Valuation of shares

Flow of the presentation
Introduction
Discounted Cash Flow
CAPM
Dividend Growth
WACC
The General Model
The Gordon Growth Model
Two Stage DDM
H Model
Three Stage DDM
FCFE
Two Stage FCFE
P/E, P/BV, P/S
PEG & YPEG
Black & Scholes Model

CAPM
P/E
Ratio
Gordon’s
Model
Dividend
Growth
Model
Net
Asset
Value
Liquidation
Value
Method
DCF
I need
assistance
EV

What is Valuation?
Valuation is the first step toward intelligent investing.
The object of investment is to find assets that are worth more than they
cost
Valuation is the process of estimating how much an asset is worth
Valuation encompasses many considerations
 how the value of an asset is determined
 why the asset has a certain value, and not a higher or lower one
 how to compare asset values, as a basis for investment decision
making
What is Valuation?

Reasons for Valuation
M&A’s
Buyouts
ESOP
Divorces
Estate Planning
Keyman Life Insurance
Financing of Potential Investors
Reasons for Valuation

Who Uses Valuation
Investors (Active & Passive)
Fundamental Analysts
Franchise Buyer
Chartists
Information Traders
Market Timers
Efficient Marketers
Who Uses Valuation

Concepts of Value
Book Value
Replacement Value
Liquidation Value
Going Concern Value
Market Value
Concepts of Value

APPROACHES TO ASSET
VALUATION
• Balance Sheet Value method
(Net Book Value Method).
• Adjusted Book Value method.
 Liquidation Value method.
 Replacement Cost method.

BALANCE SHEET METHOD
…Net Book Value
Value of a asset will be represented by the book
value reflected in the balance sheet.
Vo = Total assets at balance sheet values – Total
Liabilities(excluding networth)
Number of ordinary shares issued
Or,
Vo = Share Capital + Reserves and Surplus
Number of ordinary shares issued

ILLUSTRATION:
The balance sheet of Ahuja Ltd shows share
capital of Rs 100 crores. (10 CRORE
SHARES OF Rs 10 Each) and reserves and
surplus of Rs 100 crores. Estimate the value
of the firm’s equity shares.

…Net Book Value

SOLUTION:

Share Capital = Rs.100 Crs (10 crs shares of Rs.10
each).
Reserves & Surpluses = Rs 100 Crs.
∴ Net Book Value = Rs. 200 Crs (100 Crs + 100 Cr)
NBV per share = 200 Crs/10 Crs shares
= Rs. 20 per share.

One can compare NBV with the going market price
while taking investment decisions.
…Net Book Value

LIMITATIONS:
It does not take into account the future earning
capacity of the business.
It does not take into account the present value or the
change in the historical value of the asset over a
period of time as the valuation is based on the
historical value of the assets.
Technological advances renders some of the existing
assets worthless which is not accounted for in this
model.
These limitations of the NBV method is somewhat
rectified by the Adjusted Book Value method of
valuation.
…Net Book Value

ADJUSTED BOOK VALUE METHOD
…Improvement Over NBV
It involves determining the FAIR MARKET VALUE
of the assets and liabilities of the firm as a going
concern.
Assets are not taken at historical costs but are valued
at market price.
This fair market value of an asset can be determined
by either Replacement Cost method, or
Liquidation Value method.

REPLACEMENT COST METHOD
…For Adjusted Book
Value
The value of business is arrived at by
determining the current cost of putting up
similar facilities or buying similar assets.
Net book values are substituted by current
replacement costs.
The Table on the next page illustrates how replacement
costs for various assets are considered.

Debtors Valued at Face Value. Provide for bad debts if doubtful.
Inventories R.M. at most recent cost of acquisition
WIP at Cost of R.M + Cost of processing
FG at Realizable S.P – (holding, transport & selling costs)
Other C.A. Other C.A. like deposits, prepaid expenses and accruals
valued at Book Value
Fixed Assets (Land, P&M, Buildings valued at Market Price ) +
(transportation, installation & selling expenses if any).
Non-
operating
assets
Financial securities, excess land & buildings valued at Fair
Market Value
REPLACEMENT COST METHOD
…For Adjusted Book Value

…Replacement Cost per share
Total assets at
replacement cost
Total liabilities
(excluding networth)
No. of Outstanding shares

LIQUIDATION VALUE METHOD
…For Adjusted Book
Value
For approximating the fair market value of the
assets on the balance sheet of a firm is to
find out what they would fetch if the firm were
liquidated immediately
The value of the business is arrived at by
totaling up the realizable value of various
assets of the unit minus the liabilities.

…LIQUIDATION VALUE per share
The value realized from
liquidating all the assets
of the firm.
Less amount paid to all
the creditors and
preference share holders
No. of outstanding shares

LIQUIDATION VALUE METHOD
…For
Adjusted Book Value
LIMITATIONS:
This approach is relevant mainly for sick units that
are beyond redemption.
It is not suitable for going concerns as instead of
valuing the company as a whole, it values it as a
collection of assets to be sold individually.
One of the major drawback of this model is that it
does not take into account the future earning
potential of the firm and just concentrates on the
liquidation costs of the assets.

Enterprise Value (EV)
Measure of what the market believes a
company's ongoing operations are worth
Enterprise value discusses the aggregate
value of a company as an enterprise rather
than just focus on its current market
capitalization.

