
200 200
Additional information:
(i) Its variable expenses will amount to 40 per cent of
sales revenue. Fixed cash operating costs are estimated
to be Rs 16 million per year for the first 4 years and at
Rs 20 million for years 5 - 8. In addition, an extensive
advertisement campaign will be launched, requiring
annual outlays as follows:
(ii) Long-term assets are subject to 15 per cent rate of
depreciation on diminishing balance method,
(iii) The company has' planned the following capital
expenditure (assumed to have been incurred in the
beginning of each year) for the next 8 years,
(iv) Working capital in terms of investment in current
assets are estimated at 20 per cent of sales revenue,
(v) It is expected to have non-operating assets in terms
of investments in marketable securities in the initial
year. The expected after tax non-operating cash flow in
year 1 = Rs 0.5 million.
(vi) Given the tax benefits available to Sagar, the
effective tax rate estimated is 30 per cent.
(vii)The corporate equity capital is estimated at 16 per
cent.
(viii) The free cash flow of the firm are expected to
grow at 5 per cent per annum, after 8 years. Determine
the discounted cash flow (DCF) value of the (i) firm
and (ii) equity.
(Rs million)
1 Rs. 5
2-3 15
4-6 30
7-8 10
(Rs million)
Year 1 Rs. 5
2 8
3 20
4 25
5 35
6 25
7 15
8 10
Solution
(i) Determination of Weighted Average Cost
of Capital
Source of
Funds
Cost (%) Weights Total (%)
Equity 16 0.6* 9.60
12% Debt 8.4 0.4** 3.36
12.96 = 13(Rs 120 million/Rs 200 million); *.* (Rs 80
million/Rs,200 million)
(ii) Determination of Depreciation (Years 1 - 8)
(Rs million)
Year Long-term assets at beginning of year
Additions during the year
Total at the year-end
Depreciation @15%
1 Rs.
170.00
Rs 5 Rs.
175.00
Rs. 26.25
2 148.74 8 156.75 23.51
3 133.24 20 153.24 22.99
4 130.25 25 155.25 23.29
5 131.96 35 166.96 25.04
6 141.92 25 166.92 25.04
7 141.88 15 156.88 23.53
8 133.35 10 143.35 21.50
(iii) Determination of Investment [Capital Expenditure
+ Current Assets, (CA)] Required, Years 1-8
(Rs million)
Year Investment required Existing
investm
ents in
CA
Additio
nal
investm
ents
required
Capital
expendit
ure
CA
(Sales x
0.2)
Total
1 Rs 5 Rs. 16 Rs. 21 30* Nil
2 8 20 28 25** 3
3 20 30 50 20 30
4 25 44 69 30 39
5 35 60 95 44 51
6 25 52 77 60 17
7 15 46 61 52 9
8 10 40 50 46 4*including marketable securities
**Balance of CA in year 1: Rs 30 million - Capital
expenditure incurred in year 1, Rs 5 million
(iv) Determination of Present Value for Explicit Period
Projections (years 1-8)
(Rs million)
Particulars Years
1
2 3 4 5 6 7 8
A Sales
revenue
80 100 150 220 300 260 230 200
B Less :
Expenses
Variable
Costs
32 40 60 88 120 104 92 80
Fixed cash
operating
costs
16 16 16 16 20 20 20 20
Advertiseme
nt
5 15 15 30 30 30 10 10
Depreciation 26.25 23.51 22.99 23.29 25.04 25.04 23.53 21.50
C EBIT (A-
B)
0.75 5.49 36.01 62.71 104.9
6
80.96 84.47 68.50
D Less:
Taxes (0.30)
0.22 1.65 10.80 18.81 31.49 24.29 25.34 20.55
E NOPAT 0.53 3.84 25.21 43.90 73.47 56.67 59.13 47.95
F Non-
operating
income
0.50 - - - - - - -
G Gross
cash flow
(E+F+Depre
ciation)
27.28 27.35 48.20 67.19 98.51 81.71 82.66 69.45
H
Less:Invest
ment in
Capital
expenditure
plus current
assets)
- 3 30 39 51 17 9 4
I Free cash
flow (G-H)
27.28 24.35 18.20 28.19 47.51 64.71 73.66 65.45
J PV Factor
(0.13)
0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376
K Total
PV(IxJ)
24.14 19.07 12.61 17.28 25.80 31.06 31.31 24.61
(v) Determination of PV in Respect of Continuing
Value (CV)
CV8 = FCF9/(k0 - g) = Rs 65.45 million (1.05)/(13% -
5%) = 68.7225 million/8%
= Rs 68.7225/0.08 = Rs. 859.03 million
PV of CV0 = Rs 859.03 million/(1.13)8 = Rs 859.03 x
0.376 = Rs 323 million
(vi) Total Value of the Firm, Based on the DCF
Approach of Free Cash Flows:
(Rs million)
PV of free cash flows during explicit period Rs. 185.88
PV of free cash flows after explicit period (known as
CV) Rs. 323
Total value Rs. 508.88
(vii)Value of Equity:
