Corporate Finance Theory - 2017 - Universität zu Köln · 6 Overview Why would we be interested in valuing a company or its specific assets? Corporate transactions Purchase price

Corporate Finance Theory

I. Corporate Valuation

1. Valuation Approaches

2. Cost of Capital

3. Application Issues

II. Acquisitions, Divestitures, Restructuring

1. M&A Activity and Explanations

2. Defense tactics

2

Introduction

Course material: www.ilias.uni-koeln.de

(“Corporate Finance Theory”)

Password:

Content: Lecture Slides

Tutorials + Solutions etc.

3

Schedule Date Time Content NoteTu. Oct 10 10:00 ‐ 13:30 LectureTh. Oct 12Fr. Oct 13Tu. Oct 17 10:00 ‐ 13:30 LectureTh. Oct 19 10:00 ‐ 13:30 TutorialFr. Oct 20 12.00 – 15:30 TutorialTu. Oct 24 10:00 – 13:30 Lecture HKCFTh. Oct 26 10:00 ‐ 13:30 TutorialFr. Oct 27 12:00 – 15:30 TutorialTu. Oct 31 ReformationstagTh. Nov 02Fr. Nov 03Tu. Nov 07 10:00 ‐ 13:30 LectureTh. Nov 09 10:00 – 13:30 TutorialFr. Nov 10 12:00 ‐ 15:30 TutorialTu. Nov 14 10:00 ‐ 13:30 LectureTh. Nov 16 10:00 – 13:30 TutorialFr. Nov 17 12:00 ‐ 15:30 TutorialTu. Nov 21 10:00 ‐ 13:30 LectureTh. Nov 23 17:45 ‐ 21:00 TutorialFr. Nov 24 10:00 ‐ 13:30 TutorialTu. Nov 28 10:00 ‐ 13:30 LectureTh. Nov 30 10:00 – 13:30 Tutorial Q&A SessionFr. Dec 01 12:00 ‐ 15:30 Tutorial Q&A SessionSa. Dec 02 08:45 Final Exam

4

Literature

CWS Copeland/Weston/Shastri: Financial Theory and Corporate Policy, 4th

Edt., New York, 2005.

KGW Koller/Goedhart/Wessels: Valuation: Measuring and Managing the Value of Companies, 5th Edt., New York, 2010.

HHHLS Heinrichs/Hess/Homburg/Lorenz/Sievers: Extended Dividend, Cash Flow and Residual Income Valuation Models - Accounting for Deviations from Ideal Conditions, 2013, Contemporary Accounting Research, Vol. 30, p. 42-79.

HKM Hess/Kaul/Meuter: The Performance of Mechanical Earnings Forecasts, 2015, Working Paper.

5

Overview

In this course we ask:

(1) What is the value of a company or specific assets of this company? Why would we want to know at all? Appropriate formulas? Required inputs? Obstacles & practical problems? …

(2) Why would we want to buy another company or its assets? How to “generate value”? Who profits? Investor communication?

(3) What to do if someone else wants to buy our company? Defend ourselves? Why? How to communicate?

6

Overview

Why would we be interested in valuing a company or its specific assets?

Corporate transactions Purchase price in takeovers, mergers, acquisitions, …

Strategic planning Identify value drivers, enhance value, prepare a business for sale, …

Asset management Portfolio allocation in private equity or public funds, insurance comp., …

Many regulatory purposes Fair value opinions for shareholders Allocation of purchase price to specific assets, e.g. brand names Goodwill accounting Taxation of inheritances, divorces, …

7

Overview

Main purpose of lecture: obtain knowledge how to value companies

General framework:

Practical problems:

( )0

1 (1 )t

tt

E XV

k

¥

=

=+

åPresent value of expected future payoffs

Net Income, Dividend, ...What exactly is payoff?

kEstimate appropriate discount rate

( ) ( ) ( )1 2 3, , , ...E X E X E XForecast future payoffs over infinite horizon

8

Sales– Cost of Goods Sold– Selling, General & Administrative Expense– Depreciation & Amortization= Operating Profit after Depreciation

– Interest & Related Expense+ Non-operating Income+ Special Items = Pretax Income EBT

Income Taxes Non-controlling Interest= Income before Extraordinary Items

+ Extraordinary Items + Discontinued Operations= Net Income NI

Earnings Scheme

Overview

9

Overview

Income Statements

Income Statements of S&P 500 Firms (Average, in Mill. $)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014463 467 466 467 500 497 496 500 497 499 500 500 500 498 499

Sales/Turnover (Net) 12,702 13,050 12,293 13,270 14,432 15,984 17,494 18,583 18,518 16,674 18,118 20,033 20,542 21,100 21,534Cost of Goods Sold 8,516 8,924 8,306 8,899 9,327 10,376 11,131 11,941 12,708 11,083 11,717 13,072 13,389 13,678 13,888Selling, Gen. & Admin. 1,617 1,736 1,702 1,887 2,176 2,306 2,526 2,718 2,809 2,761 2,871 3,047 3,153 3,183 3,317Depreciation & Amortization 656 737 626 643 652 675 708 766 829 799 837 879 947 1,005 1,052Operating Inc. after Depr. 1,913 1,654 1,659 1,842 2,277 2,627 3,129 3,158 2,172 2,030 2,694 3,035 3,053 3,234 3,276

