Investment appraisal & company valuation for beginners

Learning

Company
VALUATIONS
www.antonioalcocer.com
@antonioalcocer


4. Company valuation methods

3. Investment appraisal for economic feasibility

PRESENTS

2. Compound interest & CAGR

1. Time value of money definition

Why ($100, today) are not equivalent to
($100, when I was younger)?


TIME VALUE
OF
MONEY


*!$%?


TIME VALUE OF MONEY
TIME VALUE
OF
MONEY TIME VALUE OF MONEY
OPPORTUNITY COST


Opportunity cost

“Money can be invested
today in different options
with a different return
ovetime”


OPTION 1
($398 in t21=2011)

OPTION 2

($100 in t21=2011)

($100 in t0=1990) OPTION 3
($0 in t21=2011)

CAGR= Compound Annual Growing Rate
Apple share price: 01/08/1990: $9.96 – 01/08/2011: $396.75 – CAGR: 19.17%
Money at home below my pillow: 01/08/1990: $100 – 01/08/2011: $100 – CAGR: 0%
Money placed at a default subprime product: 01/08/1990: $100 – 01/08/2011: $0 – CAGR: -100%

TIME VALUE OF MONEY
MEANS OPPORTUNITY COST
MEANING
THAT IN FINANCE
WE TALK
ABOUT
THE
PAIR:

($,time)

That is why different cash-flows at different moments in time
cannot be operated unless moved to the same point in time


How can be
cash-flows
moved
in time?

Compound interest formula
VF=V0 x (1+i)^t

Two cash-flows are equal in time at a given interest rate
VF: Future value of the cash-flow
V0: Present or actual value of the cash-flow
i: Compound annual interest or growing rate
t: Time between both cash-flows

CAGR = ((V /V )^(1/t))-1
F O

R”
“CAG
n as
know
Also

CAGR=Compound Annual Growing Rate
t in years so CAGR on a yearly basis

…and moving cash-flows to the future
is called:

N
T IO
SA
LI
TA
PI
C A
VF=V0 x (1+i)^t

…and moving cash-flows from the future
is called:

Ic%
VO Vf
DISCOUNTING
Vo=VF / (1+i)^t


And what about simple interest?

Simple interest - Is
VF=V0 x (1+i*t)
“Interests earnt are not re-invested”

Compound interest - Ic TIME VALUE OF MONEY

VF=V0 x (1+i)^t
“Interests earnt are re-invested”

Yield =12%
[annual]

I12=1% I6=2% I4=3% I2=6%
MONTHLY BI-MONTHLY QUARTERLY SEMI-ANNUALLY

NO REINVESTMENT REINVESTMENT

Is Ic
By convention yields are provided in a yearly basis IF NOT SPECIFIED www.antonioalcocer.com

EXAMPLE 1

Banking deposit
3-years time
10% annual interest rate (*)
Initial investment: €1.000

(*) The 10% interest rate is an annual yield. It depends if there are reinvestment of interests, using compound interest.
In the case there are not re-investment of interests we use simple interest formula

+€1000+€100+€100+€100

Is (+€100) (+€100) (+€100)

1 2 3

VF = 1000*(1+10%*3) = €1300
-€1000

+€1000+€100+€110+€121

Ic (+€100) (+€110) (+€121)

1 2 3

VF = 1000*(1+10%)^3 = €1331
-€1000

Calculations made for a 3-years bank deposit with a 10% annual interest rate and €1000 initial investment
As you can see due to “time value of money”, and if interests are reinvested or not reinvested; €1000 at t0 are equal to €1331 at a10% compound interest rate or €1300 at a 10% simple interest
Simple interest is used if the interests earnt are not reinvested. Compound interest is used if interests are reinvested
As general rule, investments lasting less than 1 year use simple interest and investments lasting>=1 year use compound interest but which one to use if determined by the existance or not of the re-investment of the interests

EXAMPLE 2

Banking deposit
2-years time
10% annual interest rate
Bi-monthly re-investment of interests
4 semesters
Initial investment: €1.000

