Fundamentals of Valuation
P.V. Viswanath
Based on Damodaran’s Corporate Finance
Cash Flows:
The Accountant’s Approach
 The objective of the Statement of Cash Flows,
prepared by accountants, is to explain changes in
the cash balance rather than to measure the health
or value of the firm
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The Statement of Cash Flows
Figure 4.3: Statement of Cash Flows
Net cash flow from operations,
after taxes and interest expenses
Cash Flows From Operations
Includes divestiture and acquisition
of real assets (capital expenditures)
and disposal and purchase of
financial assets. Also includes
acquisitions of other firms.
+ Cash Flows From Investing
Net cash flow from the issue and
repurchase of equity, from the
issue and repayment of debt and after
dividend payments
+ Cash Flows from Financing
= Net Change in Cash Balance
This is a historical approach. We will modify this to create a model of
cashflows for valuation
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Cash Flows:
The Financial Analyst’s Approach
 In financial analysis, we are concerned about


Cash flows to Equity: These are the cash flows generated by the
asset after all expenses and taxes, and also after payments due on the
debt. Cash flows to equity, which are after cash flows to debt but
prior to cash flows to equity
Cash flow to Firm: This cash flow is before debt payments but after
operating expenses and taxes. This looks at not just the equity
investor in the asset, but at the total cash flows generated by the asset
for both the equity investor and the lender.
 These cash flow measures can be used to value assets, the
firm’s equity and the entire firm itself.
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Free Cashflows to the Firm
 Free Cashflows to the firm (FCFF) are defined as cashflows
available for distribution to (all) the stakeholders of the firm
without impairing the long-run profitability of the firm.


Free Cash Flow to Firm = EBIT (1-t) – Net Reinvestment where
Net Reinvestment = Incr in Non-cash Working Cap + Cap Exp –
Depreciation
 Alternatively,

FCFF = Net Income + Interest (1-t) + Net Reinvestment
 Note that we do not take into account the tax benefit of
interest in computing FCFF because the tax benefit of
interest is accounted for in the discount rate.
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Free Cashflows to the Firm
 We can compute historical, i.e. ex-post FCFF by using information in
the Statement of Cashflows:

FCFF = Cashflow from Operations + Interest (1-t) – Capital Expenditures

Note that Cashflows from Operations already include changes in working
capital so we do not need to subtract this out again. However,
They also include interest as a negative flow, so we add it back
 For valuation purposes, we need forecasts of these quantities and the
disaggregated model is more useful.
 The value of the firm is the discounted present value of cashflows to the
firm + Any cash position that the firm might have. Cash is considered
separately because it is usually interest bearing and its present value is
simply its current value.
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Cashflows to Equity
 Free Cash Flow to Equity (FCFE) is another cashflow
measure that focuses on cash flows to equityholders alone.
 FCFE = Net Income + Depreciation – (Change in noncash
Working Capital) – Capital Expenditures – Net Debt Paid.
 FCFE can also be computed (as an historical quantity) from
the statement of cashflows as

FCFE = Cashflow from Operations – Capital Expenditures – Net
Debt paid (short-term and long-term)
 If there are other non-common stock securities, cashflows
associated with them, such as preferred dividends are also
subtracted.
 The value of common equity is the discounted present value
of free cashflows to equity.
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Two Measures of Discount Rates
 Cost of Equity: This is the rate of return required
by equity investors on an investment. It will
incorporate a premium for equity risk -the greater
the risk, the greater the premium. This is used to
value equity.
 Cost of capital: This is a composite cost of all of
the capital invested in an asset or business. It will
be a weighted average of the cost of equity and the
after-tax cost of borrowing. This is used to value
the entire firm.
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Equity Valuation
Figure 5.5: Equity Valuation
Assets
Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth
Liabilities
Assets in Place
Growth Assets
Debt
Equity
Discount rate reflects only the
cost of raising equity financing
Present value is value of just the equity claims on the firm
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Valuing Equity in a Finite Life Asset
 Assume that you are trying to value the Home Depot’s
equity investment in a new store.
 Assume that the cash flows from the store after debt
payments and reinvestment needs are expected will be
$850,000 a year, growing at 5% a year for the next 12 years.
 In addition, assume that the salvage value of the store, after
repaying remaining debt will be $ 1 million.
 Finally, assume that the cost of equity is 9.78%.
Value of Equity in Store
 (1.05)12 