Interest and Related Expense 644 657 570 543 514 663 880 1,047 631 393 391 383 374 364 367Nonoper. Income (Expense) 138 90 47 98 30 85 94 111 23 -26 -18 2 19 36 75Special Items -53 -442 -392 -154 -186 -102 -86 -226 -504 -177 -122 -225 -256 -172 -205Pretax Income 1,355 658 764 1,243 1,606 1,947 2,256 1,995 1,061 1,433 2,163 2,429 2,441 2,734 2,779

Income Taxes 493 313 330 398 515 617 707 710 482 414 619 656 727 746 803Noncontrolling Interest 7 14 17 18 23 27 34 38 29 32 52 52 57 55 37Income bef. Extraord. Items 855 332 417 828 1,068 1,303 1,515 1,247 550 987 1,492 1,722 1,657 1,934 1,939

Extraord. Itm. & Discont. Oper. -4 5 -358 11 -14 25 60 44 33 10 10 28 10 54 20Net Income (Loss) 851 336 60 838 1,054 1,328 1,575 1,291 583 997 1,502 1,749 1,667 1,988 1,959

--

-

-

+

-

-

+

+

10

Cash Flow

Overview

Net Income+ Interest Payments Tax Shield (i.e. tax savings due to deductable interest)= Net Operating Profit Less Adjusted Taxes

+ Depreciation (and other non-cash cost components) Capital Expenditures (i.e. investments in fixed assets) Net Working Capital Increases= Free Cash Flow

+ Tax Shield Interest Payments+ Change in Debt (– Debt Redemptions, + New Debt Issued)= Flow to Equity

11

Overview

Cash Flow

Cash Flows to Equity of S&P 500 Firms (Average, in Mill. $)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Net income 851 336 60 838 1,054 1,328 1,575 1,291 583 997 1,502 1,749 1,667 1,988 1,959

+ Depreciation & Amortization 656 737 626 643 652 675 708 766 829 799 837 879 947 1,005 1,052

– CAPEX -858 -921 -738 -671 -729 -818 -971 -1,028 -1,152 -909 -965 -1,149 -1,268 -1,293 -1,396– Acquisitions -392 -275 -204 -181 -157 -298 -453 -533 -367 -236 -367 -403 -449 -311 -366– Other Long-term Investments -749 -862 -836 -771 -1,444 -815 -1,254 -1,209 -1,002 746 3 -671 -1,014 -1,171 -1,020

– Delta Working Capital -91 430 652 179 38 -197 -575 -406 1,197 646 321 470 360 669 249

+ Change in Debt 848 841 554 492 438 480 1,285 1,927 67 -1,277 -788 -645 15 143 757+ Other Financing 278 217 66 161 890 678 913 815 421 -84 167 1,160 825 470 336

FTE 543 503 181 689 743 1,032 1,227 1,622 577 682 710 1,391 1,084 1,499 1,572

12

Overview

Income vs. Cash Flow

Net Income and Cash Transfers to ShareholdersAverage S&P 500 Firm (in Mill. $)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Net Income 851 336 60 838 1,054 1,328 1,575 1,291 583 997 1,502 1,749 1,667 1,988 1,959

FTE 543 503 181 689 743 1,032 1,227 1,622 577 682 710 1,391 1,084 1,499 1,572

Cash Dividends 264 264 263 286 361 475 474 536 525 469 449 506 588 669 743Share Buybacks

– New Issuances 152 89 138 159 232 473 756 869 -120 106 338 698 593 725 908Dividends & Substitutes 416 353 400 445 593 948 1,229 1,406 405 574 787 1,204 1,182 1,394 1,651

Payout Ratio (Cash only) 31% 78% 441% 34% 34% 36% 30% 42% 90% 47% 30% 29% 35% 34% 38%

Payout Ratio (incl. Subst.) 49% 105% 672% 53% 56% 71% 78% 109% 69% 58% 52% 69% 71% 70% 84%

13

Literature: Copeland/Weston/Shastri (2005), Ch. 14


1. Valuation Approaches1.1. Fundamental Valuation Principle1.2. Multiples1.3. Discounted Cash Flow1.4. Residual Income Model

2. Cost of Capital



14

1.1. Fundamental Valuation Principle

Fundamental Valuation Principle – Present Value

The value of any security is solely determined by its expected future payments Xt to the holder of the security over its entire life time T

where k is the appropriate discount rate, i.e., the return investors require considering the riskiness of payments.

( )0

1 (1 )

Tt

tt

E XV

k=

=+

å

15


This is applicable to wide range of securities, for example,

Bonds: Xt more or less secure future coupon and redemption paymentsT fixed repayment date

Stocks: Xt uncertain future cash payments to shareholders, i.e., expected dividends or dividend substitutes

T=∞ uncertain life of the company, in principle, infinite horizon

Options: Xt uncertain proceeds from exercising the option,e.g., difference between future stock price and strike price

T fixed expiration date

( )0

1 (1 )

Tt

tt

E XV

k=

=+

å

16


Dividend Discount Model

Infinite horizon problem T=∞

Assuming that dividends grow at a constant growth rate g, i.e., · 1 g ,leads to the standard Gordon Growth Model

0 0

1

1

1

gEQ D

k g

Dk g

+= ⋅

-

= ⋅-

( )0

1 (1 )

t

tt

E DEQ

k

¥

=

=+

å

Remember1

(1 ) 1

(1 )

t

tt

g g

k gk

¥

=

+ +=

-+å

17


Exercise:

Data/Assumptions

What is the fair value of the stock?

