ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 18: Business valuations
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Example
A company has just paid an annual dividend of $0.63. This dividend is expected to
remain constant for two more years, but from Year 3 it is expected to grow by 3%
each year into the foreseeable future. The cost of shareholders’ funds is 10%.
What should be the current market value of the company’s shares?
Answer
The dividend valuation model and the dividend growth model calculate the present
value of all expected future dividends by discounting them at the cost of equity
capital. A valuation can be obtained in this example using discount tables.
When dividend growth begins in Year 1, we can obtain a Year 0 valuation using the
dividend growth model. In this example, we know that dividend growth is
expected to begin in Year 3. We can therefore obtain a Year 2 valuation using the
dividend valuation model.
The expected value of the share (ex dividend)
at the end of Year 2 can be calculated
using the dividend growth model as follows:
P
2
=
0.63 1.03
()
0.10 −0.03
= $9.27
The expected current value of the share is:
this valuation at the end of Year 2 discounted to a Year 0 value,
plus the present value of the expected dividends at the end of Year 1 and Year 2.
Year
Dividend/future
valuation
Discount
factorat10%
Current
valuation
$ $
1 Dividend 0.63 0.909 0.57
2 Dividend 0.63 0.826 0.52
2 EndofYear2value 9.27 0.826 7.66
Sharevalue
8.75
3.3 Retained earnings: the earnings retention valuation model
Dividend growth can be achieved by retaining some profits (retained earnings) for
reinvestment in the business. Reinvested earnings should provide extra profits in
the future, so that higher dividends can be paid. When a company retains a
proportion of its earnings each year, the expected annual future growth rate in
dividends can be estimated using the formula:
g = br
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where:
g = annual growth rate in dividends in perpetuity
b = proportion of earnings retained (for reinvestment in the business)
r = the cost of equity capital, which is also assumed to be the rate of return that the
company will make on its investments of retained earnings.
The dividend growth model can therefore be –restated as follows. (This is
sometimes called the Gordon growth model as well as the earnings retention
valuation model.)
P
0
= D
0
(1 + br)
(r
e
– br)
Example
A company has just achieved annual earnings per share of $0.50, of which 40% has
been paid in dividends and 60% has been reinvested as retained earnings. The
company is expected to retain 60% of its earnings every year and pay out the rest as
dividends. The cost of equity capital is 8%.
The current annual dividend is 40%
× $0.50 = $0.20.
The anticipated annual growth in dividends = br = 60% × 8% = 4.8% or 0.048.
Using the dividend growth model, the expected value per share is:
()
$6.55
0.0480.08
1.048 0.20
P
0
=
−
=
Chapter 18: Business valuations
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Cash flow valuation method
Discounted cash flow basis
Discounting estimated free cash flows and shareholder value analysis
Measuring free cash flow
4 Cash flow valuation method
4.1 Discounted cash flow basis
A discounted cash flow basis might be used when a takeover of a company is under
consideration, to value either (1) the company in total (equity and debt capital) or
(2) the company’s equity shares only.
The basic assumptions in a DCF-based valuation are as follows.
The acquisition of the target company is a form of capital investment by the
company making the acquisition.
Like any other capital investment, it can be evaluated by DCF, using the NPV
method.
After the target company is acquired, its cash flows will come under the control
of the company making the acquisition.
A maximum valuation for the target company can therefore be obtained by
estimating the future cash flows from acquiring the company, and discounting
these to a present value at a suitable cost of capital (perhaps the acquiring
company’s WACC).
Study the following example carefully.
Example
Ruffin Company is considering the acquisition of 100% of Tread, a private company.
It is expected that if the takeover bid is successful, it will be necessary to invest $6
million immediately in capital equipment which will qualify for capital allowances
at an annual rate of 25% by the straight-line method. This equipment will have no
expected residual value.
It is expected that annual cash profits of the acquired company would be $1 million
in the first year, rising to $2 million in the second year, $3 million in the third year
and $4 million in the fourth and subsequent years.
Taxation is 30% and is payable in the same year as the profits to which they relate.
The cost of capital for evaluating the acquisition is 14%.
Required
What is the maximum price that Ruffin Company should offer to acquire the whole
of Tread?