Total value of firm Rs. 508.88
Less: Value of debt 80.00
Value of equity 428.88
Market Value Based Approach to Valuation
The market value, as reflected in the stock market
quotations, is another method for estimating the value
of a business. The market value of securities used for
the purpose can be either (i) twelve months average of
the stock exchange prices or (ii) the average of the high
and low values of securities during a year. Alternatively,
some other fair and equitable method of averaging (on
the basis of the number of months/years) can' be
worked out, The justification of market value as an
approximation of the true worth of a firm is derived
from the fact that market quotations by and huge
indicate the consensus of investors as to the firm's
earning potentials and the corresponding risk. The
market value approach is one of the most widely-used
in determining value, in particular of large listed firms.
The major problem with this method is that the market
value of a firm is influenced not only by financial
fundamentals but also by speculative factors. As a
result, this value can change abruptly due to speculative
influences, market sentiments and personal
expectations. Market makers as well as other 'willing
buyers or sellers' (interested in purchases or sales) can
at times significantly influence these prices. Another
limitation of this approach is that this approach cannot
be applied if the shares are unlisted or are not actively
traded.
Apart from the limited applicability of this method only
to listed corporate enterprises, whose shares/securities
are actively traded, the valuation of a business is not in
tune with the going concern concept. Nevertheless, it
may be/is of immense usefulness in deciding swap
ratios of shares in merger decisions. In fact, the market
prices of the two companies can be the objective of the
decision. Alternatively, a certain percentage of
premium, above the market price may be offered as an
inducement to the shareholders of the acquired
company to convince them to agree to sell their shares
or to make them agree to the merger decisions.
Fair Value Method
The fair value method is not an independent method of
share valuation like those discussed above. This method
uses the average/weightage average or one or more of
the above methods. Since this method uses the average
concept, its virtue is that it helps in smoothening out
wide variations in estimated valuations as per different
methods. In other words, this approach provides, in a
way, the 'balanced' figure of valuation.
In general, this method has limited application for
business valuation. For instance, this method of
valuation of shares had been used till the early 1990's,
by the erstwhile Controller of Capital Issues (CCI) in
India, for fixing the price of new equity issues. In case
the equity shares were to be issued at a premium, the
amount of premium was based as the CCI guidelines.
To sum up, no one method is appropriate for all
circumstances/situations/requirements. Therefore, it is
important to recognise that the different methods are
based on different assumptions and depending on the
circumstances, some methods may be more appropriate
than others. For instance, where there is paucity of
information about profits, say (i) in the case of new
companies whose accounts do not serve as a guide to
future profits, (ii) in the case of companies operating at
a loss with no prospects of earning profits in the near
future and (in) in the case of companies having
unreliable statistics of profits owing to factors such as
disruption of business, the net asset method of valuation
seems would be more appropriate. In normal situations,
the DCF (based on free cash flows) method would be
suitable. In the event of wide variations in the
valuations as per these two methods, the fair value
method may be, used. In fact, it is useful for the finance
manager/investor/valuer/analyst to know a range of
values from various perspectives.