Ic
12% ANNUAL YIELD = 12% / 2 = 6% BI-MONTHLY YIELD

CAGR = ((V /V )^(1/t))-1=((1263/1000)^(1/2))-1
F O +€1000+€60+€63.6+€67.4+€71.4

12.38%
(+€60) (+€63.6) (+€67.4) (+€71.4)

1s 2s 3s 4s

VF = 1000*(1+6%)^4 = €1263
-€1000

Annual yield is used to obtain the bi-monthly yield, and then apply compound interest formula for calculations in order to obtain €1263
But this investment has not a compound annual growing rate (CAGR)=12% due to the bi-monthly reinvestment. www.antonioalcocer.com

but as a general rule in finance we assume…



…reinvestment of interests
& use compound interest!


Compound interest’s power it’s one
of the strongest powers on Earth
Albert Einstein

Example 1: Investment in the S&P500 – CAGR: 7.16%

Vf
$337.494

Vo
$30.000

t0=30 t35=65

S&P500 CAGR = 7.16% in the period 01/02/1950-01/02/2010
VF=30.000*(1+7.16%)^35=Vf*(1+i)^t www.antonioalcocer.com

You better would
have invested in
Berkshire Hathway
- Oracle of Omaha’s word -


Example 2: Investment in Berkshire Hat. – CAGR: 20.3%

Vf
$19.338.296

Vo
$30.000

t0=30 t35=65

Warren Buffet’s Berkshire Hathway Investment Fund CAGR = 20.3% in the period 1965-2009 year ending

I rather go for Apples

www.antonioalcocer.com - Get back soon Steve! -

Example 3: Investment in Apple shares – CAGR: 23.06%

Vf
$42.812.697

Vo
$30.000

t0=30 t35=65

Apple shares’ CAGR = 23.06% in the period 27 August 1985 – 27 August 2011

$42.812.697?

*!$%?

www.antonioalcocer.com REDBUBBLE.COM

Yes, $42.8 million

But in 35-years time

& we know about time value of money

& the pair ($,t)

& moving cash-flows in time

& discounting cash-flows

Using Vo=Vf / (1+i)^t

So you are telling me that today I would not be
worthy $42.8 million?


Yes, because of INFLATION!

CPI CAGR=2.7%

CAGR Consumer Price Index (inflation) in the period 1920-2005 = 2.7%


$42.8 millions
in t=35 years
would be
$16.85 millions
today at a 2,7%

Vo=Vf/(1+i)^35=42.8/(1+2.7%)^35=$16.85 millions

So you better assume

your purchasing
power today
would be

$16.85 million
rather than

$42.8 million


Yes, if you would have invested in Apples
HAVE YOU?

Now
We are ready to understand
Investment appraisal methods
Used in Finance to study
The economic feasibility
Of a project


INVESTMENT APPRAISAL METHODS

1. NET PRESENT VALUE (NPV)
2. INTERNAL RATE OF RETURN (IRR)
3. PAYBACK PERIOD

(*) Most important discussed

GOLDEN RULE

“We always work with cash-flows in
investment appraisal”

“Cash-flow is a fact,
net income
just an opinion”
-Pablo Fernández IESE-

The net income amount is affected by accounting methods & assumptions made
(i.e. depreciation & amortization that are not “real” cash inflows or outflows) www.antonioalcocer.com
Cash-flows are real money “entering” or “exiting” the company or project

P&L (*)
Net sales
-Cost of goods sold
GROSS PROFIT
HOW GOOD IS YOUR BUSINESS
-Selling, General & Administration GENERATING “$” DUE THE OWN
-Other operating expenses NATURE OF THE BUSINESS
EBITDA
-Depreciation & Amortization
-Impairment
EBIT
-Interests FINANCING STRUCTURE
INCOME BEFORE TAXES
-Taxes
CORPORATE TAXES FRAMEWORK
NET INCOME

(*) P&L=Profit & Loss account simplified
P&L and Net Income are affected due to the accounting methods used
Net income is an opinion due to it depends on the calculation
of the cost of goods sold, amortization method used & impairment
Net income is not real cash-flow outlays of money www.antonioalcocer.com
Depreciation, amortization & impairment are not real cash-flow outlays

“So
now
I understand
in investment appraisal
we use CASH-FLOWS”

But how many
cash-flows exist?


