Prof. Ian Giddy New York University Valuation IBM

Prof. Ian GiddyNew York University

Valuation

IBM

Copyright ©2000 Ian H. Giddy Valuation 3

What’s a Company Worth?

Required returns Types of Models

Balance sheet modelsDividend discount modelsCorporate cash flow modelsPrice/Earnings ratios

Estimating Growth Rates Application

IBMIBM


Equity Valuation: From the Balance Sheet

Value of Assets Book Liquidation Replacement

Value of Liabilities

Book Market

Value of Equity


Equity Valuation: From the Balance Sheet

Value of Assets Book Liquidation Replacement

Value of Liabilities

Book Market

Value of Equity

Book ValueLiquidation

ValueReplacement

ValueTobin’s Q:

Market/Replacement tends to 1?


Estimating Future Cash Flows

Dividends? Free cash

flows to equity?

Free cash flows to firm?


Cash Flow to Firm

Claimholder Cash flows to claimholder

Equity Investors Free Cash flow to Equity

Debt Holders Interest Expenses (1 - tax rate)

+ Principal Repayments

- New Debt Issues

Preferred Stockholders Preferred Dividends

Firm = Free Cash flow to Firm =

Equity Investors Free Cash flow to Equity

+ Debt Holders + Interest Expenses (1- tax rate)

+ Preferred Stockholders + Principal Repayments

- New Debt Issues

+ Preferred Dividends


Relative Valuation

Do valuation ratios make sense?• 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

It depends on how they are used -- and what’s behind them!


Disney: Relative Valuation

Company PE Expected Growth PEGKing World Productions 10.4 7.00% 1.49Aztar 11.9 12.00% 0.99Viacom 12.1 18.00% 0.67All American Communications 15.8 20.00% 0.79GC Companies 20.2 15.00% 1.35Circus Circus Enterprises 20.8 17.00% 1.22Polygram NV ADR 22.6 13.00% 1.74Regal Cinemas 25.8 23.00% 1.12Walt Disney 27.9 18.00% 1.55AMC Entertainment 29.5 20.00% 1.48Premier Parks 32.9 28.00% 1.18Family Golf Centers 33.1 36.00% 0.92CINAR Films 48.4 25.00% 1.94Average 27.44 18.56% 1.20

PE ratio divided

by the growth rate


Discounted Cashflow Valuation: Basis for Approach

where n = Life of the asset CFt = Cashflow in period t r = Discount rate reflecting the

riskiness of the estimated cashflows

Value = CFt

(1+ r)tt =1

t = n


Start with theWeighted Average Cost of Capital

Choice Cost1. Equity Cost of equity

- Retained earnings - depends upon riskiness of the stock

- New stock issues - will be affected by level of interest rates

- Warrants

Cost of equity = riskless rate + beta * risk premium

2. Debt Cost of debt

- Bank borrowing - depends upon default risk of the firm

- Bond issues - will be affected by level of interest rates

- provides a tax advantage because interest is tax-deductible

Cost of debt = Borrowing rate (1 - tax rate)

Debt + equity = Cost of capital = Weighted average of cost of equity and

Capital cost of debt; weights based upon market value.

Cost of capital = kd [D/(D+E)] + ke [E/(D+E)]


Valuation: The Key Inputs

A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever.

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 = CF

t

(1+ r)tt = 1

t =

Value = CFt

(1 + r)t

Terminal Value

(1 + r)N

t = 1

t = N


Dividend Discount Models:General Model

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

V0 = Value of Stock Dt = Dividend k = required return


Specified Holding Period Model

01

12

2

1 1 1V D

kD

kD P

kN N

N

( ) ( ) ( )...

PN = the expected sales price for the stock at time N

N = the specified number of years the stock is expected to be held


No Growth Model

VD

ko

Stocks that have earnings and dividends that are expected to remain constant

Preferred Stock


No Growth Model: Example

E1 = D1 = $5.00

k = .15

V0 = $5.00 / .15 = $33.33

VD

ko

Burlington Power & Light has earnings of $5 per share and pays out 100% dividend

The required return that shareholders expect is 15%

The earnings are not expected to grow but remain steady indefinitely

What’s a BPL share worth?

Burlington Power & Light has earnings of $5 per share and pays out 100% dividend


The earnings are not expected to grow but remain steady indefinitely

What’s a BPL share worth?


Constant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

g = constant perpetual growth rate


Constant Growth Model: Example

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

E1 = $5.00b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

Motel 6 has earnings of $5 per share. It reinvests 40% and pays out 60%dividend


The earnings are expected to grow at 8% per annum

What’s an M6 share worth?