Enterprise Value (EV)
Equity value
 Market value of shareholders’ equity (shares outstanding x current
stock price)
Enterprise value
 Measure of what the market believes a company's ongoing
operations are worth
 Market value of all capital invested in the firm
 Equity, debt (short-term and long-term), preferred stock, minority
interest
Equity
Debt
Preferred Stock
Minority Interest
Enterprise
Value
LiabilitiesAssets
=

Calculating EV
To calculate enterprise value, we start with a company's market
cap, add debt (on a company's balance sheet), and subtract
cash and Equivalents (on the balance sheet).
To get total debt, add together long-term and short-term debt.
Market Cap = Current share price * Total shares Outstanding
Debt = Long Term Debt + Short Term Debt
E V = Market Capitalization + Debt – Cash & Equivalents

Example
Tata Steel Ltd.
Total shares Outstanding = 553472856
Current share price (Rs.) = 347.70
Long-Term Debt (Rs. In crores) = 24,681.80
Short-Term Debt (Rs. In crores) = 2,715.20
Cash & Equivalents = 2467.20
Market Cap = (553472856*347.70)
= 19244.25
∴Enterprise Value = 19244.25 +(24681.20 +2715.20) –
2467.20
= 44173.45 crores

EV/ Sales
• Ratio measures the total company value as
compared to its annual sales
• A high ratio means that the company's value is
much more than its sales.
• When valuing companies that do not have
earnings, or that are going through unusually
rough times

EV/ EBITDA
Higher the number, the more expensive
the company is.
Best way to use EV/EBITDA is to
compare it to that of other similar
companies

Approaches To Valuation
Discounted cash-flow valuation (Intrinsic
Value), relates the value of an asset to the present
value of expected future cash-flows on that asset.
Relative valuation, estimates the value of an asset
by looking at the pricing of 'comparable' assets
relative to a common variable like earnings, cash-
flows, book value or sales.
Contingent claim valuation, uses option pricing
models to measure the value of assets that share
option characteristics.

Valuation Models
DCF Model
Relative Valuation
Model
Equity / Balance Sheet
Valuation Models
Book Value
Liquidation Value
Replacement Cost
P/E Ratio
Economic Profit Model
Entity DCF Model
Dividend Models
Dividend Discount
Constant Growth
DDM

Discounted cash-flow (DCF)
DCF method entails estimating the free cash
flow available to debt and equity investors
(i.e., the annual cash flows generated by the
business, and the terminal value of the
business at the end of the time horizon) and
discounting these flows back to the present
using the weighted average cost of capital as
the discount rate to arrive at a present value
of the assets

DCF (contd..)
DCF is often the primary valuation methodology in
M&A
 Comparable public company and comparable acquisition
analysis are often used as confirming methodologies
DCF is the PV of 2 main types of free cash flows:
1. Free cash flows to all capital providers (debt and equity)
2. Free cash flows to equity capital providers
 special case: dividend discount model
Fundamental in nature, DCF allows for questioning
all of the assumptions and for performing sensitivity
analysis
One can easily estimate equity value from firm value
by subtracting the market value of debt today

DCF Valuation in 5 Steps…
1. Project the free cash flows of a business over the
forecast period
 Typical forecast period is 10 years. However, the range can
vary from five to 20 years
1. Use the weighted average cost of capital (WACC) to
determine the appropriate discount rate range
2. Estimate the terminal value of the business at the
end of the forecast period
3. Determine the value for the enterprise by
discounting the projected free cash flows and
terminal value to the present
4. Interpret the results and perform sensitivity analysis

DCF (contd..)
Calculation of free cash flow begins with financial
projections
 Comprehensive projections (i.e., fully-integrated income
statement, balance sheet and statement of cash flows)
typically provide all the necessary elements
Quality of DCF analysis is a function of the quality of
projections
 Confirm and validate key assumptions underlying
projections
 Sensitize variables that drive projections
Sources of projections include
 Target company’s management
 Acquiring company’s management
 Research analysts
 Bankers

DCF – FCF: What is it?
Free cash flow is un-levered cash available to
creditors and owners after taxes and
reinvestment
 Un-levered means free from financing
considerations
 Contrast with Cash Flow from Operations (which
consists of Net Income plus Depreciation and
Amortization plus Deferred Taxes and Non-Cash
charges)
 Free cash flows can be forecast from a firm’s
financial projections, even if those projections
include the effects of debt

DCF – FCF: How to calculate it?
Net Sales (Revenue)
- Cost of goods sold (COGS)
- Selling, general, and administrative (SG&A)
=Earnings before interest, taxes, depreciation and amortization
(EBITDA)
- Depreciation & Amortization (D&A)
= Earnings before interest and taxes (EBIT)
- Taxes (tax rate*EBIT)
=Net operating profit/loss after taxes (NOPLAT)
+ Depreciation & Amortization (D&A)
- Capital Expenditure (Capex)
- Change in Net working capital (∆NWC)
=Free cash flow (FCF)

DCF – FCF: How to forecast?
Income Statement
Project growth in Net Sales by basing assumptions on
 Research reports
 Client forecasts (if available)
 Industry trends
 percent growth is usually an input; aggregate sales is derived from
this input
Estimate the following by percent of sales
 Cost of Goods Sold (COGS)
 Selling, General and Administrative (SG&A) Expenses
Determine Interest Expense
 Refer to the debt schedule and calculate the weighted average
interest rate.
 If no debt schedule is available, then compute Interest Expense as
a percent of average Long-Term Debt= (Beginning LTD + Ending
LTD)/2
Assess tax rate based on the marginal tax rate (federal, state
and local) and current tax regulation

DCF – FCF: How to forecast? (contd..)
Depreciation
 Sometimes expressed as % of Property,
Plant and Equipment (PP&E)
Capital Expenditures (Capex)
 Expenditures necessary to maintain the
required capital intensity

DCF – FCF: How to forecast? (contd..)
Balance Sheet Items
Working Capital excluding cash and cash equivalents
and STD
 WC = (Current Assets–Cash and Cash Equivalents)–
(Current Liabilities–STD)
 Estimate WC as a percent of sales
 Possible to squeeze cash from WC by operating more
efficiently
 Three major components of working capital are: inventories,
receivables and payables
Property, Plant and Equipment (PP&E):
 Project by capital intensity/efficiency: sales divided by
(PP&E)
 Beginning PP&E–Depreciation+ CapEx = Ending PP&E

DCF – WACC
Weighted Average Cost Of Capital (WACC)
 Ascertain the costs of the various sources of capital for the
company, with a given capital structure
 Debt
 Equity
 The after-tax costs of the various sources are then averaged to
arrive at an appropriate discount rate to value unlevered cash flows
 Debt and equity market values used should represent the “target”
capital structure (the capital structure that includes planned debt
and equity financings, if any)
( )
ED
E
r
ED
D
TrWACC equitydebt
+
×+
+
×−×= 1

