Firm Valuation: A Summary
P.V. Viswanath
Class Notes for Corporate Finance and
Equity Valuation
Discounted Cashflow Valuation
t = n CF
t
Value = 
t
t =1 (1 + r)
where,



n = life of the asset
CFt = cashflow in period t
r = discount rate reflecting the riskiness of the
estimated cashflows
P.V. Viswanath
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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.
P.V. Viswanath
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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
Free Cash Flow to Equity = Net Income – Net Reinvestment (capex as well as
change in working capital) – Net Debt Paid (or + Net Debt Issued)
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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.
Free Cash Flow to the Firm = Earnings before Interest and Taxes (1-tax rate) – Net
Reinvestment
Net Reinvestment is defined as actual expenditures on short-term and long-term assets less
depreciation.
The tax benefits of debt are not included in FCFF because they are taken into account in the firm’s
cost of capital.
P.V. Viswanath
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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.
P.V. Viswanath
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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 =
P.V. Viswanath
$
$
$
$
$
$
$
$
$
$
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
8
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
P.V. Viswanath
9
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%.
P.V. Viswanath
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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
11
What discount rate to use?
 Since financial resources are finite, there is a hurdle that
projects have to cross before being deemed acceptable.
 This hurdle will be higher for riskier projects than for safer
projects.
 A simple representation of the hurdle rate is as follows:
Hurdle rate = Return for postponing consumption +
Return for bearing risk
Hurdle rate = Riskless Rate + Risk Premium
 The two basic questions that every risk and return model in
finance tries to answer are:


How do you measure risk?
How do you translate this risk measure into a risk premium?
P.V. Viswanath
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The Capital Asset Pricing Model
 Uses variance as a measure of risk
 Specifies that a portion of variance can be diversified away,
and that is only the non-diversifiable portion that is
rewarded.
 Measures the non-diversifiable risk with beta, which is
standardized around one.
 Relates beta to hurdle rate or the required rate of return:
Reqd. ROR = Riskfree rate + b (Risk Premium)
 Works as well as the next best alternative in most cases.
P.V. Viswanath
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From Cost of Equity to Cost of Capital
 The cost of capital is a composite cost to the firm of
raising financing to fund its projects.
 In addition to equity, firms can raise capital from
debt
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Estimating the Cost of Debt
 If the firm has bonds outstanding, and the bonds are traded,
the yield to maturity on a long-term, straight (no special
features) bond can be used as the interest rate.
 If the firm is rated, use the rating and a typical default spread
on bonds with that rating to estimate the cost of debt.
 If the firm is not rated,


and it has recently borrowed long term from a bank, use the interest
rate on the borrowing or
estimate a synthetic rating for the company, and use the synthetic
rating to arrive at a default spread and a cost of debt
 The cost of debt has to be estimated in the same currency as
the cost of equity and the cash flows in the valuation.
P.V. Viswanath
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Estimating Cost of Capital: Boeing
 Equity



Cost of Equity = 5% + 1.01 (5.5%) = 10.58%
Market Value of Equity =
$32.60 Billion
Equity/(Debt+Equity ) =
82%
 Debt



After-tax Cost of debt =
Market Value of Debt =
Debt/(Debt +Equity) =
5.50% (1-.35) = 3.58%
$ 8.2 Billion
18%
 Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17%
P.V. Viswanath
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Estimating the Expected Growth Rate
Expected Growth
Net Income
Retention Ratio=
1 - Dividends/Net
Income
X
Operating Income
Return on Equity
Net Income/Book Value of
Equity
Reinvestment
Rate = (Net Cap
Ex + Chg in
WC/EBIT(1-t)
P.V. Viswanath
X
Return on Capital =
EBIT(1-t)/Book Value of
Capital
17
Expected Growth in EPS
gEPS = (Retained Earningst-1/ NIt-1) * ROE
= Retention Ratio * ROE
= b * ROE
• ROE = (Net Income)/ (BV: Common Equity)
• This is the right growth rate for FCFE
• Proposition: The expected growth rate in earnings
for a company cannot exceed its return on equity in
the long term.
P.V. Viswanath
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Expected Growth in EBIT And
Fundamentals
 Reinvestment Rate and Return on Capital
gEBIT = (Net Capex + Change in WC)/EBIT(1-t) * ROC
= Reinvestment Rate * ROC
 Return on Capital =
(EBIT(1-tax rate)) / (BV: Debt + BV: Equity)
 This is the right growth rate for FCFF
 Proposition: No firm can expect its operating income to
grow over time without reinvesting some of the operating
income in net capital expenditures and/or working capital.
P.V. Viswanath
19
Getting Closure in Valuation
 A publicly traded firm potentially has an infinite
life. The value is therefore the present value of cash
t =  CF
t
Value = 
flows forever.
t
t = 1 (1+ r)
 Since we cannot estimate cash flows forever, we
estimate cash flows for a “growth period” and then
estimate a terminal value, to capture the value at the
end of the period: Value = t =N CFt t  Terminal Value
t = 1 (1 + r)
P.V. Viswanath
N
(1 + r)
20
Stable Growth and Terminal Value
 When a firm’s cash flows grow at a “constant” rate forever,
the present value of those cash flows can be written as:
Value = (Expected Cash Flow Next Period) / (r - g) where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate
 This “constant” growth rate is called a stable growth rate
and cannot be higher than the growth rate of the economy in
which the firm operates.
 While companies can maintain high growth rates for
extended periods, they will all approach “stable growth” at
some point in time.
 When they do approach stable growth, the valuation formula
above can be used to estimate the “terminal value” of all
cash flows beyond.
P.V. Viswanath
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Relative Valuation
 In relative valuation, the value of an asset is derived from
the pricing of 'comparable' assets, standardized using a
common variable such as earnings, cashflows, book value or
revenues. Examples include -• Price/Earnings (P/E) ratios

and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples)
• Price/Book (P/BV) ratios

and variants (Tobin's Q)
• Price/Sales ratios
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Multiples and DCF Valuation
 Gordon Growth Model: P  rDPS
g
 Dividing both sides by the earnings,
1
0
n
P0
Payout Ratio * (1  g n )
 PE =
EPS0
r-gn
 Dividing both sides by the book value of equity,
P0
ROE * Payout Ratio * (1  g n )
 PBV =
BV 0
r-g
n
 If the return on equity is written in terms of the retention
ratio and the expected growth rate
P0
ROE - gn
 PBV =
BV 0
r-gn
 Dividing by the Sales per share,
P0
Profit Margin * Payout Ratio * (1  g n )
 PS =
Sales 0
r-gn
P.V. Viswanath
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