What would be the fair value with zero growth?

Expected Earnings per Share Expected Dividend per Share (to be paid at t=1)

1,50 USD1,50 USD

Expected long‐term growth

Required rate of return

3%

10%

0 11 1

1.50 15.000.10

EQ Dk

= ⋅ = ⋅ =

0 11 1

1.50 21.450.10 0.03

EQ Dk g

= ⋅ = ⋅ =- -

18



Instead, if we assume that dividends do not grow right away (i.e., from time t=0 on)but that constant growth kicks in at a later point in time (i.e., from time T on) we get a “2-phase version” of the Gordon Growth Model

( )0 1

1

1 1

(1 ) (1 )

Tt

Tt Tt

E DEQ D

k gk k+

=

= + ⋅ ⋅-+ +

å

2nd phase

Constantdividend growth

1st phase

Individualdividend forecasts

1 2 T T+3T+1 T+2

. . .…

19


Exercise:Data/Assumptions

Find the fair value according to DDM !

Analyst Estimates (EPS) t=1 1,50 USDt=2 2,10 USD

Historical payout ratio 30%Required rate of return 10%Assumed long‐term growth 3%

t Earn p Sh payout ratio Div p Sh PV0 ‐‐ 30% ‐‐1 1,50 30% 0,45 0,412 2,10 30% 0,63 0,523 2,16 30% 0,6489 7,66

8,59

t Earn p Sh payout ratio Div p Sh PV

0 ‐‐ 30% ‐‐

1 1,50

2 2,10

3

2 2,10

33

10

1

(1 ) (1 ) ( )

TTt

t Tt

DDV

k k k g+

=

= ++ + -

å

20

Literature: Copeland/Weston/Shastri (2005), Ch. 14Koller/Goedhart/Wessels (2010), Ch. 14



2. Cost of Capital



21

1.2. Multiples

Basic Idea:

Some (target) company is valued based on current market prices of other companies with similar characteristics

(comparable company approach)

Assessment is based on financial data related to company’s (future) profitability, e.g., (expected) Net Income, EBIT, EBITDA, …

22

Comparable Company Approach(stock market oriented)

Similar Public Company MethodShare price in relation to certain keyfinancial data of an enterprise

Recent Acquisition Method Prices of recent public transactions in relation to certain key data of anenterprise

Other Comparison Methods(not focused on stock market)

Sales Methode.g. determine corporate value

based on sales

Other Quantitative Comparisonse.g. value a taxi company

based on number of taxi licenses

→ “Multiples”

Main Versions:

1.2. Multiples

23

Basic procedure:

1. Select a peer group

Try find many companies with similar characteristics(especially companies that are similar w.r.t. value drivers, i.e., profit growth, operative risk, leverage, payout, …)

2. Calculate certain multiple(s) for the peer group companies

Calculate average / median multiple for the peer group

3. Apply average multiple(s) to target company

Market value Average multiple Comparison value

Market valueMultiple

Comparison value

1.2. Multiples

24

In practice, lots of different multiples are used

Typical denominators :

Earnings (with various definitions: NI, EBIT, EBITDA, Earnings excl. special items, … )

Cash Flows

Sales figures

Book value of equity

…

Typical numerators:

enterprise value (= market value of equity + debt)

equity value (= market value of equity alone)

1.2. Multiples

25

Example: The many different definitions of earnings and their impact on PER

The first step when discussing a valuation based on a multiple is to ensure that everyone is using the same definition for that multiple

1.2. Multiples

26

1.2. Multiples

Caterpillar (in mill. $) 2013 2014Cash and Short-Term Investments 6,322 7,476 PER SHARE FIGURESTotal Current Assets 38,335 38,867Total Assets 84,896 84,681 Assets per Share 131.58 137.20Total Liabilities 64,018 67,855 Book Debt per Share 99.22 109.94Stockholders Equity 20,878 16,826 Book Equity per Share 32.36 27.26Liabilities and Stockholders Equity 84,896 84,681

Sales 55,656 55,184 Sales per Share 86.26 89.41Cost of Goods Sold 37,646 36,607Gross Profit (Loss) 18,010 18,577Selling, General and Admin. Expense 7,593 7,832Operating Income before Depreciation 10,417 10,745 EBITDA per share 16.15 17.41Depreciation and Amortization 3,081 3,160Operating Income after Depreciation 7,336 7,585 EBIT per Share 11.37 12.29Interest & Related Expense 1,192 1,108Nonoperating Inc., Special Items, Other -1,008 -1,370Income Taxes 1,319 1,380Net Income (Loss) 3,789 3,695 NI per Share 5.87 5.99Stock Price ($, fiscal year end) 90.81 91.53 Equity Value (per Share) 90.81 91.53Common Shares Outst. (mill., fisc yr end) 645.20 617.20 Enterprise Value (per Share) 190.03 201.47

P/E-Ratio (NI) 15.5 15.3

Enterprise Value / EBIT 16.7 16.4Enterprise Value / EBITDA 11.8 11.6Enterprise Value / Sales 2.2 2.3

Market to Book 2.8 3.4

Given Caterpillars last annual financial information, what would be reasonable multiples?