DCF – WACC (contd..)
Cost of debt
Consult with the debt capital markets group for a 10-
year maturity all-in new issue rate at the credit rating
corresponding to the targeted capital structure. As
part of this process, you should look at the yield on
new issues of comparable companies since the cost
of debt is a function of the risks associated with a
given business/industry
If the company has public debt outstanding and you
do not intend to change its capital structure, find the
debt rating

DCF – WACC (contd..)
Cost of equity
Use the Capital Asset Pricing Model (CAPM)
The risk-free rate can be taken as the interest rate on
a generic 10-year government note
 Roughly matches the maturity of projections
β = cov(r,rM)/var(rM), usually estimated using a
regression
Estimation issues
 Betas may change over time
 Don’t use data from too long ago
 Five years of monthly data is reasonable
( ) premiumriskEquityratefree-Risk ×+= βfequity rr
( ) ttftMtft rrrr εβα +−+=− ,,,

Reliance has a beta of 1.5. Assuming the treasury rate as 5%. The cost
of equity can be calculated as follows:
Cost of Equity = 5% + (1.5 * 8%)
= 17%
The market premium of 8% was based upon historical data and is the
premium earned by stocks on an average over treasury bills. The cost
of equity of 17% will be used to discount dividends and cashflows to
equity and to obtain the value of Reliance.
Capital Asset Pricing Model
Example: Reliance

Limitations of CAPM
The model does not appear to adequately explain the variation
in stock returns.
The model assumes that all investors agree about the risk and
expected return of all assets.
The model assumes the existence of a risk-free rate, that all
investors have access to the risk-free rate, and that there is no
limit to the amount that may be borrowed or lent at this amount.
The model assumes that there are no taxes or transaction costs
Non stability of beta
Capital Asset Pricing Model

DCF – Terminal value
Terminal value is the value of all future cash
flows after the explicit forecast period of 10
years
)(
FCF
)(
1Noplat
TV 1T
1T
T
gWACCgWACC
ROIC
g
−
=
−






−×
= +
+

DCF – Terminal value
Key value drivers
Growth rate of NOPLAT (g)
Return on invested capital ROIC
 Value is higher if ROIC is higher than WACC
 Higher growth rate is good because our projects have a
ROIC greater than the cost of capital
 Value is lower if ROIC is higher than WACC
 Higher growth rate is bad because our projects have a
ROIC lower than the cost of capital

DCF – Terminal value (contd..)
Can also estimate terminal value using an exit
multiple
Terminal value = Statistic x Multiple
Forecast 10 explicit years of FCF, EBITDA, Net
Income
Use a multiple of any relevant figure: Book Value, Net
Income, Cash Flow from Operations, EBIT, EBITDA,
Sales, etc.
 Terminal Value should be an Enterprise Value; NOT ALL
multiples produce an Enterprise Value (e.g., P/Es)
Multiply and estimate Terminal Value

DCF – Terminal value: exit multiple

DCF – Terminal value: perpetuity growth

DCF (contd..)
Validate and test projection assumptions
Carefully consider all variables in the calculation of
the discount rate
Consistency of assumptions concerning interest
rates, inflation rates, tax rates and the cost of capital
is critical
Thoughtfully consider terminal value methodology
Do sensitivity analysis (base projection variables,
synergies, discount rates, terminal values, etc.)

DCF – Walmart exampleDecember 2007 Treasury rates
3-month 3.00%
1-year 3.26%
5-year 3.49%
20-year 4.57%
December 2007 AAA yield 5.49%
Risk premium for AA rate bonds 2.2%
Equity risk premium 5.0%
Tax Rate 33%
Beta 0.71
Cost of debt (rd) 6.80%
=rf+risk premium
Cost of equity (re) 8.13%
=rf+β*(rm-rf)
Net debt (D) 37.00
Market cap (E) 192.00
Total Value (V=D+E) 229.00
D/V 16.2%
E/V 83.8%
WACC 7.56%
=rd(1-tax) D/V + re E/V

Walmart FCF assumptions
The sales at the end of 2007 were $370 billion. They are
projected to grow by 10% during the next year. The growth rate
of sales will decline by 0.5% each year for the next 10 years
COGS is currently 76% of sales and is expected to decline by
0.1% during the next 10 years
SG&A is currently 17% of sales and is expected to increase by
0.1% during the next 10 years
D&A are currently 1.7% of sales and are expected to remain at
the same level
Capex is currently 3.5% of sales and is expected to remain at
the same level
NWC is 0.5% of sales and is expected to remain at the same
level

Walmart FCF’s
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Sales 370,000 407,000 445,665 485,775 527,066 569,231 611,923 654,758 697,317 739,156 779,810
Sales growth 10.0% 9.5% 9.0% 8.5% 8.0% 7.5% 7.0% 6.5% 6.0% 5.5%
COGS 308,913 337,814 367,732 398,462 429,769 461,390 493,033 524,383 555,106 584,857
% of Sales 76.0% 75.9% 75.8% 75.7% 75.6% 75.5% 75.4% 75.3% 75.2% 75.1% 75.0%
SGA 69,597 76,654 84,039 91,709 99,615 107,698 115,892 124,122 132,309 140,366
% of Sales 17.0% 17.1% 17.2% 17.3% 17.4% 17.5% 17.6% 17.7% 17.8% 17.9% 18.0%
D&A 6,919 7,576 8,258 8,960 9,677 10,403 11,131 11,854 12,566 13,257
% of Sales 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7%
Capex 14,245 15,598 17,002 18,447 19,923 21,417 22,917 24,406 25,870 27,293
% of Sales 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5%
NWC 1,850 2,035 2,228 2,429 2,635 2,846 3,060 3,274 3,487 3,696 3,899
% of Sales 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5%
EBIT 21,571 23,620 25,746 27,934 30,169 32,432 34,702 36,958 39,175 41,330
Tax 7,118 7,795 8,496 9,218 9,956 10,703 11,452 12,196 12,928 13,639
NOPLAT 14,453 15,826 17,250 18,716 20,213 21,729 23,250 24,762 26,247 27,691
+D&A 6,919 7,576 8,258 8,960 9,677 10,403 11,131 11,854 12,566 13,257
-∆ NWC 185 193 201 206 211 213 214 213 209 203
-Capex 14,245 15,598 17,002 18,447 19,923 21,417 22,917 24,406 25,870 27,293
FCF 6,942 7,610 8,305 9,022 9,756 10,501 11,251 11,997 12,733 13,451
Discount factor 0.930 0.864 0.804 0.747 0.695 0.646 0.601 0.558 0.519 0.483
Discounted cash flows 6,454 6,579 6,675 6,742 6,778 6,783 6,757 6,699 6,610 6,492
Total (excl Cont Value) 66,569