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Answer
Workings
Capital allowances on the equipment purchased
Year TaxWDV
Allowance
claimed
Taxbenefit
(30%)
$ $ $
0(Cost) 600,000
1 (150,000) 150,000 45,000
2 (150,000) 150,000 45,000
3 (150,000) 150,000 45,000
4 (150,000) 150,000 45,000
Annual cash flows
Year Capital
equipment
Cashprofits
lesstaxat30%
Taxbenefit
fromcapital
allowances
Netcashflow
$ $ $ $
0 (6,000,000) (6,000,000)
1 700,000 45,000 745,000
21,400,000 45,000 1,445,000
32,100,000 45,000 2,145,000
42,800,000 45,000 2,845,000
5onwards 2,800,0002,800,000
The cash flows from Year 5 onwards in perpetuity are $2,800,000 per year. These can
be converted into a Year 4 value by discounting them at the cost of capital 14%.
Year 4 value of $2,800,000 per year in perpetuity from Year 5 onwards
= $2,800,000/0.14 = $20,000,000
DCF valuation
The maximum amount at which Tread should be valued is calculated as follows:
Year
Netcashflow/
valuation
Discountfactor
at14%
Present
value
$$
0(6,000,000) 1.000 (6,000,000)
1 745,000 0.877 653,365
21,445,000 0.769 1,111,205
32,145,000 0.675 1,447,875
42,845,000 0.592 1,684,240
5onwards 20,000,000 0.592 11,840,000
NPV 10,736,685
Chapter 18: Business valuations
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The maximum that should be offered for the entire capital of Tread is about $10.737
million, say $10.5 million.
4.2 Discounting estimated free cash flows and shareholder value analysis
In the previous example, the expected annual cash flows from the acquisition of the
target company were given. How are they estimated?
One way of estimating the cash profits or cash flows from a major acquisition is to
estimate the
free cash flows of the target company and discount these to a present
value. Free cash flow is the annual cash flow after paying for all essential
expenditures.
This method makes the following assumptions:
Free cash flow can be defined in a variety of different, although similar ways.
One definition is that free cash flow in each year is the total earnings before
interest, tax, depreciation and amortisation, less essential payments of interest,
tax and purchases of replacement capital expenditure. Another definition of free
cash flow is explained later.
The annual free cash flows that a company is expected to earn in perpetuity can
be discounted to a present value, using the
company’s weighted average cost of
capital
(WACC) as the discount rate.
This discounted value of future free cash flows gives a total valuation for the
company’s equity capital (shares) plus its debt capital.
The fair value of the company’s shares is therefore the present value of these free
cash flows minus the current market value of the company’s debt. This is known
as shareholder value and the approach is sometimes known as
shareholder
value analysis (SVA)
.
Note that free cash flow is based on annual operating
cash flows, not annual
operating
profit.
Shareholder value analysis
Shareholder value analysis estimates a value for the equity capital of a company by:
Calculating the present value of all future annual free cash flows to obtain a
valuation for the entire company, and then
Deducting the value of the company’s debt capital.
Value of shares
= PV of expected free cash flows (as defined) minus Market value of debt capital
Example
A company is expected to have an operating cash flow of $6 million every year
before interest and taxation, and taxation payments are expected to be $1.5 million
each year. Capital expenditure is expected to be $2 million each year. The weighted
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average cost of capital of the company is 8% (after tax). The current market value of
the company’s debt is $7 million.
Using the SVA method, the fair value of the company’s shares is estimated as
follows:
Annual free cash flow = $(6 – 1.5 – 2) = $2.5 million
If this free cash flow is expected every year in perpetuity, the PV of the free cash
flows is
$2.5 million
0.08
= $31.25 million
This is a valuation for the company’s share capital plus debt capital.
The estimated fair value of the company’s shares is obtained by deducting the
market value of the debt capital:
= $31.25 million - $7 million = $24.25 million.
4.3 Measuring free cash flow
Free cash flow can be defined as the amount of cash that is available for
management to use in any way they want (at their discretion), after all essential
payments have been made. Essential payments include payments of taxation on
profits, and should also include payments for the purchase of essential replacement
non-current assets.
However, there is no standard measurement of free cash flow. If an examination
question does not give a definition of free cash flow, you should choose a definition
and state your definition in your answer.
The example below uses one definition of free cash flow, but others might be used.
Example
A company measures its free cash flow as follows:
$
EBIT (1 – t) X
Plus Depreciation (X)
Plus or minus Changes in working capital X or (X)
Minus Expenditure on non-current assets (X)
Equals Free cash flow X
where:
EBIT = earnings before interest and tax
t = the tax rate as a percentage.