Free CASH-FLOW of the project (FCFF)=

Available “$” for the funds providers:
_BANKS
_SHAREHOLDERS


Free CASH-FLOW of the project (FCFF)=

+EBIT (1-t) X

+D&A
+/-WORKING CAPITAL CHANGE

-CAPEX

FCFF= Real money generated by the project after accounting adjustments (no real cashflows outlays)
D&A=Depreciation & Amortization (added because no real cash-outlay happened)
CAPEX=Capital Expenditures (Investment in fixed assets)
Working Capital Change= Investment in current assets
t=Corporate taxes in %
(*) Simplified formula of the cashflow, there are other terms: non-cash transactions adjustments, other current assets changes, proceeds from long term assets sales, changes in long term assets; to be considered

Equity Free CASH-FLOW (FCFE)=

Available “$” for the
equity providers:
_SHAREHOLDERS


Equity Free CASH-FLOW (FCFE)=

+FCFF

+PROCEEDS NEW BANKING DEBT
- AMORTIZATION CURRENT DEBT

- INTERESTS OF DEBT * (1-t)

- DIVIDENDS PAID & T.S. REPUR.
FCFE=Equity free cash-flow.
Cash-flow available for shareholders after paying the banking funs providers.
FCFE would be the money available for shareholders
T.S. REPUR= Treasury stock repurchase

…and many others


NOW
WE ARE READY
FOR AN EXAMPLE!


Investment appraisal of a project with these free-cashflows

+
+$300m
+$175m +$200m

t0=0 t1=1 t2=2 t3=3

-$150m

-$300m
-

Diagram of the project free-cashflows (FCFF)
Data in millions of US$ www.antonioalcocer.com
Yearly data

Houston, we have a problem:
Funding needed:
$300 mill. in 1st year
$150 mill. in 2nd year


Don’t worry
Funds providers:
_banks
_shareholders
will gently dispose
them


“OK, have your funds, but [BANK]
at a 6.6% annual interest rate
rat
& maximum amount 65%

Kd= 6.6%


Ke= 20% [SHAREHOLDERS]

“OK, have your funds,
but at a 20% annual
interest rate & 35%
maximum amount”


So,
which amount/ratio should I ask for
Don E. Botín [banks]
& Don C. Slim [shareholders]?


It seems clear that
The cost of financing this project
Would be the
Weighted average
Cost of capital

WACC


OPTIMAL FINANCING STRUCTURE

[BANK]
50% 60% 65%

[SHAREHOLDERS]
50% 40% 35%

WACC Cheapest

12.31% 10.77% 10%

WACC= % equity * expected return on equity + % banking_debt*(1-corporate tax)*cost of banking debt
WACC= 35%*20%+65%*(1-30%)*6.6%=10%

So the $300 mill. + $150 mill.
will be financed
by a 65% banking debt
by a 35% shareholders’ equity
with a WACC=10%


Profitability of the project = 50% in 3-years? www.antonioalcocer.com

+$300m
+$175m +$200m

t0=0 t1=1 t2=2 t3=3

-$150m

-$300m

+300 + 175 + 200 - 300 - 150
%return= = 50%
450

Data in millions of US$
Yearly data

Noooooo!!!!!!!!!

TIME
VALUE
OF MONEY


INVESTMENT APPRAISAL METHODS

1. NET PRESENT VALUE (NPV)
3. PAYBACK PERIOD

(*) Most important discussed www.antonioalcocer.com

1. NET PRESENT VALUE = NPV www.antonioalcocer.com

1) All FCFF are discounted to today & summed
2) Using compound interest formula
3) At a WACC rate

1. NET PRESENT VALUE=$0
[Undertake project]

Cash-flows generated exactly pay the cash-flows expectations requested by
the banking & shareholders (funds providers)

1. NET PRESENT VALUE>$0 www.antonioalcocer.com

[Undertake project]