Walmart continuation value
Continuation Value 381,123
PV(Continuation Value) 183,953 73%
Firm value 250,522
Less Debt value 37,000
Equity value 213,522
Number of shares 4,170
Equity value per share 51.20
NOPLATT+1(1-g/ROIC)/(WACC-g)

Walmart sensitivity analysis
51.20 2.0% 2.4% 2.8% 3.2% 3.6% 4.0% 4.4% 4.8% 5.2% 5.6% 6.0%
6.0% 46.32 45.28 44.04 42.52 40.66 38.33 35.36 31.46 26.17 18.63 7.09
6.4% 47.54 46.87 46.06 45.06 43.81 42.24 40.22 37.56 33.92 28.72 20.73
6.8% 48.62 48.28 47.84 47.29 46.59 45.69 44.51 42.93 40.76 37.62 32.77
7.2% 49.59 49.53 49.43 49.27 49.06 48.75 48.32 47.71 46.84 45.54 43.48
7.6% 50.45 50.64 50.84 51.05 51.26 51.49 51.73 51.99 52.28 52.62 53.05
8.0% 51.22 51.65 52.12 52.65 53.25 53.96 54.80 55.84 57.18 58.99 61.67
8.4% 51.92 52.56 53.27 54.09 55.05 56.19 57.57 59.32 61.60 64.76 69.46
8.8% 52.56 53.38 54.32 55.41 56.69 58.22 60.10 62.48 65.63 70.00 76.55
51.20 2.0% 2.4% 2.8% 3.2% 3.6% 4.0% 4.4% 4.8% 5.2% 5.6% 6.0%
6.0% 71.48 71.72 71.97 72.22 72.47 72.71 72.96 73.21 73.45 73.70 71.33
6.4% 64.99 65.21 65.44 65.66 65.88 66.11 66.33 66.55 66.78 67.00 67.22
6.8% 59.32 59.52 59.72 59.93 60.13 60.33 60.53 60.73 60.94 61.14 61.34
7.2% 54.32 54.51 54.69 54.88 55.06 55.24 55.43 55.61 55.80 55.98 56.16
7.6% 49.90 50.06 50.23 50.40 50.57 50.74 50.90 51.07 51.24 51.41 51.58
8.0% 45.95 46.11 46.26 46.41 46.57 46.72 46.87 47.03 47.18 47.34 47.49
8.4% 42.42 42.56 42.70 42.84 42.98 43.12 43.26 43.40 43.55 43.69 43.83
8.8% 39.24 39.37 39.49 39.62 39.75 39.88 40.01 40.14 40.27 40.40 40.53
TerminalROIC
Terminal growth rate
WACC=ROIC
Terminal growth rate

Discounted Cashflow Valuation
where,
– n = Life of the asset
– CFt = Cashflow in period t
– r = Discount rate reflecting the riskiness of the estimated cashflows

Equity Valuation versus Firm Valuation
Value just the equity stake in the business
Value the entire business, which includes, besides equity, the
other claimholders in the firm

Equity Valuation
The value of equity is obtained by discounting expected cashflows to
equity, i.e., the residual cashflows after meeting all expenses, tax
obligations and interest and principal payments, at the cost of equity
where,
CF to Equity t = Expected Cashflow to Equity in period t
ke = Cost of Equity

Firm Valuation
The value of the firm is obtained by discounting expected cashflows to
the firm, i.e., the residual cashflows after meeting all operating expenses
and taxes, but prior to debt payments, at the weighted average cost of
capital, which is the cost of the different components of financing used by
the firm, weighted by their market value proportions
where,
CF to Firm t = Expected Cashflow to Firm in period t
WACC = Weighted Average Cost of Capital

Assume that you are analyzing a company with the following cashflows
for the next five years.
Year CF to Equity CF to Firm
1 $ 50 $ 90
2 60 100
3 68 108
4 76.2 116.2
5 83.49 123.49
Terminal
Value
1603.008 2363.008
Assume also that the cost of equity is 13.625% and the firm can
borrow long term at 10%. (The tax rate for the firm is 50%.)
The current market value of equity is $1,073 and the value of debt
outstanding is $800.

Method 1: Discount CF to Equity at Cost of Equity to get value of
equity
Cost of Equity = 13.625%
PV of Equity = 50/1.13625 + 60/1.136252
+ 68/1.136253
+
76.2/1.136254
+ (83.49+1603)/1.136255
= $1073
Method 2: Discount CF to Firm at Cost of Capital to get value of
firm
Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%
WACC = 13.625% (1073/1873) + 5% (800/1873) = 9.94%
PV of Firm = 90/1.0994 + 100/1.09942
+ 108/1.09943
+ 116.2/1.09944
+ (123.49+2363)/1.09945
= $1873
PV of Equity = PV of Firm - Market Value of Debt
= $ 1873 - $ 800 = $1073

But Always Remember
Never mix and match cash flows and discount rates.
The key error to avoid is mismatching cashflows and discount rates,
since discounting cashflows to equity at the weighted average cost of
capital will lead to an upwardly biased estimate of the value of equity,
while discounting cashflows to the firm at the cost of equity will yield a
downward biased estimate of the value of the firm.