27

1.2. Multiples

B/S

Current Assets

Fixed Assets

Total Assets

Current Liabilities

Long-term Liabilities

Total Liabilities

Shareholders’ Equity

Total Liabilities & Shareholders’ Equity

I/S

Sales

– operating costs

EBITDA

– Deprec. & Amortization

EBIT

– Interest expense

EBT

– Taxes

Net Income

Equityalone

Debt&

Equity

B/S

Current Assets

Fixed Assets

Total Assets

Current Liabilities

Long-term Liabilities

Total Liabilities

Shareholders’ Equity

Total Liabilities & Shareholders’ Equity

I/S

Sales

– operating costs

EBITDA

– Deprec. & Amortization

EBIT

– Interest expense

EBT

– Taxes

Net Income

28

Multiples based on entity value(Enterprise- / Entity- / Asset-Value-Multiples)

applied market prices:Entity value (aggregated market price of equity and debt)

– non-operating assets= Enterprise value

(Market value of operating business activity)

applied reference value :should be generated by total capital, e.g., EBIT, EBITDA, Oper. Cash Flow, Sales, …

Multiples based on equity value(Equity-Multiples)

Applied market values:Equity value (market capitalization)

applied reference value:should be related to equity (e.g. earnings, EBT, equity book value, FTE, …)

However, also multiples using total capital based denominator and equity based numerator, e.g. EntV EntV EntV

EBITDA EBIT Sales

Price PriceEquity book value / Share Earnings / Share

Market capitalizationSales

1.2. Multiples

29

Theoretical foundation of P/E ratio

Starting point DDM:

01 (1 )

t

tt

DPk

tt

t

PPERNI with Pt market price per share

NIt net income per share

with Dt dividend per share

k risk adjusted interest rate

1.2. Multiples

30

Assume that payout ratio p is fixed,i.e., Dt = p ∙ NIt , then

Moreover, assume that net income (and dividend) grows at a constant rate g, then

Then the P/E ratio is

01

1

(1 )

(1 )

tt

t

tt

t

DP

k

p NI

k

¥

=

¥

=

=+

⋅=

+

å

å

0 01

g

P p NIk g

+= ⋅

-

0

0

1

P gp

NI k g

+= ⋅

-

1.2. Multiples

31

Hence, the P/E ratio depends on

the companies risk adjusted discount rate kor the company’s expected risk

the (expected) growth rate of earnings g

the (expected) payout ratio p

So, company valuation based on P/E ratios only makes sense if the peer group has very similar risk, growth and payout characteristics

Can we assume that this is given within an industry?

P E ratio0

0

1 /

P gp

NI k g

+= = ⋅

-

1.2. Multiples

32

Theoretical foundation of multiples (contd.)

Price to sales ratio

Substitute NI0 = pm ∙ S0into the P/E ratio

Then, we get the price sales ratio as

P S 0

0

/ P

S=

0 0

0 0

1

P P gp

NI pm S k g

+= = ⋅

⋅ -(with pm = profit margin)

0

0

1

P gpm p

S k g

+= ⋅ ⋅

-

1.2. Multiples

33

Theoretical Foundation of multiples (contd.)

Price to book ratio:

Substitute NI0 = RoE ∙ BV0 into the P/E ratio

with RoE = return on equityBVt = book value of equity

Then we get the price to book ratio as

0 0

0 0

1

P P gp

NI RoE BV k g

+= = ⋅

⋅ -

0

0

1

P gRoE p

BV k g

+= ⋅

-

1.2. Multiples

34

1.2. Multiples

Some Empirical Findings

Average Payout Ratio (last 10 years)

P/E

Rat

io

P/E

Rat

io

Std RoE (last 10 years)

P/E Ratios of S&P 500 firms based on last available financial statements: FY 2014

35

1.2. Multiples

Enterprise Value / EBITDA per Share(S&P 500, 5%-95% Fractile, 1964-2014)

Price / NI per Share(S&P 500, 5%-95% Fractile, 1964-2014)

36

1.2. Multiples

Enterprise Value / EBITDA per Share(only S&P 500 companies with “reasonable” EV/EBITDA ratios, 2014)

Price / NI per Share(only S&P 500 companies with “reasonable” P/E ratios, 2014)

37

Summary

Valuation based on multiples is widely applied in practice

Advantages:

Multiples are easy to apply and deliver quick resultsMultiples require only a few easily available data (market prices, company data), calculation as well very easy

Easy to understand and to communicateConcept is (seemingly) easy to understand for clients, press…and by comparison easy to communicate

Close to market valuationValuation based on current market prices reflecting how the market prices similar assets