Cash-flows generated pay all the cash-flows requested by fund providers in
order to meet their profit expectations (NPV=0) & additional cash-flow=NPV
goes as excess profit for shareholders

1. NET PRESENT VALUE<$0
[Do not undertake project]

Cash-flows generated are not enough
to pay the cash-flows demmands by
funds providers according to their
profit expectations (=WACC)

1. Net present value = NPV – WACC=10% www.antonioalcocer.com

+$300m
+$175m +$200m

t0=0 t1=1 t2=2 t3=3

-$150m

-$300m
Undertake project NPV>0

+300 -150 +175 +200
NPV = $131.2 = -300 + + +
(1+10%)^1 (1+10%)^2 (1+10%)^3

Yearly data
+$131.2 million of excess cash-flow that shareholders get above their profit (20%) & cash-flow expectations


=
Project’s CAGR

=
_solve NPV=0

_get IRR


2. Internal Rate of Return (IRR) = 32.24% > WACC =10%
Undertake project

+$300m
+$175m +$200m

t0=0 t1=1 t2=2 t3=3

-$150m

-$300m
Solve non-linear equation

+300 -150 +175 +200
NPV = $0 = -300 + + +
(1+IRR)^1 (1+IRR)^2 (1+IRR)^3

Yearly data www.antonioalcocer.com
IRR is obtained solving the equation

1&2. Net present value summary

IRR>WACC NPV>0 Fund providers more than happy
NPV excess for shareholders

IRR=WACC NPV=0 Fund providers exactly happy

Fund providers unhappy
IRR<WACC NPV<0


3. PAYBACK PERIOD Years to recover
investment…
…you better pay

Expected number of years in order
cumulative (+) cash-flows>=
cumulative (-) cash-flows

3. Payback period= 1.85 years www.antonioalcocer.com

+$300m
+$175m +$200m

t0=0 t1=1 t2=2 t3=3

-$150m

-$300m
Cumulative
-300 -300+300-150 -300+300-150+175 -300+300-150+175+200

-300 -150 +25 +225

Payback period does not take into account time value of money, so it should not be used in a stand alone basis but as complementary info to NPV and IRR
Yearly data
Payback period: Positive cumulative cashflows are > negative cumulative cashflows in year 1-2
175/12=14.58
-150/14.58=10.29 months = 10.29/12= 0.85 years


RE

Time value of money
Compound interest
Moving cash-flows in time
We have learnt: Investment appraisal methods
Project free cashflows
WACC
NPV+IRR+Payback

[now we can strike back the Empire!]
[and go for company valuations…]


WHAT IS THE
VALUE OF
A COMPANY?


THIS ONE MUST BE INFINITE


THIS ONE…


∞ = Infinite
^∞
∞


= Enteprise value [EV]

HEY!!!!
WHAT IS THE
VALUE OF A
COMPANY?


“But

in company’s valuation

we need

to calculate

the “intrinsic” or “fair value”

of the company’s equity

“updated”

based on its

future performance=

cashflows”

But before we start remember the 2nd GOLDEN RULE:

PRICE IS WHAT YOU PAY

[demmand falls in love with supply]

VALUE IS WHAT YOU GET www.antonioalcocer.com

[VALUATION METHODS USED]

1. fast 2. right
MULTIPLES DISCOUNTING CASH-FLOWS
PER Free-cashflows (FCFF)
Sales Equity cashflows (FCFE)
EBITDA Dividends
Others Other cash-flows

gross fine tune
past future
(*) I will not cover other valuation methods based: book value, adjusted book value, etc.
PER = Price Earning Ratio = Share Price in stock market / earnings per share

MULTIPLES VALUATION DISCOUNTING CASH-FLOWS

1. It is wrong
2. Does not consider time value of money
3. Based in “static” data: P&L
4. Based in past performance
5. Does not consider future cash-flows
6. Assumes future = present
7. But it is fast
8. And it is widely used by investors
9. Get a “rough” company value estimate 1. It is the right one method
2. Does consider time value of money
3. It is based in “dinamic” data:
4. Does consider future cash-flows
5. But it is a lot of work
6. Used to fine-tune the multiples valuation