Effects of Mismatching
Error 1: Discount CF to Equity at Cost of Capital to get equity
value
PV of Equity = 50/1.0994 + 60/1.09942
+ 68/1.09943
+ 76.2/1.09944
+
(83.49+1603)/1.09945
= $1248
Value of equity is overstated by $175.
Error 2: Discount CF to Firm at Cost of Equity to get firm value
PV of Firm = 90/1.13625 + 100/1.136252
+ 108/1.136253
+ 116.2/ 1.136254
+
(123.49+2363)/1.136255
= $1613
PV of Equity = $1612.86 - $800 = $813
Value of Equity is understated by $ 260.
Error 3: Discount CF to Firm at Cost of Equity, forget to subtract
out debt, and get too high a value for equity
Value of Equity = $ 1613

Limitation
Firms in trouble
Cyclical firms
Firms with unutilised assets
Firms with patents or product options
Firms in the process of restructuring
Firms involved in acquisitions
Private firms

Formula
Po = Present Value of expected dividends = DPS / (ke – g)
Where,
Po = Price of stock today
DPS = Expected dividends per share next year
Ke = Cost of equity
g = growth rate in dividends
A simple manipulation of this formula yields Ke = ( DPS / po ) + g
Dividend Growth Model

In 1992, Southwestern Bell paid dividends per share of $ 2.82 and the
stock traded at $66 in December 1992. The estimated growth rate in
dividends was 5.5% and the firm is assumed to be in steady state.
Expected dividends in 1993 = $ 2.82 * 1.055 = $ 2.98
Cost of Equity = $2.98 /$66 + 5.5%
= 10%
Dividend Growth Model
Example: Southwestern Bell

Weighted Average Cost Of Capital

Cost of Debt
After tax cost of debt = Pre tax cost of debt (1 – tax rate)
Siemens AG had 4.244 bn DM of debt outstanding in July 1993. Due to
its low leverage and substantial cash balances, its default risk was
minimal at it could borrow at 6.72%. The tax rate it faced was 38%.
After tax cost of debt = 6.72%(1-0.38)
= 4.17%
WACC

Cost of Preferred Stock
Kps = Preferred Dividend per share / Mkt price of preferred share
At the end of 1992, GM had preferred stock which paid a dividend of $
2.28 annually and traded at $ 27.
Kps = $2.28/$27
= 8.44%
WACC

WACC: Pepsi Example
WACC = ke (E/[E+D+PS]) + Kd (D/[E+D+PS]) + Kps (PS/[E+D+PS])
In Dec 1992, Pepsi Cola Corp had a cost of equity of 12.83% and after
tax cost of debt of 5.28%.
Equity = 76.94%
Debt = 23.06%
WACC = (12.83% * 0.7694) + (5.28% * 0.2306)
= 11.09%
WACC

WACC
Market Value v/s Book Value
• Rationale
• Standard arguments against using market value
1. Book value is more reliable & less volatile
2. Perception- lenders will not lend on basis of market value.
3. Be more conservative, it assumes market value debt is lower.
BUT……?

Illustration
IN 1992 PepsiCo had
Market value Book value
Equity $30.02 $6.438
Debt $9.00 $8.894
Book value debt ratio = 58.01%
Market value debt ratio = 23.07%
WACC

Value of a stock = future expected cash flows
Expected dividends & price on sale
Required rate of dividend:krf + b(km – krf)
Growth in dividend can be calculated by:
 Using historical growth rate
 Generating your own forecast
 Using formula g=br
Dividend Discount Models

Rationale
Rate appropriate to riskiness of the CF
2 basic inputs: expected dividends & required rate of return on
equity
Assumptions on expected future growth in earnings & payout
ratios
RRoE is determined from by its riskiness
The General Model

As per General Model
 Value per share of stock = DPSt
(1+r)t
where DPSt = expected dividends per share
r = required rate of return
The General Model

Only for forms in “STEADY STATE”
A stable growth rate in long run
other measures to grow at the same rate
growth rate in the economy
Cannot be greater than nominal rate
Likely for “above – stable” growth
Adding premium to average growth rate
It cannot be greater than 1 or 2 %

Illustration
Value of stock = DPS1
r – g
Where DPS1 = expected div one year from now
r = RRoR for equity investors
g = growth rate in dividends forever

Example
Dividend per share next period of Rs.2.50, a discount rate of
15% and an expected growth rate of 8% forever
Value = 2.50/(.15-.08) =Rs 35.71
Expected growth rate of 14%
Value = 2.50/(.15-.14) = Rs. 250

Two Stage Dividend Discount Model

Initial stage of extraordinary growth (n yrs)
A subsequent steady state
Suitability (patents, super – normal growth)
The Two Stage Dividend Discount Models

Extraordinary growth rate
g % each year
1 2 3 4 5 6…..
Stable growth for ever
PV of dividends during extraordinary growth period + PV
of terminal price

Po = DPSt + Pn
( 1 + r )t ( 1 + r )t
Where DPSt = expected div. Per share in year t
r = required rate of return in high growth period
Pn = price at the end of year n
Pn = DPS n+1/(rn – gn)
g = growth rate forever after year n

Limitations
Defining the length of high growth rate (duration of PLCs)
Overnight transformation of growth rate.
Over or under estimating growth rate

2 stage, growth rate declines linearly
Assumption – earnings growth starts at high initial
rate ga
Extraordinary rate to last for 2H periods
Constant dividend payout
H Model

ga
gn
Extraordinary growth 2H
yrs
Infinite growth
H Model

Value of expected dividends in H model –
Po = DPSo (1+ gn) + DPSo * H(ga – gn)
r – gn r – gn
stable growth extraordinary growth
r = required return on equity
ga = growth rate initially
gn = growth rate at end of 2H yrs.
H Model

Example
Syntex corp. was expected to have EPS of $2.15 in 1993 and
payout div. Of $ 1.08.Earnings grew @18% p.a. for 5 yrs but
declined linearly @ 2 % a year over the next 6 yrs to a stable
growth rate of 6 %
Beta = 1.25
Treasury bond rate = 7 %
H Model

Expected return on equity
= 7% + 1.25 ( 5.5)=13.88%
Value of extraordinary
= 1.08*6/2 (.18-.06)/.1388-.06= 4.91
Value of stable growth
= 1.08*1.06/.1388-.06= 14.47
Therefore value = 4.91 + 14.47 = $ 19.38
Stock was trading @ $19.00 in May 1993
H Model

Limitations
Decline has to follow the strict structure
Constant payout, when it should be increasing.
H Model