OTHER APPROACHES TO VALUE
MEASUREMENT
In recent years, a number of new
approaches/techniques/methods to measure value (with
focus on shareholders) have been developed and
practised. The two major approaches are market value
added (MVA) and economic value added (EVA). They
are explanied in this Section.
Market Value Added Approach (MVA)
The MVA approach measures the change in the market
value of the firm's equity vis-a-vis equity investment
(consisting of equity share capital and retained profits).
Accordingly,
MVA = Market value of firm's equity - Equity capital
investment/funds (14)
Though the concept of MVA is normally used in the
context of equity investment (and, hence, is of greater
relevance for equity shareholders), it can also be
adapted (like other previous approaches) to measure
value from the perspective of providers of all invested
funds (i.e., including preference share capital and debt).
MVA = [Total market value of firm's securities - (Equity
shareholders funds
+ Preference share capital + Debentures)] (15)
The MVA approach cannot be used for all types of
firms. It is applicable to only firms whose
market prices are available. In that sense, the method
has limited application. Besides, the value provided by
this approach may exhibit wide fluctuations, depending
on the state of the capital market/stock market in the
country.
Example 7 Suppose, Supreme Industries has an equity
market capitalisation of Rs 3,400 crore. in current year.
Assume further that its equity share capital is Rs 2;000
crore and its retained earnings are Rs 600 crore.
Determine the MVA and interpret it.
Solution
MVA = (Rs 3,400 core - Rs 2,600 crore) = Rs 800 crore.
The value of Rs 800 crore implies that the management
of Supreme Industries has created wealth/value to the
extent of Rs 800 crore for its equity shareholders. Well
managed companies (engaged in sunrise
businesses),"having good growth prospects, and
perceived so by the investors, have positive MVA.
Investors may be willing to pay more than the net
worth. In contrast, companies relatively less known or
engaged in businesses that do not hold future growth;
potentials may have negative MVA.
Example 8
Suppose, Hypothetical Limited has equity market
capitalisation of Rs 900 crore in the current year. Its
equity share capital and accumulated losses are of Rs
1,200 crore and Rs 200 crore respectively. Determine
the MVA of the film.
Solution
MVA = (Rs 900 crore - Rs 1,000 crore) = (-Rs 100
crore).
The firm has negative MVA of Rs 100 crore. The
investors discount its value/worth, as it is loss incurring
firm.
The market value added approach reflects market
expectations and is essentially a future-oriented and
forward looking approach. The investors, willing to pay
a different price (other than one suggested by book
value), are guided by the individual company's future
prospects, future growth rates, risk complexion of the
firm, industry to which the firm belongs, required rate
of return and so on.
Economic Value Added (EVA)
The EVA method is based on the past performance of
the corporate enterprise. The underlying economic
principle in this method is to determine whether the
firm is earning a higher rate of return on the entire
invested funds than the cost of such funds (measured in
terms of the weighted average cost of capital, WACC).
If the answer is positive, the firm's management is
adding to the shareholders value by earning extra for
them. On the contrary, if the WACG is higher than the
corporate earning rate, the firm's operations have eroded
the existing wealth of its equity shareholders. In
operational terms, the method attempts to measure
economic value added (or destroyed) for equity
shareholders, by the firm's operations, in a given year.
Since WACC takes care of the financial costs of all
sources of providers of invested funds in a corporate
enterprise, it is imperative that operating profits after
taxes (and not net profits after taxes) should be
considered to measure EVA. The accounting profits
after taxes, as reported by the income statement, need
adjustments for interest costs. The profits should be the
net operating profits after taxes and the cost of funds
will be product of the total capital supplied (including
retained earnings) and WACC.