Sound theoretical foundationClose relation to DDM value drivers (though often only proxies used)

1.2. Multiples

38

Summary

Disadvantages:

Empirical Results somewhat disappointing weak relation to value driver proxies; extreme values; wide fluctuations

Important to be precise in definition of multipleMultiples coming under same name may be defined differently

Difficult to select appropriate “peers”especially if „peers“ differ w.r.t value drivers (growth, risk)

One-dimensional comparisonvaluation is based on one single corporate key financial (e.g., EBIT or sales);statistical analysis beneficial (e.g., regression to account for value drivers)

Multiples provide only relative valuation problematic if market / peer group is overvalued; self-reinforcing in „hot markets“

1.2. Multiples

39

Literature: Copeland/Weston/Shastri (2005), Ch. 14Koller/Goedhart/Wessels (2010), Ch. 2, 6



2. Cost of Capital



40

Model overview

Standard approach to calculate the “fair value” of companies:

where Xt is some expected payoff (e.g., “Dividends”, “Free Cash Flow”, “Cash Flow to Equity”, “Residual Income”, …) and k is a risk-adjusted discount rate, e.g., obtained via the CAPM:

This discount rate may be adjusted for the firm’s leverage and its tax situation.

( )f m fk r E r rb é ù= + ⋅ -ë û

( )0

1 (1 )

t

tt

E XV

k

¥

=

=+

å

1.3. Discounted Cash Flow

41

( )0

1 (1 )

t

tt

E DEQ

k

¥

=

=+

å

( )0 0

1 (1 )

t

tt

E ResIncEQ BookValue

k

¥

=

= ++

å

( )0 0

1 (1 )t

tt

E FCFEQ Debt

WACC

¥

=

+ =+

å

Major model types


Discounted Cash Flow Model (e.g. WACC Model)

Residual Income Valuation Model (Ohlson Model)


42

Required inputs:

1. Estimate expected uncertain payoffs Xt of a company for year 1, 2, …e.g., dividend, free cash flow, flow to equity, residual income, …

2. Determine relevant risk-adjusted rate of return, e.g. k, WACC, …

Note: numerator and denominator must fit together


43

Cash Flow Scheme

Net Income+ Interest paid (a)+ Taxes paid= Earnings before interest and taxes (EBIT)– Taxes on EBIT (= taxes paid + tax shield) (b)= Net Operating Profit Less Adjusted Taxes (NOPLAT)+ Depreciation and other non-cash expenditures (c)– Investments in tangible/intangible assets (CapEx) (d)– Working capital increases (e)

= Free Cash Flow (FCF)+ Tax shield

= Total Cash Flow (TCF)

– Interest & debt service (f)

= Flow to Equity (FTE) Net Cash Flow(considers actual debt financing)

Gross Cash Flow (theoretical 100% equity-financing)

Gross Cash Flow (considers actual debt financing)


44

Comments

non-cash income Revaluations (if in I/S) Release of provisions (I/S)

(c) non-cash expenditures Depreciation (I/S) Amortization (I/S) Additions to provisions (I/S)

(d) Investment payouts: Investments in fixed assets, intangible assets

and long-term financial assets

(b) Taxes on EBIT = Taxes payable if company would have no debt= Taxes actually paid + Tax Shield (i.e., savings due to deductible interest)

(a) Interest expense Only explicit interest or also implicit interest?


45

Comments

(f) Debt service= Net redemption of debt = Debt repayments – Debt issuance

(e) Decrease/increase in working capital

Δ WC = Δ Current Assets – Δ Current Liabilities

= Δ cash + Δ Inventories + Δ accounts receivables + Δ securities + …– Δ prepayments received – Δ accounts payables – Δ notes payable …

What about „excess cash“?


46

Differences between FTE and Dividend?

FTE not paid out entirely but some part reinvested, e.g., to facilitate more growth?


47

Net Income

+ Depreciation CapEx Δ Working Capital

+ Net Change in Debt (– Redemptions + Issuances)

= Flow to Equity

Net Income+ Interest Tax Shield+ Depreciation CapEx Δ Working Capital

= Free Cash Flow


Cash Flow Scheme – Shortcuts

48

Example: We have the following projected financial statements


0 1Current Assets 200.00 210.00Fixed Assets 500.00 525.00Total Assets 700.00 735.00

Current Liabilities 20.00 21.00Long term Liabilities 300.00 315.00Comon Stock 320.00 320.00Ret Earn 60.00 79.00Equity 380.00 399.00Liab. & Equity 700.00 735.00

0 1Sales 1,000.00 1,050.00CoGS 850.00 895.00Depreciation 50.00 50.00EBIT 100.00 105.00Interest 15.00 15.75EBT 85.00 89.25Taxes 25.50 26.78Net Income 59.50 62.48

49

From this we can calculate FCF and FTE as


t = 1 t = 1Net Income 62.48 Net Income 62.48

+Int. Paid 15.75‐Tax Shield 4.73+Depreciation 50.00 +Depreciation 50.00‐CapEx 75.00 ‐CapEx 75.00‐WC Increas 9.00 ‐WC Increas 9.00