Combines 2 stage and H model.
No restrictions on dividend payout ratio
Removes many constraints by other DDMs
However requires number of inputs
Three Stage Dividend Discount Model

High growth
Transition
Infinite growth
ga
gn
Low payout ratio Increasing P/o
High P/o

Formula

H-model will generate result similar to the three
phase model if one assumes that H is half way
between the transition period of the three phase
model.
That is, H is half way between A & B of the three
phase model. Under this assumption, H can be
interpreted in either of two ways:
 H is half the amount of time required for the growth rate to
change from ga
to gn.
OR
 In context of the three phase model, H is assumed to be half
way through the transition period A to B.
THE H-MODEL & THREE STAGE MODEL
…Relation Between The Two

THE H-MODEL AND THREE STAGE MODEL
…Relation Between The Two

ILLUSTRATION:
It is estimated that for company XYZ, the
stock’s dividend will increase at a rate of 6%
for the next 2 years, the rate will then
decline over the next 3 years to a rate of 3%,
which will remain constant thereafter. Also
the discount rate is estimated to be 8%.
Estimate the value of stock. Given that the
company’s stock dividend for the previous
year was Re 1.
…Example1

SOLUTION:
In this example we can see that, A = 2 years, ga
= 6%
B = 3 years, gn
= 3%
K = 8%, D0
= 1
As we know H is halfway between A & B, hence H = 3 ½ years.
Hence substituting in the equation (14), we have:
V0
= 1[(1.03) + (0.06-0.03)] / (0.08 –
0.03)
Therefore, V0
= Rs 22.70
If we compare this answer with the values given by the three
phase model, we find that in most of the cases, both the models
will give a similar result.
…Example1

ILLUSTRATION:
In FEB 1985, Satyam ltd was selling for Rs 59 per
share. Dividend paid out was Rs 4.25 per share. At
that time, at dividend growth rate of 11% was
forecasted for the next four years. It was estimated
that the firm’s long run normal growth rate would be
5%. It was also assumed that the firm would attain
this growth rate after 12 years. Also it is known that
the expected rate of return is 14.25%. Kindly estimate
the value of the Satyam ltd equity and compare with
the prevalent market price.
…Example2

SOLUTION:
We will illustrate the given case with the
example of the chart as shown below:
…Example2

As we can see, H is halfway between A and B,
hence H = 4 + (12 – 8)/2. Therefore H=8.
V0
= D0
[(1 +gn
) + H( ga
– gn
)] / (k – gn
)
V0
= 4.26[(1 +0.05) + 8( 0.11 – 0.05)] /
(0.1425 – 0.05)
= Rs 70.46
…Example2

Free CashFlows to Equity - FCFE
FCFE Model
$ What is FCFE?
$ Levered firm
$ FCFE = Net Income + Dep. – Capex – Change in WC –
Principal repayments + New Debt issues
$ Debt Ratio
$ FCFE = Net Income - (1-Debt Ratio)[(Capex-Dep.)+
(Change in WC)]
$ Dividends v/s FCFE
a. Desire for Stability, b. Future investment needs
c. Tax Factors d. Signaling Prerogatives

Example: ACC Ltd. – 2004-05 (Rs.in cr.)
$ Net Income = Rs.379; Dep.=Rs.225.Capex= Rs.291.7;
Debt=Rs.1492; Cap.Emp.=Rs.3318; Chg.inWC= Rs.76.4
$ Debt Ratio = Debt/Cap.Emp = 0.45
$ FCFE = 379 - (1-0.45)[(291.7 - 225.7)+(100.19 - 23.76)]
= 379 - (0.55)[(66)+(76.43)]
= 379 - 78.33 = Rs.300.67 cr.
$ Dividend paid = Rs.125.3 cr.
$ Dividend – FCFE ratio = 125.3/300.67*100 = 41.67%
$ Retained Cash = 457.3 – 125.3 = Rs. 175.37 cr.
FCFE Model

Stable Growth FCFE Model
$ Stable Growth Rate
$ Model: Po = FCFE1/r – gn
where Po - Value of stock today
FCFE1 - Expected FCFE next year
r - Cost of Equity of the firm
gn - Growth rate in FCFE forever
$ Assumptions:
a. Nominal Growth rate; b. Average Risk
c. Capex is offset by Depreciation
$ Suitability
FCFE Model

Example: AT&T – 1993-94 ($)
$ DPS = 1.32; FCFE per share = 2.49; EPS = 3.15;
Capex/sh.= 3.15; Dep./sh.= 2.78; Debt Fin.ratio=25%;
Ch.in WC per share = 0.50
$ Earnings, Capex, Dep., WC to grow at 6% a year
$ Beta = 0.90, Treasury bond rate (Rf) = 7.5%
$ Cost of Equity = 7.5% + (0.9*5.5%) = 12.45%
$ FCFE = EPS – (1-0.25)[(Capex - Dep.)+(Change in WC)]
= 3.15 – (0.75)[(3.15 – 2.78)+(0.5)]
= 3.15 – (0.75)(0.87) = 3.15 – 0.6525 = 2.49
$ Value per share = 2.49*1.06/(0.1245 - 0.06) = 41
FCFE Model

Rationale
$ Too big a company
$ Growth in tandem with economy
$ Pays much less dividends
FCFE Model

$ Faster & constant growth initially
$ Later, a stable growth rate
$ Model:
PV of stock = PV of FCFE per year + PV of Terminal Price
= Σ FCFEt/(1+r)^t + Pn/(1+r)^n
where FCFEt - FCFE in year t
Pn – price at end of extra-ordinary growth period
r – Req.ROR in high growth period
$ Terminal Value: Pn = FCFEn+1/(rn – gn)
where gn – growth rate after terminal year forever
rn – Req.ROR in stable growth period
2 Stage FCFE Model
2 Stage FCFE Model

2 Stage FCFE Model
$ Assumptions
a. Growth is high initially & then becomes stable
b. Consistency in Terminal year
$ Suitability
$ Better results than Dividend Discount Model
2 Stage FCFE Model