5 minutes time 2 weeks time

I was captured by the dark side, and although I know it is WRONG…

…explain me the MULTIPLES VALUATION method

[MULTIPLES VALUATION] www.antonioalcocer.com

EV=ENTERPRISE VALUE [$5-9 millions]
Industry comparable multiple x Company’s metric

1. Choose a metric: EBITDA

2. Company’s EBITDA = $1 million

3. Company in the food & beverage industry (F&B)

4. Comparable purchasing transactions in F&B industry: 5-9 times

[DISCOUNTING CASH-FLOWS VALUATION METHOD]

WHAT IS THE VALUE OF A COMPANY?


HOW much would you pay for a cow?

Depends on the future milk
that it can provide
[& not the milk that provided in the past]


What is the value of a company?

Depends on the future cash-flows it can generate
[you decide using either FCFF or FCFE_it’s up to you]


& the annual growing rate “g”(%)
of these future cash-flows

[Should not be greater than a economy’s GDP in the long run <3%]
[In the short term cash-flows growth can exceed long term trend]

Assuming the company will last forever [=infinite]


& the company’s financing structure: WACC

%E equity [41%]
Ke(%) profit expectations: 9.7%

%L banking debt [59%]
Kd(%) cost of debt 6.3%

How do I calculate Ke=shareholders’ profit expectations?

4.54% 6.18%

Ke=RF+B*(RM-RF)
9.7% 0.83

RF: Money invested at no risk (RF=10-years german bonds yield considered a risk free investment)
B*(RM-RF): Upside return/premium for investing in a company with specific risk
RM=Return of the stock market benchmarked = CAGR Ibex 35 in the 1995-2008 period = 10.72%
B=Company beta = sistematic risk of the company versus the market = Let’s assume 0,83. Beta calculation is biased and depends on the time period analysed

WACC & g calculations www.antonioalcocer.com

59% 28.2% 6.3% 41% 9.7%
WACC= %L*(1-t)*Kd + %E*Ke

WACC= 6,62%

g=2,5% (*)

(*) GDP for the European Union in the 1996-2008 period according to Central European Bank (2,2%). We will asume a g=2.5%
T=Effective corporate tax rate paid by the company. It is less than 30% due to fiscal benefits awarded from previous years
%L=proportion of banking debt %E=Proportion of equity

[DISCOUNTED CASH-FLOW METHOD SUMMARY]

FCFF
1. [Determine which cash-flows you want to use] FCFE

2. [Determine company’s 5-years future cash-flows (*)]

3. [From year “n+5”, future cash-flows grows at “g” rate (**)] <3%

@WACC if FCFF
4. [Calculate the NPV today of the infinite cash-flows] @Ke if FCFE

[Enteprise value= NPV of all infinite future cashflows @ WACC]

(*) The number of years range from 5 to 10, in terms of estimating the future P&L, balance sheet and company cash-flows.
More adecuate calculation should range 10 years.
(**) Future cash-flows from year n+5 growth as an infinite geometric progression with a “g” growing rate. This geometric progression with infinite terms is called RESIDUAL VALUE

EXAMPLE: Company free cash-flows [FCFF]

5-YEARS CASH-FLOWS ESTIMATION CASH-FLOWS GEOMETRIC PROGRESSION
X (1+g)^(n-3)

X (1+g)
X (1+g)
X (1+g)

195
190
185

181
g=2,5%
149
123
102
87

2011 2012E 2013E 2014E 2015E 2016E 2017E 2018E 2019E ………. INFINITE
TODAY

RESIDUAL VALUE

Data in millions of $
Please note that we assume the company will last forever, so from year 2017 onwards we have infinite cash-flows
The 5-years cashflows estimation must be done according to the mid-range business plan & investment/capex plan; and using the P&L & balance sheet & cashflow statements
After the 5th year, in 2017, we calculate cash-flows as a geometric progression increasing in a “g%”=2,5% every year the latest cash-flow. CFn=CFn-1*(1+g)
It can be demonstrated that the geometric progression with infinite cash-flows starting at 2017, equal a single cash-flow located in 2016 year and value=Cf2017/(WACC-g)
The infinite cash-flows from 2017 onwards are called RESIDUAL VALUE

