Valuation of shares

Flow of the presentation

IntroductionDiscounted Cash FlowCAPMDividend GrowthWACCThe General ModelThe Gordon Growth ModelTwo Stage DDMH ModelThree Stage DDMFCFETwo Stage FCFEP/E, P/BV, P/SPEG & YPEGBlack & 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.

BALANCE SHEET METHOD

…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 acquisitionWIP at Cost of R.M + Cost of processingFG 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

EnterpriseValue

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.) = 347.70Long-Term Debt (Rs. In crores) = 24,681.80 Short-Term Debt (Rs. In crores) = 2,715.20 Cash & Equivalents = 2467.20Market 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 ModelRelative 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 Cashflow Valuation

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 analysisOne 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

2. Use the weighted average cost of capital (WACC) to determine the appropriate discount rate range

3. Estimate the terminal value of the business at the end of the forecast period

4. Determine the value for the enterprise by discounting the projected free cash flows and terminal value to the present

5. 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

Er

ED

DTrWACC equitydebt

1

DCF – WACC (contd..)

Cost of debtConsult 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/industryIf 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

= 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

premiumrisk Equity rate free-Risk fequity rr

ttftMtft rrrr ,,,

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 CAPMThe 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

)(

1NoplatTV 1T

1T

T gWACCgWACCROIC

g

DCF – Terminal value

Key value driversGrowth 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 multipleTerminal 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 assumptionsCarefully consider all variables in the calculation of the discount rateConsistency of assumptions concerning interest rates, inflation rates, tax rates and the cost of capital is criticalThoughtfully consider terminal value methodologyDo sensitivity analysis (base projection variables, synergies, discount rates, terminal values, etc.)

DCF – Walmart exampleDecember 2007 Treasury rates3-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+*(rm-rf)

Net debt (D) 37.00Market cap (E) 192.00Total Value (V=D+E) 229.00D/ V 16.2%E/ V 83.8%

WACC 7.56%=rd(1-tax) D/ V + re E/ V

Walmart FCF assumptionsThe 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 levelCapex is currently 3.5% of sales and is expected to remain at the same levelNWC is 0.5% of sales and is expected to remain at the same level

Walmart FCF’s2007 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 41,330Tax 7,118 7,795 8,496 9,218 9,956 10,703 11,452 12,196 12,928 13,639NOPLAT 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 27,293FCF 6,942 7,610 8,305 9,022 9,756 10,501 11,251 11,997 12,733 13,451Discount factor 0.930 0.864 0.804 0.747 0.695 0.646 0.601 0.558 0.519 0.483Discounted cash flows 6,454 6,579 6,675 6,742 6,778 6,783 6,757 6,699 6,610 6,492Total (excl Cont Value) 66,569

Walmart continuation value

Continuation Value 381,123PV(Continuation Value) 183,953 73%

Firm value 250,522Less Debt value 37,000Equity value 213,522Number of shares 4,170Equity 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 7.096.4% 47.54 46.87 46.06 45.06 43.81 42.24 40.22 37.56 33.92 28.72 20.736.8% 48.62 48.28 47.84 47.29 46.59 45.69 44.51 42.93 40.76 37.62 32.777.2% 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 61.678.4% 51.92 52.56 53.27 54.09 55.05 56.19 57.57 59.32 61.60 64.76 69.468.8% 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 71.336.4% 64.99 65.21 65.44 65.66 65.88 66.11 66.33 66.55 66.78 67.00 67.226.8% 59.32 59.52 59.72 59.93 60.13 60.33 60.53 60.73 60.94 61.14 61.347.2% 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 47.498.4% 42.42 42.56 42.70 42.84 42.98 43.12 43.26 43.40 43.55 43.69 43.838.8% 39.24 39.37 39.49 39.62 39.75 39.88 40.01 40.14 40.27 40.40 40.53

Ter

min

al R

OIC

Terminal growth rate

WA

CC

= R

OIC

Terminal growth rate


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 ValuationThe 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 ValuationThe 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 RememberNever 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 = $ 1613Value of Equity is overstated by $ 540


LimitationFirms 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


Dividend Growth Model

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


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%


Example: Southwestern Bell

Weighted Average Cost Of Capital

Cost of DebtAfter 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 hadMarket value Book value

Equity $30.02 $6.438Debt $9.00 $8.894

Book value debt ratio = 58.01%Market value debt ratio = 23.07%

WACC

Dividend Discount Models

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

The General Model

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

The Gordon Growth Model

Only for forms in “STEADY STATE”

A stable growth rate in long runother measures to grow at the same rategrowth 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


LimitationsDefining the length of high growth rate (duration of PLCs)

Overnight transformation of growth rate.

Over or under estimating growth rate


H Model

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

Three stage DDM

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 growthga

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 22.70If 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

FCFE Valuation Models

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

2 Stage FCFE Model

$ Faster & constant growth initially

$ Later, a stable growth rate

$ Model:

PV of stock = PV of FCFE per year + PV of Terminal

Price

= 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

Example: Amgen Inc. – 1993-94($) 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

Example: Amgen Inc. – 1993-94$ 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 Price/Book Value Multiples

$ 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


OvervaluedLow ROE – High PBV

High ROE – High PBV

Low ROE – Low PBV

UndervaluedHigh ROE – Low PBVROE – Required Return

PBVRatio

High

HighLow

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

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

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 CreativeSometimes 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

Black & Scholes Model

Black & Scholes Model

$ The model can be written as:

Value of the call = SN(d1) – Ke-rtN(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 : 10.3Tata Steel PE : 5.8Economy 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 • EV / EBITDA

• 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 Firm

Value of Firm

Value of EquityAsset BasedDCF approach

Value Of Firm

• Firm Value / Sales• Firm Value / EBIT • Firm Value / BV• EVA, MVA, RVG

In Short…

Campus Overview

907/A Uvarshad, GandhinagarHighway, 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

Business

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