Example: Amgen Inc. – 1993-94
$ Rev./sh.= $12.4; EPS = $3.1; Capex/sh.= $1;Dep./sh.= $0.6
$ High growth period: 5 years; ROE = 18.78%; Beta = 1.3;
Retention Ratio = 100%; Growth rate = 18.78%;
Bond rate = 7.5%; Debt ratio = 18.01%; WC = 20%Rev.;
Capex, dep., Rev. to grow at 18.78%
$ Cost of Equity = 7.5% + 1.3(5.5%) = 14.65%
$ Stable growth period: Growth rate = 6%; Beta = 1.1;
Capex to offset dep.; WC to be 20% of Rev.;
Debt ratio = 18.01%
$ Cost of Equity = 7.5% + (1.1*5.5%) = 13.55%
2 Stage FCFE Model

($) Year 1 Year 2 Year 3 Year 4 Year 5
Earnings 3.68 4.37 5.19 6.17 7.33
(-)(Capex-Dep.)*
(1-1.3)
0.39 0.46 0.55 0.65 0.78
(-)(Chg.in WC)*
(1-1.3)
0.38 0.45 0.54 0.64 0.76
= FCFE 2.91 3.46 4.11 4.88 5.79
Present Value
(14.65%)
2.54 2.63 2.72 2.82 2.92
PV of FCFE during high growth phase
= 2.54+2.63+2.72+2.82+2.92 = $13.64
2 Stage FCFE Model

$ Terminal Price = Exp. FCFEn+1/(r-gn)
$ Exp.EPS6 = $7.33 * 1.06 = $7.77
$ Exp.FCFE = EPS6 – Ch.in WC (1-Debt Ratio)
= $7.77 - $0.35(1-0.1801) = $7.48
$ Terminal price = $7.48/(0.1355 – 0.6) = $99.07
$ Ch.in WC is 10% of change in revenue in year 6
$ PV of Terminal Price = $99.07/1.14655
= $50.01
$ PV today = PV of FCFE (high growth)+ PV of TP
= 13.64 + 50.01 = $63.65
2 Stage FCFE Model

Rationale
$ History of Extra-ordinary growth
$ Growth is moderating due to:
a. A much larger company,
b. Maturing products
$ No dividends paid
$ FCFE to increase over a period of time
2 Stage FCFE Model

Price/Earnings Multiples
$ Simple to compute - popular
$ Eliminates need to make assumptions of:
a. risk, b. growth, c. payout ratios
$ Reflects market moods & perceptions
$ Weaknesses
a. avoidance of risk & growth factors
b. wrong judgement
$ PE Ratio is:
a. increasing function of Payout ratio & growth rate,
b. decreasing function of riskiness of the firm.

PE Ratio
$ Firm growing at a rate similar to economic growth rate
$ Determined by:
a. Payout ratio – PE increases with increase in PR
b. Riskiness – PE lowers as riskiness increases
c. Expected growth rate in Earnings
$ Since DPS = EPS0(Payout Ratio)(1+gn)/(r-gn),
Value of Equity P0 = EPS0(Payout Ratio)(1+gn)/(r-gn)
$ PE Ratio = P0/EPS0 = (Payout Ratio)(1+gn)/(r-gn)

Example: Deutsche Bank (DM)
$ EPS = 46.38; DPS = 16.50; Beta = 0.92
$ Growth in Earnings & Dividends = 6%; Bond rate = 7.5%
$ Premium = 4.5%
$ Div.Payout Ratio = 16.5/46.38*100 = 35.58%
Cost of Equity = 7.5% + (0.92*4.5%) = 11.64%
$ PE Ratio = 0.3558*1.06/(0.1164 – 0.6) = 6.69
$ If FCFE = 25 per share; Beta = 0.93, then COEq.= 11.69%
FCFE Payout ratio = 25/46.38*100 = 53.9%
$ PE Ratio = 0.6105*1.06/(0.1169 – 0.06) = 11.37

Price/Book Value Multiples
$ What is Book Value?
$ Book Value v/s Market Value
$ Advantages:
a. Simple benchmark for comparison
b. Firms with negative earnings can use P/B value
$ Disadvantages:
a. Affected by accounting policies across firms & nations
b. Not of any use to Service firms

PBV Ratio
$ Growth rate similar or lower than economic growth rate
$ P0 = DPS1/r-gn (Gordon growth model)
$ Substituting EPS0[Payout ratio(1+gn)] for DPS1,
P0 = EPS0*Payout ratio*(1+gn)/(r-gn)
$ Since ROE = EPS0/BV of Equity,
P0 = BV0*ROE*Payout Ratio*(1+gn)/r-gn
$ PBV = P0/BV0 = ROE*Payout ratio*(1+gn)/(r-gn)
$ If ROE is based on Exp.earnings in next time period,
PBV = P0/BV0 = ROE*Payout ratio/(r-gn)
$ Relating growth to ROE, g = ROE(1-Payout ratio)
PBV = P0/BV0 = ROE – gn/(r-gn)

PBV Ratio
$ Determined by:
a. Difference between ROE & Req.ROR on projects
b. If ROE > Req.ROR, Price > BV of Equity
c. If ROE < Req.ROR, Price < BV of Equity
$ Used for firms not paying out dividends

Example: Amoco – 1993-94 ($)
$ EPS = 3.82; DPR = 60%; ROE = 15%; Beta = 0.65
$ Growth rate in Earnings & Dividend = 6%
$ Treasury bond rate = 7.5%
$ Cost of Equity = 7.5% + (0.65*5.5%) = 11.08%
$ PBV Ratio based on fundamentals
= (0.15*0.6*1.06)/(0.1108-0.06) = 1.88
$ PBV Ratio based on return differential
= (0.15-0.6)/(0.1108-0.6) = 1.77
$ Amoco was selling at a PBV ratio of about 2 in March’95

PBV Ratio - ROE
Overvalued
Low ROE – High PBV High ROE – High
PBV
Low ROE – Low PBV Undervalued
High ROE – Low PBV
ROE – Required Return
PBV
Ratio
High
High
Low

Price/Sales Multiples
$ Examines effects of Corporate strategy
$ Advantages:
a. Available to troubled firms,
b. Difficult to manipulate,
c. Not much volatile as PE
$ Disadvantages:
a. Stability of using Revenues
b. Revenues may not decline inspite of drop in Earnings