Motel 6 has earnings of $5 per share. It reinvests 40% and pays out 60%dividend


The earnings are expected to grow at 8% per annum

What’s an M6 share worth?

Plowback rate


Estimating Dividend Growth Rates

g ROE b g ROE b

g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate

i.e.(1- dividend payout percentage rate)


Or Use Analysts’ Expectations?


Shifting Growth Rate Model

V Dg

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2V D

g

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2

g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1


Mindspring pays dividends $2 per share. The required return that shareholders expect is 15%

The dividends are expected to grow at 20% for 3 years and 5% thereafter

What’s a Mindspring share worth?

Mindspring pays dividends $2 per share. The required return that shareholders expect is 15%

The dividends are expected to grow at 20% for 3 years and 5% thereafter

What’s a Mindspring share worth?

Shifting Growth Rate Model: Example

D0 = $2.00 g1 = 20% g2 = 5%

k = 15% T = 3 D1 = 2.40

D2 = 2.88 D3 = 3.46 D4 = 3.63

V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3

+ D4 / (.15 - .05) ( (1.15)3

V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40


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.


Choosing a Growth Pattern: Examples

Company Valuation in Growth Period Stable Growth

Disney Nominal U.S. $ 10 years 5%(long term Firm (3-stage)nominal

growth rate in the U.S. economy

Aracruz Real BR 5 years 5%: based upon Equity: FCFE (2-stage)

expected long term real growth rate for Brazilian economy

Deutsche Bank Nominal DM 0 years 5%: set equal to Equity: Dividends nominal

growth rate in the world

economy


The Building Blocks of Valuation

Choose aCash Flow Dividends

Expected Dividends to

Stockholders

Cashflows to Equity

Net Income

- (1- ) (Capital Exp. - Deprec’n)

- (1- ) Change in Work. Capital

= Free Cash flow to Equity (FCFE)

[ = Debt Ratio]

Cashflows to Firm

EBIT (1- tax rate)

- (Capital Exp. - Deprec’n)

- Change in Work. Capital

= Free Cash flow to Firm (FCFF)

& A Discount Rate Cost of Equity

Basis: The riskier the investment, the greater is the cost of equity.

Models:

CAPM: Riskfree Rate + Beta (Risk Premium)

APM: Riskfree Rate + Betaj (Risk Premiumj): n factors

Cost of Capital

WACC = ke ( E/ (D+E))

+ kd ( D/(D+E))

kd = Current Borrowing Rate (1-t)

E,D: Mkt Val of Equity and Debt

& a growth pattern

t

g

Stable Growth

g

Two-Stage Growth

|High Growth Stable

g

Three-Stage Growth

|High Growth StableTransition


The Building Blocks of Valuation

Choose aCash Flow Dividends

Expected Dividends to

Stockholders

Cashflows to Equity

Net Income

- (1- ) (Capital Exp. - Deprec’n)

- (1- ) Change in Work. Capital

= Free Cash flow to Equity (FCFE)

[ = Debt Ratio]

Cashflows to Firm

EBIT (1- tax rate)

- (Capital Exp. - Deprec’n)

- Change in Work. Capital

= Free Cash flow to Firm (FCFF)

& A Discount Rate Cost of Equity

Basis: The riskier the investment, the greater is the cost of equity.

Models:

CAPM: Riskfree Rate + Beta (Risk Premium)

APM: Riskfree Rate + Betaj (Risk Premiumj): n factors

Cost of Capital

WACC = ke ( E/ (D+E))

+ kd ( D/(D+E))

kd = Current Borrowing Rate (1-t)

E,D: Mkt Val of Equity and Debt

& a growth pattern

t

g

Stable Growth

g

Two-Stage Growth

|High Growth Stable

g

Three-Stage Growth

|High Growth StableTransition

Spreadsheet example

Equity Valuation:Two Applications



Equity Valuation in Practice

Estimating discount rate Estimating cash flows Estimating growth Application with constant growth: Optika Application with shifting growth: Fong


Optika OptikaGrowth 5%Tax rate 35%Initial Revenues 3125COGS 89%WC 10%Equity Market Value 1300Debt Market Value 250Beta 1Treasury bond rate 7%Debt spread 1.5%Market risk premium 5.50%

T+1Revenues 3281-COGS 2920-Depreciation 74=EBIT 287EBIT(1-Tax) 187-Change in WC 16=Free Cash Flow to Firm 171Cost of Equity (from CAPM) 12.50%Cost of Debt (after tax) 5.53%WACC 11.38%

Firm Value 2278

CAPM:

7%+1(5.50%)

Debt cost

(7%+1.5%)(1-.35)

WACC:

ReE/(D+E)+RdD/(D+E)

Value:

FCFF/(WACC-growth rate)