EVA .= [Net Operating profits after taxes - (Total
capital x WACC)] (16)
The computation of EVA is illustrated in Example 9
Example 9 Following is the condensed income
statement of a firm for the current year: (Rs lakh)
Sales revenue
Less: Operating costs
Less: Interest costs
Earnings before taxes
Less: Taxes (0.40)
Earnings after taxes
Rs 500
300
12
188
75.2
112.8The firm's existing capital consists of Rs 150 lakh
equity funds, having 15 per cent cost and of Rs 100 lakh
12 per cent debt. Determine the economic value added
during the year.
Solution
(i) Determination of Net Operating Profit After Taxes
(Rslakh)
Sales revenue
Less : Operating Costs
Operating profit (EBIT)
Less: Taxes (0.40)
Net operating profit after taxes (NOPAT)*
Rs. 500
300
200
80
120* Alternatively, [EAT, Rs 112.8 lakh + Interest Rs 12
lakh - (Tax savings on interest, Rs 12 lakh x 0.4 = Rs
4.8 lakh)]
(ii) Determination of WACG
Equity (Rs 150 lakh x 15%)
12% Debt (Rs:100 lakh x 7.2%)*
Total cost
WACC (29.7 lakh/Rs 250 lakh)
= Rs 22.5
lakh
= 7.2
29.7
11.88%*Cost of debt = 12% (1 - 0.4 tax rate) = 7.2 per cent
(iii) Determination of EVA
EVA = NOPAT* - (Total capital x WACC)
Rs 120 lakh-(Rs 250 lakh x 11.88%)
Rs 120 lakh - Rs 29.7 lakh = Rs 90.3 lakh
During the current year, the firm has added an
economic value of Rs 90.3 lakh to the existing wealth
of the equity shareholders. Essentially, the EVA
approach is a modified accounting approach to
determine profits earned after meeting all financial
costs of all the providers of capital. Its major advantage
is that this approach reflects the true profit position of
the firm. What may happen is that the firm may exhibit
positive profits after taxes (as per the conventional
income statement) ignoring costs of shareholders funds,
giving an impression to the owners as well as outsiders
that the firm's operations are profitable. The profit
picture, in fact, may be illusory. Consider Example 10.
Example 10
For Example 53.8, assuming sales revenues are Rs 330
lakh, compute the earnings after taxes.
Solution
Income Statement (Conventional)
(Rs lakh)
Sales revenue
Less: Operating costs
Less: Interest costs
Earnings before taxes
Less: Taxes (0.40)
Earnings after taxes
Rs 330
300
12
18
7.2
10.8
The firm has registered profits of Rs 10.8 lakh during
the current year on the equity funds of Rs 150 lakh,
which has financial costs of Rs 22.5 lakh. Therefore, the
firm has, suffered a loss, (of Rsll.7 lakh) as the
opportunity costs of equity funds invested by equity
holders is more than what has been earned by the firm
for them. This point is brought to the fore by the EVA
approach. It is for this reason that the EVA approach is
getting more attention. It is superior to the conventional
approach of determining profits.
Determination of EVA
(Rs. lakh)
(a) Sales revenue
Less : Operating Costs
Operating Profits
Less : taxes (0.4)
Net operating profits after taxes
(b) EVA = Rs. 18 Lakh – (Rs. 29.7 lakh,
already computed above) = -Rs. 11.7
lakh
Rs. 330
300
30
12
18
Example 10 demonstrates that there may be a
substantial difference between profits determined as per
accounting approach and the EVA approach. Profits
shown ass per the EVA approach are conceptually
realistic than shown by traditional accounting approach.
In no way, the firm can be said to have earned profits
without meeting financial costs of all sources of
finance. The EVA approach is in tune with the basic
financial tenet of cost-benefit analysis; financial
benefits have to be more than financial costs to have
true profits.