PS Ratio
$ Put EPS0(Payout Ratio)(1+gn) in place of DPS in GordonM
$ Profit Margin(PM) = EPS0/Sales per share
$ Hence, P0 = Sales0*PM*Payout Ratio*(1+gn)/(r-gn)
$ PS = P0/Sales0 = PM*Payout Ratio*(1+gn)/(r-gn)
$ If PM is based on expected earnings in next time period,
PS = P0/Sales0 = PM*Payout Ratio/(r-gn)
$ It is increasing function of PM, Payout Ratio & growth rate
$ It is decreasing function of riskiness of the firm

International Multifoods – 1993-94 ($)
$ Rev./sh.= 134.7; EPS = 1.5; Payout Ratio = 55%;
$ Beta = 0.8; Treasury bond rate = 7.5%;
$ Growth rate in earnings & dividend = 6%
$ Net Profit Margin = Net Income/Revenues
= 1.5/134.7*100 = 1.11%
$ Cost of Equity = 7.5% + (0.8+5.5%) = 11.9%
$ PS Ratio = 0.011*0.55*1.06/(0.119 – 0.06) = 0.1097
$ The co. was selling at PS ratio of 0.14

PS Ratio
$ PS Ratio is determined by:
a. Net Profit Margin – EPS/RPS,
b. Payout ratio,
c. Riskiness, and
d. Expected growth

P/E & Growth Ratio (PEG)
PEG Ratio
$ Assumption – P/E = EPS rate of growth
$ Annualised rate of Growth
$ Comparison with current market price
$ Future growth makes sense
$ Growth of ABC over next 2 yrs is 10% & P/E = 10
then PEG for ABC = 1 (fair value)
$ If P/E = 5, PEG = 0.5; If P/E = 20, PEG = 2
$ Used for Growth companies

Year-ahead P/E & Growth Ratio (YPEG)
YPEG Ratio
$ Valuing larger, established firms
$ Looks at 5-year growth rates
$ If P/E is 10, growth over next 5 yrs.is exp.to be 20%
then YPEG = 0.5

Be Creative
Sometimes standard valuation ratio will simply
not be available and you simply have to devise
your own.
E.g. In 1990s some analyst valued Retail Internet firms
based on the no. of Hits their sites received. As it turns
out, they valued these firms using too generous “Price to
hits” ratio.
OTHER MULTIPLES
…For Relative Valuation

$ The model can be written as:
Value of the call = SN(d1) – Ke-rt
N(d2)
where d1 = [ln(S/K) + (r+σ2
/2)*t]/σ(sq.root of t)
d2 = d1 - σ(sq.root of t)
$ S – current value of underlying asset;
K – strike price of the option;
t - life to expiration of the option;
r – riskless interest rate corresponding to life of option;
σ2
– variance in the ln(value) of underlying asset.

CASE STUDY
…Tata
Steel Ltd.
COMPANY SNAPSHOT:
The Tata Iron and Steel Company Limited was formed
in 1907 at Mumbai.
The Company manufactures rails, fishplates, bars, light
structurals, heavy structurals, plates, black sheets,
galvanised sheets, tin bars, sleeper bars, sleepers,
blooms, billets, sheet bars, wheels, tyres and axles,
skelp and strip, and special steels tools such as picks,
beaters, hammers and shovels and red-oxide, coal tar,
sulphate of ammonia, etc.

FINANCIAL DATA …Tata Steel
FY00-01 FY01-02 FY02-03 FY03-04 FY04-05
Equity Share Cap 3,679.70 3,679.70 3,679.70 3,691.80 5,536.70
Res & Surplus 43,804.60 30,779.90 28,168.40 41,466.80 65,062.50
No. of Equity shares
o/s 367,771,901 367,771,901 367,771,901 367,771,901 553,472,856
Dividend/ Share 5.00 4.00 8.00 10.00 13.00
Industry avg PE : 10.3
Tata Steel PE : 5.8
Economy Growth Rate : 7.0%
Risk Free Rate of Return : 6.25%(Reserve Bank of India)
Beta (ß) for Tata Steel : 1.13 (besindia.com)

ASSUMPTIONS
Company is growing at the same rate as
the economy. (Hence g = 7%).
Expected market Rate of Return E(rm)=
12%

CALCULATIONS
k = RISKFREE RETURN + BETA * (MARKET RISK
PREMIUM)
k = 6.25% + 1.13 (12 - 6.25%) = 12.75%
V0
= D0
(1+g) / (k-g) = D1
/ (k-g)
= 13(1 + 0.07)/(0.1275 - 0.07)
= Rs 241.91
As on 4th
Nov. 05’ the market value of Tata steel
share was Rs 347.70. Hence we can say the
share is over valued at Rs 347.70.

INFERENCES
The P/E ratio for Tata Steel is 5.8 as against the
industry average of 10.3, hence we can say that the
investors do not consider that Tata Steel has a
potential for further growth as is reflected by their
lower PE Ratio.
Also the market value of TSL stock is overvalued as we
have seen and hence, the market is likely to correct
itself in near future.

Relative Valuation using multiples
• Firm Value /
Sales
• Firm Value /
EBIT
• Firm Value / BV
• EV / Sales
• P/E
• P/BV
• P/CF
• P/Sales
Value Of Stock
• FCFF
Estimate CF
• Dividends
• FCFE
• B/S method
• Adj. BV method
• EV
• WACC
Calc.Cost of equity
• CAPM
• APM
Value of FirmValue of FirmValue of Equity
Asset BasedDCF approach
Value Of Firm
• Firm Value / Sales
• Firm Value / EBIT
• Firm Value / BV
• EVA, MVA, RVG
In Short…

Campus Overview
907/A Uvarshad,
Gandhinagar
Highway,
Ahmedabad –
382422.
Ahmedabad Kolkata
Infinity Benchmark,
10th
Floor, Plot G1,
Block EP & GP,
Sector V, Salt-Lake,
Kolkata – 700091.
Mumbai
Goldline Business
Centre Linkway
Estate,
Next to Chincholi Fire
Brigade, Malad (West),
Mumbai – 400 064.

Valuation of shares

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