Equity Value:

Firm Value - Debt Value

= 2278-250 = 2028


Valuing a Firm with DCF: An Illustration

Historical financial results

Adjust for nonrecurring aspects

Gauge future growth

Adjust for noncash items

Projected sales and operating profits

Projected free cash flows to the firm (FCFF)

Year 1 FCFF

Year 2 FCFF

Year 3 FCFF

Year 4 FCFF

Terminal year FCFF

Stable growth model or P/E comparable

Present value of free cash flows

+ cash, securities & excess assets

- Market value of debt

Value of shareholders equity

…

Discount to present using weighted average cost of capital (WACC)


Valuation Example

Fong Industries (Pte) Ltd SingaporeProfit & Loss (S$'000)FYE 30 Jun 1994 1995 1996 1997 1998 1999

Turnover 9,651 57,888 125,010 120,323 136,003 134,813

Directors' Fees & Rem 107 249 368 820 961 964Amortisation 0 269 279 280 35 39Depreciation 639 1,041 1,277 3,812 4,673 4,494Interest Expense 227 445 615 1,002 1,078 697Bad Debts W/O 100Fixed Assets W/O 4 543 27FX loss 85 282

Profit b/f Tax 933 1,990 838 1,250 3,774 6,897

Assoc Co (74) 37 (14)

933 1,990 838 1,176 3,811 6,883

Tax 3 96 292 929 178

Profit a/f Tax 930 1,990 742 884 2,882 6,705

Effective Tax Rate 0.32% 0.00% 11.46% 24.83% 24.38% 2.59%

EOI 7,292 (768) (7) (156)

EBITDA 1,799 3,745 108.17% 3,009 -19.65% 6,270 108.37% 9,597 #### 12,113ISC 792.51% 841.57% 489.27% 625.75% 890.26% 1737.88%

Fong Industries (Pte) Ltd SingaporeProfit & Loss (S$'000)FYE 30 Jun 1994 1995 1996 1997 1998 1999

Turnover 9,651 57,888 125,010 120,323 136,003 134,813

Directors' Fees & Rem 107 249 368 820 961 964Amortisation 0 269 279 280 35 39Depreciation 639 1,041 1,277 3,812 4,673 4,494Interest Expense 227 445 615 1,002 1,078 697Bad Debts W/O 100Fixed Assets W/O 4 543 27FX loss 85 282

Profit b/f Tax 933 1,990 838 1,250 3,774 6,897

Assoc Co (74) 37 (14)

933 1,990 838 1,176 3,811 6,883

Tax 3 96 292 929 178

Profit a/f Tax 930 1,990 742 884 2,882 6,705

Effective Tax Rate 0.32% 0.00% 11.46% 24.83% 24.38% 2.59%

EOI 7,292 (768) (7) (156)

EBITDA 1,799 3,745 108.17% 3,009 -19.65% 6,270 108.37% 9,597 #### 12,113ISC 792.51% 841.57% 489.27% 625.75% 890.26% 1737.88%


Valuation Example

Fong IndustriesGrowth1 25% for 3 yearsGrowth2 5% thereafterTax 25% effective

Revenue 134,813 (S$'000); T0

Expenses 91.01% of Revenue

EBIT 7,580 (S$'000)WC 10% of Revenue (unlevered) 1.06 (levered) 1.09

Kd 5.50%

MVe 218,993 (S$'000) PERMkt 32.66

MVd 7,379 (S$'000)

Combined 226,372 (S$'000)

Rm 12.00%

Rf 4.00%

Ke 12.69%

WACC 12.41%

Fong IndustriesGrowth1 25% for 3 yearsGrowth2 5% thereafterTax 25% effective

Revenue 134,813 (S$'000); T0

Expenses 91.01% of Revenue

EBIT 7,580 (S$'000)WC 10% of Revenue (unlevered) 1.06 (levered) 1.09

Kd 5.50%

MVe 218,993 (S$'000) PERMkt 32.66

MVd 7,379 (S$'000)

Combined 226,372 (S$'000)

Rm 12.00%

Rf 4.00%

Ke 12.69%

WACC 12.41%

T1 T2 T3 T4

Revenue 168,516 210,645 263,307 276,472-Expenses 153,375 191,719 239,648 251,631-Depreciation 4,533 4,533 4,533 4,533EBIT 10,608 14,394 19,125 20,308EBIT(1-t) 7,956 10,795 14,344 15,231+Depreciation 4,533 4,533 4,533 4,533-CapEx 4,533 4,533 4,533 4,533-Change in WC 3,370 4,213 5,266 1,317FCFF 4,586 6,582 9,078 13,915