Though the MVA and EVA are two different
approaches, the MVA of the firm (in a technical sense)
can be conceived in terms of the present value of all the
EVA profits that the firm is expected to generate in the
future.
Solved Problems
The following particulars are available in respect of a
corporate:
(i) Capital employed, Rs 500 million.
(ii) Operating profits, after taxes, for last three years
are: Rs 80 million, Rs 100 million, Rs 90 million;
current year's operating profit, after taxes, is Rs 105
million.
(iii) Riskless rate of return, 10 per cent.
(iv) Risk premium relevant to the-business of corporate
firm, 5 per cent.
You are required to compute the value of goodwill,
based on the present value of. the super profits method.
Super profits are to be computed on the basis of the
average profits of 4 years. It is expected that the firm is
likely to earn super profits for the next 5 years only.
Solution
Determination of goodwill, using super profit method
(Rs million)
Average profits (Rs 80 million + Rs 100
million + Rs 90 million + Rs 105 million
= Rs 375 million)/ 4 years
Rs. 93.75
Less: Normal profits (Rs 500 million x
0.15)
75.00
Super profits 18.75
Multiplied by the PV of .annuity for 5
years at 15 percent
(x) 3.352
PV of super profits/Value of goodwill 62.85
2. The following is the balance sheet of a corporate
firm as on March 31, current year.
(Rs lakh)
Liabilities Amo
unt
Assets Amou
nt
Share capital (of Rs 100
each fully paid-up)
Reserves and surplus
Sundry creditors and
other liabilities
Rs.
100
40
30
Land and
buildings
Plant and
machinery
Marketable
securities
Stock
Debtors
Cash and bank
balances
Rs. 40
80
10
20
15
5
170 170
Profit before tax for current year-end amount to Rs 64
lakh, including Rs 4 lakh as extraordinary income.
Besides, the firm has earned interest income of Rs 1
lakh in the current year from investments in marketable
securities. It is not usual for the firm to have excess
cash and invest in marketable securities. However, an
additional amount of Rs 5 lakh per annum, in terms of
advertisement and other expenses, will be required to be
spent for the smooth running of the business in the
years to come.
Market values of land and buildings, and plant and
machinery are estimated at Rs 90 lakh and Rs 100 lakh
respectively. In order to match the revalued figures of
these fixed assets, additional depreciation of Rs 6 lakh
is required to be taken into consideration. Effective
corporate tax rate may be taken at 30 per cent. The
capitalisation rate applicable to businesses of such risks
is 15 per cent.
From the above information, compute the value of
business, value of equity and price per equity/share,
based on the capitalisation method.
Solution
Valuation of business, value of equity and price per
equity share (capitalisation method)
(Rs lakh)
Profit before tax
Less; Extraordinary income
Less: Interest on marketable securities (not
likely to accrue in future)
Less: Additional expected recurring
expenses
Less: Additional depreciation
Expected earnings before taxes
Less: Taxes (0.30)
Future maintainable profits after taxes
Divided by relevant capitalisation factor
Value of business (Rs 33.60 lakh/0.15)
Value of equity (Rs 224 lakh - Rs 30 lakh
external liabilities)
Price per equity share (Rs 194 lakh/ 1 lakh)
64
4
1
5
6
48
14.40
33.60
0.15
224.00
194.00
194
3 Assume every thing to be the same as contained in
P.32.2: Determine the expected market price of the
share, given the P/E multiple of (0 8 times and (ii) 5
times, and interpret the result.
Solution
Determination of market price per share (P/E basis)
(Rs lakh)
Future maintainable profits after taxes
(computed in P.2)
Divided by the number of equity shares
issued and outstanding
Earnings per equity share, EPS, (Rs 33.60
lakh/1 lakh)
Multiplied by P/E ratio
(i) Market price per share (Rs 33.60 x 8
times)
Multiplied by P/E ratio
(ii) Market price per share (Rs 33.60 x 5
times)
Rs 33.60
1.00
33.60
8
268.8
5
168
Interpretation
(i) The P/E ratio of 8 times suggests that investors are
confident about the company's future prospects; they
have high expectations of future returns. It is for this
reasons that they are prepared to pay a higher market
price per equity share than warranted by the
capitalisation method (ie, Rs 194 per share), (ii) In
contrast, the P/E multiple of 5 times suggests that
investors are less optimistic about die company's future
performance. They have low confidence as well as
expectations of low returns in future years and
therefore1 are willing to pay a lower price vis-a-vis the
capitalised price.