The financial results for the year just ended are as follows:
Chapter 18: Business valuations
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$
Profitbeforeinterestandtax 1,500,000
Interest 600,000
900,000
Tax(30%) 270,000
630,000
There was an increase of $50,000 in working capital during the year and expenditure
on fixed assets (non-current assets) was $250,000. The depreciation charge for the
year was $180,000.
The company’s cost of capital is 11%. It expects free cash flow to increase by 6% each
year for the foreseeable future.
Required
Estimate a total value for the company.
Answer
$
EBIT 1,500,000
Taxat30% 450,000
1,050,000
Depreciation 180,000
Increaseinworkingcapital (50,000)
Expenditureonnon‐current
assets
(250,000)
Freecashflow 930,000
Using the growth model valuation formula, an estimate of the total value of the
company is:
P
= 930,000 (1.06)
(0.11 – 0.06)
= $19,716,000.
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Asset based valuation models
Net asset value ‘balance sheet basis’, taken from the statement of financial
position)
Net asset value (net realisable value)
Net asset value (replacement value)
5 Asset based valuation models
Asset based valuation models use the net tangible assets of a business as a
valuation. Different figures arise from the different valuation placed on the business
assets and liabilities.
5.1 Net asset value (‘balance sheet basis’, taken from the statement of
financial position)
This approach uses the book values for assets and liabilities. These figures are
readily-available from the accounts ledgers of the company. However, non-current
assets might be stated at historical cost less accumulated depreciation, and this
might bear no resemblance to a company’s current value.
Some important intangible assets such as internal goodwill and the value of the
company’s human capital (e.g. the skills of its employees) are ignored because they
are not included in the balance sheet. At best this method will provide the minimum
value of a target company.
5.2 Net asset value (net realisable value)
This method may be used when the assets of the company are valuable, and their
current disposable value might be worth more than the expected future dividends
or earnings that the company will provide from using the assets. This valuation may
be appropriate if the intention is for the business to be liquidated and the assets
sold.
A company can never be worth less than its break-up value.
Example
A company has assets that have been valued at $20 million. This valuation is based
on the current disposal value of the assets. The company has $4 million of liabilities.
It has share capital of 200,000 shares of $0.25 each.
A valuation of the shares based on the net asset value of the company would be:
$ 20 million
−
4 million
()
200,000 shares
= $80 per share
.
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5.3 Net asset value (replacement value)
Replacement value measures the value of net assets at their cost of acquisition on
the open market. Whilst this is likely to be a more accurate cost than book values it
will still undervalue the company as intangible assets will be excluded. In addition
it will be very difficult to identify and value individual assets and liabilities.
All asset-based valuation methods can be criticised, because unless there is an
intention to sell off all or some of a company’s assets, the value of a business comes
from the expected returns it will generate, not the reported value of its assets.
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The valuation of debt and preference shares
Valuation of debt securities: the basic principle
Valuation of irredeemable fixed rate debt
Valuation of redeemable fixed rate debt
Valuation of convertible bonds
6 The valuation of debt and preference shares
6.1 Valuation of debt securities: the basic principle
The valuation of debt capital is based on the same basic principle as the valuation of
shares using the dividend valuation model or dividend growth model.
The value of debt securities (bonds) is the present value of all future interest
payments and the repayment of the debt principal, discounted at the cost of the
debt.
Taxation is ignored in the valuation, because the personal tax positions of investors
differ. The valuation is obtained by discounting interest payments and the eventual
redemption value of the bonds at the pre-tax cost of the bonds.
Since the future investment income from fixed-rate bonds (interest and repayment
of the principal) are known amounts, not estimates, the valuation model for bonds
is more exact than the dividend valuation model for shares.
For fixed rate bonds, the present value of all future interest payments and the
repayment of the debt principal is therefore calculated using DCF to obtain a
present value of future cash flows from the bond.
Cost of debt securities and the valuation of debt securities
The earlier chapter on cost of capital explained how the cost of debt capital can be
calculated from the future cash flows from the bond and the market value of the
bond.
Here we are calculating the market value of a bond from the future cash flows from
the bond and the (before-tax) cost of capital.
6.2 Valuation of irredeemable fixed rate debt
The value of irredeemable fixed rate debt is the present value of interest payments
in perpetuity. The valuation model for irredeemable debt is similar to the dividend
valuation model with constant annual dividends.
d
0
r
i
P =