850,000 (1.05) 
1 12 
 (1.0978) 
1,000,000
=
+
= $8,053,999
(.0978 -.05)
(1.0978)12
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Firm Valuation
Figure 5.6: Firm Valuation
Assets
Cash flows considered are
cashflows from assets,
prior to any debt payments
but after firm has
reinvested to create growth
assets
Liabilities
Assets in Place
Growth Assets
Debt
Equity
Discount rate reflects the cost
of raising both debt and equity
financing, in proportion to their
use
Present value is value of the entire firm, and reflects the value of
all claims on the firm.
Note that the tax benefits of debt are not included in FCFF because they are taken into
account in the firm’s cost of capital.
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Valuing a Finite-Life Asset
 Consider the Home Depot's investment in a proposed store.
The store is assumed to have a finite life of 12 years and is
expected to have cash flows before debt payments and after
reinvestment needs of $ 1 million, growing at 5% a year for
the next 12 years.
 The store is also expected to have a value of $ 2.5 million at
the end of the 12th year (called the salvage value).
 The Home Depot's cost of capital is 9.51%.
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Expected Cash Flows and present
value
Year
Expecte d Cash Flows
Value at End
PV at 9 .5 1%
1
$
1,050 ,0 00
$
958 ,8 17
2
$
1,102 ,5 0 0
$
919 ,3 29
3
$
1,157 ,6 25
$
881 ,4 68
4
$
1,215 ,5 06
$
845 ,1 66
5
$
1,276 ,2 82
$
810 ,3 59
6
$
1,340 ,0 96
$
776 ,9 86
7
$
1,407 ,1 00
$
744 ,9 87
8
$
1,477 ,4 55
$
714 ,3 06
9
$
1,551 ,3 28
$
684 ,8 88
10
$
1,628 ,8 95
$
656 ,6 82
11
$
1,710 ,3 39
$
629 ,6 38
12
$
1,795 ,8 56
$
1 ,4 44 ,1 24
$
2,500 ,0 00
Value of St ore =
P.V. Viswanath
$ 10 ,0 66 ,7 49
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Valuation with Infinite Life
DISCOUNTED CASHFLOW VALUATION
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
flow
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value
Value
Firm: Value of Firm
CF1
CF2
CF3
CF4
CF5
CFn
.........
Forever
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
P.V. Viswanath
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Valuing the Home Depot’s Equity
 Assume that we expect the free cash flows to equity at
Home Depot to grow for the next 10 years at rates much
higher than the growth rate for the economy. To estimate the
free cash flows to equity for the next 10 years, we make the
following assumptions:



The net income of $1,614 million will grow 15% a year each year
for the next 10 years.
The firm will reinvest 75% of the net income back into new
investments each year, and its net debt issued each year will be 10%
of the reinvestment.
To estimate the terminal price, we assume that net income will grow
6% a year forever after year 10. Since lower growth will require less
reinvestment, we will assume that the reinvestment rate after year 10
will be 40% of net income; net debt issued will remain 10% of
reinvestment.
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Estimating cash flows to equity: The
Home Depot
Year
1
2
3
4
5
6
7
8
9
10
Net Income
$
1,856
$
2,135
$
2,455
$
2,823
$
3,246
$
3,733
$
4,293
$
4,937
$
5,678
$
6,530
Reinvestment Needs Net Debt Paid
$
1,392
$
(139)
$
1,601
$
(160)
$
1,841
$
(184)
$
2,117
$
(212)
$
2,435
$
(243)
$
2,800
$
(280)
$
3,220
$
(322)
$
3,703
$
(370)
$
4,258
$
(426)
$
4,897
$
(490)
Sum of PV of FCFE =
$
$
$
$
$
$
$
$
$
$
FCFE
603
694
798
917
1,055
1,213
1,395
1,605
1,845
2,122
PV of FCFE
$
549
$
576
$
603
$
632
$
662
$
693
$
726
$
761
$
797
$
835
$6,833
New Investments = Change in Working Capital + Capital
Expenditures – Depreciation
Hence FCFE = Net Income – Reinvestment needs – Net Debt Paid
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Terminal Value and Value of Equity
today
 FCFE11 = Net Income11 – Reinvestment11 – Net Debt Paid
(Issued)11
= $6,530 (1.06) – $6,530 (1.06) (0.40) – (-277) = $ 4,430 million
 Terminal Price10 = FCFE11/(ke – g)
= $ 4,430 / (.0978 - .06) = $117,186 million
 The value per share today can be computed as the sum of the
present values of the free cash flows to equity during the
next 10 years and the present value of the terminal value at
the end of the 10th year.
Value of the Stock today = $ 6,833 million + $
117,186/(1.0978)10
= $52,927 million
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Valuing Boeing as a firm
 Assume that you are valuing Boeing as a firm, and
that Boeing has cash flows before debt payments
but after reinvestment needs and taxes of $ 850
million in the current year.
 Assume that these cash flows will grow at 15% a
year for the next 5 years and at 5% thereafter.
 Boeing has a cost of capital of 9.17%.
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Expected Cash Flows and Firm Value
 Terminal Value = $ 1710 (1.05)/(.0917-.05) = $ 43,049
million
Year
Cash Flow
Terminal
Value
1
$978
$895
2
3
4
5
$1,124
$1,293
$1,487
$1,710
$943
$994
$1,047
$28,864
$43,049
Value of Boeing as a firm =
P.V. Viswanath
Present
Value
$32,743
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