P.4 For facts contained in P.2, determine the value of
business as per the net assets method. Assets are to be
valued at market value for this purpose. Value of
goodwill is also to be considered to value assets. Its
value is to be reckoned as an equivalent to the present
value of super profits, which are likely to accrue for 4
years. For the purpose of determining super profits,
normal profits are to be computed with reference to the
year-end value of net assets/capital employed
(excluding goodwill). Also compute the market value of
equity share as per this approach.
Solution
Determination of valuation of business and net asset
value per share as per the net assets method (assets are
valued at market price)
(Rs lakh)
Land and buildingsPlant and machineryGoodwillMarketable securitiesStockDebtorsCash and bank, balancesTotal, assetsLess: External liabilities Net assets available for equity to shareholders Divided by the number of equity shares issued and outstanding Net assets value per share (Rs 216 lakh/1 lakh)
Rs 90100
61020155
24630
216
1
216Valuation of goodwill
Future, maintable profits after taxes
Less: Normal profit (15% of capital
Rs 33.60
employed, i.e., 0.15 x Rs 210 lakh*)
Super profits
Multiplied by PV factor at 15% for annuity
of 4 years
Value of goodwill (Rs 2.10 lakh x 2.855)
31.50
2.10
2.855
6.0*(Market value of assets, excluding goodwill, Rs 240
lakh - External liabilities, Rs 30 lakh).
Assume everything to be the same as given in P2.
Determine the fair price of an equity share. The fair
price of an equity share is to be taken as an average of
prices estimated according to the capitalisation method
and the net assets method.
Solution
Determination of a fair price of an equity share (fair
value method)
Price per equity share (capitalisation
method)
Net assets value per equity share (net assets
method)
Fair value per equity share (Rs 194 + Rs
216)/2
Rs. 194
216
205
P.6 Determine the continuing value of the firm from
the following information: (Rs million)
Cash flow frorn business operations at the end of explicit forecast period (Year 6) Investment required in capital expenditure and current assets during year 6 Expected annual growth rate in free cash flows to the firm, after forecast period (%) Weighted average cost of capital (WACC) (%)Cost of equity capital (%)
Rs. 56
12
8
12
15
Solution
Determination of PV with respect to continuing value
(CV)
CV6 = FCFF7 = Rs. 44 million * (1.08) = Rs. 47.52 million
WACC-g 12%-8% 4%
CV6= Rs 1,188 million
CV0 = Rs 1,188 million x Present value factor at
12% for 6 years
CV0 = Rs 1,188 million x 0.507
= Rs 602.316 million
*(Gross cash flows Rs 56 million - Investment required
in capital expenditures and current assets Rs 12 million
= Rs 44 million);
P.7 Hypothetical Limited is growing at an above
average rate. It foresees a growth rate of 20 per cent per
annum in free cash flows to equityholders in the next 4
years. It is likely to fall to 12 per cent in the next two
years. After that, the growth rate is expected to stabilise
at 5 per cent per annum. The amount of free cash flow
(FCFE) per equity share at the beginning of current year
is Rs 10. Find out the maximum price at which an
investor, follower of the free cash approach, will be
prepared to buy the company's shares as on date,
assuming an equity capitalisation rate of 14 per cent.
Solution Maximum price of the equity share will be the
sum of (i) PV of FCFE during 1 - 6 years and 00 PV of
expected market price at the end of year 6, based on a
constant growth rate of 5 per cent.