+Change in Debt 15.00FCF 39.50 FTE 43.48

Tax rate s = 30%

0 1Current Assets 200.00 210.00Fixed Assets 500.00 525.00Total Assets 700.00 735.00

Current Liabilities 20.00 21.00Long term Liabilities 300.00 315.00Comon Stock 320.00 320.00Ret Earn 60.00 79.00Equity 380.00 399.00Liab. & Equity 700.00 735.00

0 1Sales 1,000.00 1,050.00CoGS 850.00 895.00Depreciation 50.00 50.00EBIT 100.00 105.00Interest 15.00 15.75EBT 85.00 89.25Taxes 25.50 26.78Net Income 59.50 62.48

50


Infinite horizon problem

Solutions

(1) Growth models Assume that future payoffs grow at some average rate g

(2) Two- or three-phase modelsAssume that equilibrium growth kicks in later when firm is more mature (→ I.3. Application Issues)

( )1

0(1 )

t

tt

E XV

k=

=+

å¥ Valuation equations require

payoff forecasts over an infinite horizon

0

0 0 01

(1 )

(1 ) 1

(1 )

tt

t

tt

X X g

g gV X X

k gk=

= ⋅ +

+ += ⋅ = ⋅

-+å¥

1 2 3 40

. . .g

51

DCF Model Variants

V0 Xt kEquity approach

Flow to Equity(FTE)

EquityEQ0

FTEFTEt

Cost of equity (levered)ks

L

Entity approaches

Weigthed Average Cost of Capital (WACC)

Total capitalEQ0 + Debt0

FCFFCFt

Cost of total capitalWACCs

Adjusted Present Value (APV)

Total capitalEQ0 + Debt0

FCFFCFt

Tax shields ∙ i ∙ Debtt-1

Cost of equity (unlevered)ks

Risk-free interest ratei


( )0

1 (1 )

t

tt

E XV

k

¥

=

=+

å

52

(1) Adjusted Present Value (APV) Model

FCFt Free cash flow (to shareholders and lenders) after deducting theoretical taxes (i.e., ignoring tax shield)

s ∙ i ∙ Debtt-1 tax shield (not included in the FCF)

ks Shareholders’ required return if firm would have no debt(i.e., ignoring actual leverage)

i required rate of return on risk-free tax shield

Valuation result: Entity value !

10 0

1 1(1 ) (1 )t t

t tt ts

FCF s i DebtEQ Debt

k i

¥ ¥-

= =

⋅ ⋅= + -

+ +å å


53

(2) Flow to Equity (FTE) Model

FTEt Cash flow to equity after deducting actual taxes (i.e., accounting for tax shield)

ksL Shareholders required rate of return

(i.e., accounting for leverage L and tax s)

Valuation result: Equity value !

01 (1 )

tL tst

FTEEQ

k

¥

==

+å


( ) (1 )Ls s s

Debtk k k i s

EQ= + - ⋅ - ⋅

54

(3) WACC Model

FCFt Free cash flow (to shareholders and lenders) after deducting theoretical taxes, (i.e., ignoring tax shield)

WACCs Weighted average cost of capital(accounting for tax effects s, which were neglected in cash flow)

Valuation result: Entity value !

0 01 (1 )

tt

st

FCFEQ Debt

WACC

¥

== -

+å


0 0

0 0 0 0

(1 )Ls s

EQ DebtWACC k i s

EQ Debt EQ Debt= ⋅ + ⋅ - ⋅

+ +

55

Constant payoff growth versions

FTE:

WACC:

APV:

01

1

(1 )tL t

t s

Ls

FTEEQ

k

FTE

k g

¥

=

=+

=-

å

10 0

1 1

1 00

(1 ) (1 )t t

t tt ts

s g

FCF s i DebtEQ Debt

k i

FCF s i DebtDebt

k g i

¥ ¥-

= =

⋅

-

⋅ ⋅= + -

+ +

⋅= + -

-

å å

0 01

10

(1 )t

tt s

s

FCFEQ Debt

WACC

FCFDebt

WACC g

¥

=

= -+

= --

å


1 2 3 40

. . .g > 0

56

Example: We have the following projected statements

There is no growth (g = 0). The firm pays 4% p.a. on its debt (i = 4%)

and 30% taxes (s = 30%). If the firm would have no debt

its cost of equity would be 10% (ks = 10%).


t = 0 1, 2, 3, …Sales 5,000 5,000CoGS 4,150 4,150Depreciation 250 250EBIT 600 600Interest 60 60EBT 540 540Taxes 162 162Net Income 378 378

t = 0 1, 2, 3, …Current Assets 1,100 1,100Fixed Assets 2,500 2,500Total Assets 3,600 3,600

Current Liab. 100 100Long‐term Liab. 1,500 1,500Comon Stock 1,700 1,700Ret Earn 200 200Equity 1,900 1,900Liab. & Equity 3,600 3,600

57

From the projected statements we get FCF and FTE as

Note: with no growth we have Depreciation = CapEx

FCF = EBIT ∙ (1 – s)

FTE = NI


t = 1, 2, 3, … t = 1, 2, 3, …NI 378.00 NI 378.00

+ Int. Paid 60.00‐Tax Shield 18.00+Depreciation 250.00 +Depreciation 250.00‐CapEx 250.00 ‐CapEx 250.00‐WC Increase 0.00 ‐WC Increase 0.00