187,6554,586 6,582 196,733

Firm Value 147,773Equity Value 140,394 $0.65

PERcomputed 20.94

T1 T2 T3 T4

Revenue 168,516 210,645 263,307 276,472-Expenses 153,375 191,719 239,648 251,631-Depreciation 4,533 4,533 4,533 4,533EBIT 10,608 14,394 19,125 20,308EBIT(1-t) 7,956 10,795 14,344 15,231+Depreciation 4,533 4,533 4,533 4,533-CapEx 4,533 4,533 4,533 4,533-Change in WC 3,370 4,213 5,266 1,317FCFF 4,586 6,582 9,078 13,915

187,6554,586 6,582 196,733

Firm Value 147,773Equity Value 140,394 $0.65

PERcomputed 20.94

Equity Valuation:Alternatives


IBM


What’s a Company Worth?Alternative Models

The options approachOption to expandOption to abandon

Creation of key resources that another company would pay forPatents or trademarksTeams of employeesCustomers

Examples?

Lycos

Lycos

Messageclick.com

Messageclick.com


What’s a Company Worth?The Options Approach

Present Value of Expected Cash Flows if Option Excercised

Value of the Firm or project


The Value of a Corporate Option

Having the exclusive rights to a product or project is valuable, even if the product or project is not viable today.

The value of these rights increases with the volatility of the underlying business.

The cost of acquiring these rights (by buying them or spending money on development - R&D, for instance) has to be weighed off against these benefits.


Application


An Example of a Corporate Option

J&J is considering investing $110 million to purchase an internet distribution company to serve the growing on-line market.

A conventional NPV financial analysis of the cash flows from this investment suggests that the present value of the cash flows from this investment to J&J will be only $95 million. Thus, by itself, the corporate venture has a negative NPV of $15 million.

If the on-line market turns out to be more lucrative than currently anticipated, J&J could expand its reach a global on-line market with an additional investment of $125 million any time over the next 2 years. While the current expectation is that the PV of cash flows from having a worldwide on-line distribution channel is only $100 million (still negative NPV), there is considerable uncertainty about both the potential for such an channel and the shape of the market itself, leading to significant variance in this estimate.

This uncertainty is what makes the corporate venture valuable!


Valuing the Corporate Venture Option

The corporate option would cost an expected $15 million. But what is it worth to J&J?

Value of the underlying asset (S) = PV of cash flows from purchase of on-line selling venture, if done now =$100 Million

Strike Price (K) = cost of expansion into global on-line selling = $125 Million

We estimate the variance in the estimate of the project value by using the annualized volatility (standard deviation) in firm value of publicly traded on-line marketing firms in the global markets, which is approximately 50%. Variance in Underlying Asset’s Value = SD^2=.25

Time to expiration = Period for which “venture option” applies = 2 years

2-year interest rate: 6.5%


Option Pricing

94.5

Option Price

= Intrinsic value + Time value

Option Price

Underlying

Price94.75

Time value depends on Time Volatility Distance from the strike price

Time value depends on Time Volatility Distance from the strike price


Value of Call Option

INTRINSIC VALUE TIME VALUE

EXPECTED VALUE OF PROFIT

GIVEN EXERCISE

STRIKE

FUTURES

PRICE

SHADED AREA:

Probability distribution of the log of the futures price on the expiration date for values above the strike.


Black-Scholes Option Valuation

Call value = SoN(d1) - Xe-rTN(d2)

d1 = [ln(So/X) + (r + 2/2)T] / (T1/2)

d2 = d1 - (T1/2)

whereSo = Current stock price

X = Strike price, T = time, r = interest rate

N(d) = probability that a random draw from a normal distribution will be less than d.


Valuing the Corporate Venture Option

Value of the underlying asset (S) = PV of cash flows from purchase of on-line selling venture, if done now =$100 Million

Strike Price (X) = cost of expansion into global on-line selling = $125 Million

We estimate the variance in the estimate of the project value by using the annualized standard deviation in firm value of publicly traded on-line marketing firms in the global markets, which is approximately 50%. Variance in Underlying Asset’s Value = SD^2=0.25

Time to expiration = Period for which “venture option” applies = 2 years

2-year interest rate: 6.5%

Call Value = 100 N(d1) -125 (exp(-0.065)(2)) N(d2) = $ 24.2 Million


Conclusion?

Johnson & Johnson should go ahead and invest in the venture -- the value of the option ($24 million) exceeds the cost ($15 million)

Can this approach be used to value highly speculative ventures?


Ian H. Giddy

NYU Stern School of Business

44 West 4th Street

New York, NY 10012, USA

Tel 212-998-0563; Fax 917-463-7629

[email protected]

http://giddy.org

Documents

Prof. Ian Giddy New York University Valuation IBM