(i) Present value of FCFE (years 1 - 6)
Year FCFE per share PV factor
(0.14)
Total PV
1 Rs. 10 (1+0.20)1 =
Rs. 12
0.877 Rs. 10.52
2 10 (1+0.20)2 =
14.40
0.769 11.07
3 10 (1+0.20)3 =
17.28
0.675 11.66
4 10 (1+0.20)4 =
20.74
0.592 12.28
5 20.74 (1+0.12) =
23.23
0.519 12.06
6 23.23 (1+0.12) =
26.02
0.456 11.86
Total PV of FCFE 69.45
Market price of share at year-end 6
= FCFE7 = Rs. 26.02 (1.05)
ke-g 14% - 5%
P6 = Rs. 27.321 = Rs. 303.57
14% - 5%
(ii) PV of Rs. 303.57 = Rs. 303.57 x 0.456
= Rs. 138.43
Maximum price of share
= Rs 69.45 + Rs 138.43 = Rs 207.88
P.8 The Chemicals and Fertilizer Limited is a growing
company. Its free cash flows for equity holders (FCFE)
have been growing at a rate of 25 per cent in recent
years. This abnormal growth rate is expected to
continue for another 5 years; then these FCFE are likely
to grow at the normal rate of 8 per cent. The required
rate of return on these shares, by the investing
community, is 15 per cent; the firm's weighted average
cost of capital is 12 per cent. The amount of FCFE per
share at the beginning of the current year is Rs 30.
Determine the maximum price an investor should be
willing to pay now it = 0), based on free cash flow
approach. The issue price of share is Rs 500.
Solution
(i) Present value of FCFE (years 1-5)
Year FCFE per share PV Factor
(0.15)
Total PV
1 Rs 30 (1+0.25)1 =
Rs. 37.50
Rs. 0.870 Rs. 32.62
2 30 (1+0.25)2 = Rs.
46.86
0.756 35.43
3 30 (1+0.25)3 = 58.59 0.658 38.554 30 (1+0.25)4 = 73.23 0.572 41.895 30 (1+0.25)5= 91.56 0.497 45.51
Total PV of FCFE 194.00
Market price of share at year-end 5
= FCFE6 = Rs. 91.56 (1.08) = Rs. 1,412.64
ke-g 15% - 8%
PV at t = 0 = Rs 1,412.64 x 0.497 = Rs 702:08
Investor will be prepared to pay the maximum price at t
= 0 = Rs 194 + Rs 702.08 = Rs 896.08
P.9 The most recent accounts of a corporate firm
engaged in manufacturing business are summarized
below:.
(Rs million)
Income statement for the current year
ended March 31
Amount
Sales revenue
EBIT
Less: Interest on loan
Earnings before taxes
Less: Corporate taxes (0.35)
Earnings after taxes
Rs 93.5
18.0
1.8
16.2
5.67
10.53
Balance sheet as at March 31, current year
(Rs million)
Liabilities Amou
nt
Assets Amoun
tEquity share
capital (1 lakh
shares of Rs 100
each)
Reserves and
surplus
10% Loan
Creditors and other
liabilities
10.0
32.5
18.0
18.0
Freehold land
and buildings
(net)
Plant and
machinery (net)
Current assets:
Stock
Debtors
Bank and cash
balance
20.0
29.5
10.0
15.0
4.0
78.5 78.5
Additional Information:
CO The finance manager of the firm has estimated the
future free cash flows of the company as follows:
Year
1
Rs.
222 233 24.54 26.05 30.06 32.0
Free cash flows in subsequent years, after year 6, are
estimated to grow at 4 per cent. The company's
weighted average cost of capital is 12 per cent.
(ii) The current resale value of the following assets has
been assessed by the professional valuer as follows:
Freehold land and buildings Rs 60 million
Plant and machinery 20
Stock 11
The current resale values of the remaining assets are as
per their book values.