+Change in Debt 0FCF 420.00 FTE 378.00

58


1 00 0

4%420 30% 15001500

10% 4%

s g

FCF s i DebtEQ Debt

k g i

⋅

-

⋅ ⋅

⋅= + -

-

= + - = 3150

0 0

0 0 0 0

10 0

(1 )

3150 150012% 4% (1 30%) 9.0323%

3150 1500 3150 1500

4201500

9.0323%

Ls s

Ls

EQ DebtWACC k i s

EQ Debt EQ Debt

FCFEQ Debt

k

= ⋅ + ⋅ - ⋅+ +

= ⋅ + ⋅ - ⋅ =+ +

= - = - = 3150

FTE:

WACC:

APV:

10

( ) (1 )

10% (10% 4%) (1 30%) 1500 3150 12%

378

12%

Ls s s

Ls

k k k i s Debt EQ

FTEEQ

k

= + - ⋅ - ⋅

= + - ⋅ - ⋅ =

= = = 3150

59

Notes:

If correctly applied, APV, WACC and FTE model yield identical values!

However, FTE and WACC model require to know the firm’s leverage in order to calculate appropriate cost of capital. But to calculate leverage one needs to know the market value of equity!This is called the “Circularity Problem”.

(→ I.3 Application Issues)


60

Literature: Copeland/Weston/Shastri (2005), Ch. 14



2. Cost of Capital



61

Residual Income Model (RIM) or Economic Value Added (EVA)

Basic model:

Market Value of equity EQ0

= Book Value of equity BkEQ0

+ Present value of residual incomes PV(ResInc1, ResInc2, …)

Residual Income = Net Income above ResInct = NIt – ks

L ∙ BkEQt-1investors’ earnings demands (i.e. above required return on equity)

00 0

1

( )

(1 )t

L tt s

E ResIncEQ BkEQ

k

¥

=

= ++

å

1.4. Residual Income Model

62


Deducting RIM from DDM(or alternatively from FTE)

with Dt total dividend payments of the company (net transfer to shareholders)

E(Dt) expected dividend payments in t=0

k risk adjusted interest rate (k ≡ ksL)

00

1

( )(1 )

tt

t

E DEQ

k

¥

==

+å (I)

63

Alternative deduction from FTE (since DDM and FTE are identical)

Main assumption Cash Flow to Equityof the FTE-approach is distributed entirely

Dividends Dt = Net transfers to shareholders (Dividends + Share buybacks, Increase of capital = negative dividends)

= Cash Flow to Equity (FTEt)

Under the assumption of complete distribution, the DDM-model uses the same numerator as the FTE-approach (Dt = FTEt)Consequently the discount rate has to be the same: k = ks

F

Hence DDM and FTE are identical !


64

“Clean Surplus Relation“ (principle of congruence)

Any value changes in asset and liabilities must be passed through income statement !

No I/S independent recording in equity position (“dirty surplus accounting”)

Net capital transferto shareholder


Book value of equity at the beginning of fiscal year t BkEQt-1

+ Net income NIt

– Dividends (including all shares)+ Capital increases Dt

= Book value of equity at the end of fiscal year t BkEQt

Clean Surplus Relation: BkEQt = BkEQt-1 + NIt – Dt

65

Clean Surplus Relation: BkEQt = BkEQt-1 + NIt – Dt (II)

According to „clean surplus accounting“ the book value of equity can only change due to net income and capital transfers to shareholders (dividends)

or from shareholders (capital increase)

Other changes of the book value of equity which are not passed through income statement are called „dirty surplus accounting“, e.g. revaluations not impacting net income,

differences from foreign exchange conversion, issuance of employee shares, …


66

Solving Clean Surplus Relation (II) for Dt:

and inserting into (I)

yields (III)

Hence, the market value of equity can be expressed exclusively in terms of financial statement items (i.e., net incomes and book values of equity)

1( )t t t tD NI BkEQ BkEQ -= - -

change in book value of equity

0 10

1

( )

(1 )t t t

tt

E NI BkEQ BkEQEQ

k

¥-

=

- +=

+å

00

1

( )

(1 )t

tt

E DEQ

k

¥

==

+å


67

For notational simplicity drop the expectations operator, i.e.,

10

1

1 1 1

1

(1 )

(1 )

t t tt

t

t t t t tt

t

NI BkEQ BkEQEQ

k

NI BkEQ BkEQ k BkEQ k BkEQ

k

¥-

=

¥- - -

=

- +=

+

é ù- + + ⋅ - ⋅ê ú= ê ú+ê úë û

å

å


(III)1

01 (1 )

t t tt

t

NI BkEQ BkEQEQ

k

¥-

=

- +=

+å

1 1 10

1

1 1

1

(1 ) (1 ) (1 )

(1 )

(1 ) (1 ) (1 )

t t t t tt t t

t

t t t tt t t

t

BkEQ k BkEQ NI k BkEQ BkEQEQ

k k k

k BkEQ NI k BkEQ BkEQ

k k k

¥- - -

=

¥- -

=

é ù+ ⋅ - ⋅ê ú= + -ê ú+ + +ê úë û

é ù+ ⋅ - ⋅ê ú= + -ê ú+ + +ê úë û

å

å

insert k · BkEQt-1 – k · BkEQt-1 = 0

rearrange this equation slightly

68

expand the sum


1 10

1

0 1 0 1 1 2 1 21 1 1 2 2 2

0 11

(1 )

(1 ) (1 ) (1 )

(1 ) (1 ) + ...