EXAMPLE: Free cash-flows [FCFF] are discounted @ WACC

RESIDUAL VALUE

X (1+g)^(n-3)

X (1+g)
X (1+g)
X (1+g)

195
190
185

181
G=2,5%
149
123
102
87

2011 2012E 2013E 2014E 2015E 2016E 2017E 2018E 2019E ………. INFINITE
TODAY
5-YEARS CASH-FLOWS ESTIMATION CASH-FLOWS GEOMETRIC PROGRESSION

181*(1+2.5%)

87 102 123 149 181 6.6%-2.5%
NPV=EV=$3780= + + + + +
(1+6.6%)^1 (1+6.6%)^2 (1+6.6%)^3 (1+6.6%)^4 (1+6.6%)^5 (1+6.6%)^5
RESIDUAL VALUE


Have I done this?

COMPANY’S EV
$3780 millions


COMPANY’S ENTERPRISE VALUE=

What is the meaning?

“DYNAMIC”
BALANCE SHEET
“UPDATED”
DUE TO IMPACT OF
“STATIC” FUTURE CASH-FLOWS
BALANCE SHEET
TODAY - 2011

EO
E 41%

EV
$3780
mill. ??
L 59%

E: Equity www.antonioalcocer.com
L: Liability (net financial debt) = short term debt + long term debt – cash($)
EO = Company’s Estimated “fair value” of equity

[EO= fair value of company’s equities = 3780-400+150-50-200=$3280 mill.]

BALANCE SHEET
“UPDATED”

EO

EV
$3780 - Net Financial Debt -$400 mill.
mill. ??
+Shareholders’ right in other companies +$150 mill.

- Minority interests -$50 mill.
- Long-term pension liability -$200 mill.

EO=Intrinsic value or fair value of the company’s equity www.antonioalcocer.com
Shareholders’ rights in other companies are real cash inflows into the company due to ownership of other companies as minority stake
Net financial debt is the net financial liability position with banks. It is a cash-outflow assuming all the debt is paid.
Minority interests: It is a portion of the value of a company that it is own by “external” minority shareholders and it does not belongs to the company. Cash out-flow
Long term pension liability & other liabilities correspond to future cash-outflows to be paid by the company.

BUY?
Fair value>market value

SELL?
Fair value<market value


PRICE IS WHAT YOU PAY
MARKET CAP = $6000 mill.
# shares = 10 mill.

[demmand falls in love with supply]
www.antonioalcocer.com Market share price paid = $600

EO=$3280 mill.
# shares = 10 mill.

Equity fair/intrinsic value = $328
VALUE IS WHAT YOU GET

[CONCLUSION 1] www.antonioalcocer.com

I shouldn’t have bought new shares!!!
or
I better sell the ones I already own@$150

$328 $600
Fair value<market value

[CONCLUSION 2]

The fair value EO does not change
unless new inputs/info impact
the company’s future cashflows
overall picture & therefore EV


[CONCLUSION 3]

[95% of time_estimating 5-10 years cash-flows]

[5% estimating WACC & “g” rate (=residual value)]

…but
[Discounting cash-flows model is highly sensible to:]

WACC & “g”


SENSIBILITY ANALYSIS

Fair value per share in $ [WACC]
5% 6,62% 8%
2% 486,7 291,9 209,2

[g] 2,5% 586 328,7 229,4

3% 735 375,7 253,5


[CONCLUSION 4]

In company valuation, the most important issues to understand are:
1. Assumptions_How future cash-flows are calculated
2. Understand the risks associated to them in order they do not occur
3. Assume than in valuation we always obtain a price range
4. Company valuations can be highly manipulated by small changes in WACC & g
5. Use multiples valuation for a “rough” number & 5 minutes valuation
6. Use discounted cashflow for a “fine tuned” number & right calculation method


Thank you very much for you time!
Any comment, suggestion is more than welcome:
@antonioalcocer

Investment appraisal & company valuation for beginners

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