(iii) A similar sized company (which is listed on
Bombay Stock Exchange) and is engaged in the same
business has a P/E ratio of 7 times.
You are required to compute the value of the firm as
well as value of an equity share on the basis of the
following methods: (i) Net assets method (book value
and market value), (ii) Price-earnings ratio method and
(iii) Free cash flows to the firm.
Solution
Determination of value of firm and value of equity
share (using various methods)
(Rs million)
(i) (a) Net asset method—book value basis:
Freehold land and buildings
Plant and machinery
Stock
Debtors
Bank and cash balances
Total assets
Less: External liabilities
10°/o Loan
Rs. 20.0
29.5
10.0
15.0
4.0
78.5
36.0
Creditors and other liabilities
Net assets available to equityholders
Divided by number of equity shares outstanding
(lakh)
Net assets backing per share (Rs 42.5 million/ 1
lakh) (Rs)
(b) Market value basis:
Freehold land and buildings
Plant and machinery
Stock
Debtors
Bank and cash balances
Total assets
Less: External liabilities
Net assets at market value
Net assets backing per share (Rs 74 million/1
lakh shares)
(ii) Price-earnings ratio approach
Earnings after taxes (assumed to be normal and
expected to be maintained in future years; no
adjustment is made as there are no extraordinary
items)
42.5
1
425
60
20
11
15
4
110
36
74
740
10.53
Earnings per share (Rs 10.53 million/1 lakh
shares)
Multiplied by P/E multiple
Market price of equity share (Rs 105.30 x 7
times)
105.30
7
737.10
(iii) Free cash flow basis:
(a) PV of FCFE during explicit forecast period:
(Rs in million)
Year FCFF PV Factor
(0.12)
Total PV
1 Rs. 22 0.893 Rs. 19.6462 23 0.797 18.3313 24.5 0.712 17.4444 26.0 0.636 16.5365 30.0 0.567 17.0106 32.0 0.507 16.225
Total present
value
105.191
(b) PV of FCFF subsequent to explicit forecast period
CV6= Rs. 32 (1.04)= Rs. 33.28 = Rs. 416
0.12 – 0.04 0.08
PV0 = Rs 416, continuing value x PV factor at 12%
for 6 years
= Rs 416 x 0.507 = Rs 210.912
(c) Total PV of FCFF (Rs 105.191 + Rs 210.912)
= 316.103 million 316.103
Less: External liabilities 36.000 36.00
FCFE available to equityholders 280.103 280.103
MPS (Rs 280.103 million/
1 lakh shares) = Rs 2801.03 280.10
P.10Assume everything to be the same as given in
P.32.9, determine the economic value added during the
current year. Assume the long-term funds shown in the
balance sheet as the total capital employed in the
business.
Solution
Determination of economic value added (EVA)
(Rs. In million)
Net operating profits before taxes
Less: Corporate taxes (0.35).
Net operating profits after taxes
Less: Cost of capital employed (Rs 60.5
million" x 0.12 WACC)
Economic value added.
Rs 18
6.3*
11.7
7.26
4.44
Alternatively, corporate taxes can be conceived as sum
of (i) taxes as per income statement (Rs 5.67 million
plus (ii) tax savings on interest (Rs 1.8 million x 0.35 =
0.63 million) = Rs 6.3 million "Equity share capital Rs
10 million + Reserves and surplus Rs 32.50 million +
10% loan Rs 18 million- Rs 60.5 million.
P.11 Assume every thing to be the same as given in P9.
Assume further that the equity shares of this company
are currently quoted in the market at Rs 500 per share.
Determine the amount of market value added (MVA).
Solution
Determination of market value added
A. Market value per equity share
B. Multiplied by number of equity shares
outstanding (lakh)
C. Total market value (A x B) (Rs million)
D. Equity funds (Rs 10 million equity share
capital plus Rs 32.5 million reserves and
surplus)
E. Market value added (Rs 50 million - Rs
42.5 million)
Rs. 500
1
50
42.5
7.5