(1 ) (1 ) (1 ) (1 ) (1 ) (1 )

(1 )

(1 )

t t t tt t t

t

k BkEQ NI k BkEQ BkEQEQ

k k k

k BkEQ NI k BkEQ BkEQ k BkEQ NI k BkEQ BkEQ

k k k k k k

k BkEQ NI k BkE

k

¥- -

=

é ù+ ⋅ - ⋅ê ú= + -ê ú+ + +ê úë û

+ ⋅ - ⋅ + ⋅ - ⋅= + - + + -

+ + + + + +

+ ⋅ - ⋅= +

+

å

0 1 1 2 1 21 1 2 2 2

1 0 1 1 2 1 20 1 1 1 2 2

(1 ) + ...

(1 ) (1 ) (1 ) (1 ) (1 )

+ + ... (1 ) (1 ) (1 ) (1 ) (1 )

Q BkEQ k BkEQ NI k BkEQ BkEQ

k k k k k

NI k BkEQ BkEQ BkEQ NI k BkEQ BkEQBkEQ

k k k k k

+ ⋅ - ⋅- + + -

+ + + + +

- ⋅ - ⋅= - + + -

+ + + + +

and cancel out BkEQ terms

simplify (1+k) terms

69

Assuming that

we get

0(1 )

TT

BkEQ

k¥¥

+


1 0 2 10 0 1 2

+ + ... +(1 ) (1 ) (1 )

TT

NI k BkEQ NI k BkEQ BkEQEQ BkEQ

k k k¥¥

- ⋅ - ⋅= +

+ + +

The remaining terms are:

1 0 2 10 0 1 2

10 0

1

+ + ... (1 ) (1 )

+ (1 )

t tt

t

NI k BkEQ NI k BkEQEQ BkEQ

k k

NI k BkEQEQ BkEQ

k

¥-

=

- ⋅ - ⋅= +

+ +

- ⋅=

+å

(IV)

70

finally yields the Residual Income Model:

(V)

0 01

(1 )

tt

t

ResIncEQ BkEQ

k

¥

=

= ++

å

Present value of expected future residual incomes

(= Goodwill)

Fair value of equity

Current book value of equity

1t t tResInc NI k BkEQ -= - ⋅

Residual-Income

adequaterate of return

on equity

Net incomeof period t

(VI)

Inserting the definitionof Residual Incomeinto (IV)


71

Interpretation:

Residual income represents the income in excess of shareholders’ required (risk adjusted) return on book equity

If a company “only” generates the return shareholders require (i.e., k)then the market value equals the book value of equity

If a company is able to generate a higher return than what shareholders require, it generates additional value, i.e., it adds economic value for shareholders.

The terms “abnormal earnings“, “excess earnings“ or “economic value added” are synonymously used for “residual income”.

0 01 (1 )

tt

t

ResIncEQ BkEQ

k

¥

=

= ++

å


1t t tResInc NI k BkEQ -= - ⋅

0 0EQ BkEQ=

1

0(1 )

tt

t

ResInc

k

¥

=

>+

å

72

Example (contd.):


g = 0, s = 30%, i = 5%, ks = 10%, ks

L = 12%

1 1 0

10 0

378 12% 1,900 150

1501,900

12%

Ls

Ls

ResInc NI k BkEQ

ResIncEQ BkEQ

k

= - ⋅ = - ⋅ =

= + = + = 5,150

t = 0 1, 2, 3, …Current Assets 1,100 1,100Fixed Assets 2,500 2,500Total Assets 3,600 3,600

Current Liab. 100 100Long‐term Liab. 1,500 1,500Comon Stock 1,700 1,700Ret Earn 200 200Equity 1,900 1,900Liab. & Equity 3,600 3,600

t = 0 1, 2, 3, …Sales 5,000 5,000CoGS 4,150 4,150Depreciation 250 250EBIT 600 600Interest 60 60EBT 540 540Taxes 162 162Net Income 378 378

73


Note:

If correctly applied, the Residual Income Model yields the same value as APV, WACC or FTE

In the example, residual income is positive, i.e., the company is earning a higher return on its book equity than investors require:

Therefore, the company is more worth than its “net asset book value”, i.e., the book value of equity

11

0

37819.9%

1,900

NIRoE

BkEQ= = =

74

Extensions of basic model:

Ohlson (1995)

Residual income follows AR(1) process without drift

If a company is able to generate a residual income, that income should gradually be decreasing as competition sets in. Other companies will try to imitate an above average business model, if the company is not able to protect it (through patents, entry barriers…)

Ohlson/Jüttner-Nauroth (2005)

Introduction of alternative excess profit dynamic (eps growth)


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