Valuation Formulas

7/31/2019 Valuation Formulas

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Important Formulas Valuation and Value Creation

1 Company value

The value of the company is the EXPECTED future cash flows

gWACC

NOPAT

WACC

CEcompanyV

tt

t

1

1

0

)1(

)()( (1a)

In most cases g is set to zero for the entire future period forecast period + residual period), unless

very good reasons can be made explicitly to do not so. In the NOPAT formula depreciation is

assumed to be a proxy for the replacement investmentcash flow. This is approximately a good

assumption for low growth/non-growth mature companies. For these companies only replacement

investments are needed to maintain the current free cash flow level. In this case no investments

are made for growth.

If ADDITIONAL investments are made for growth this formula becomes

gWACC

ROICgNOPAT

gWACC

FCF

WACC

CEcompanyV

tt

t

)/1(

)1(

)()( 11

1

0(1b)

In this case the free cash flow equals NOPAT(1-IR), IR is the reinvestment rate ONLY FOR

GROWTH investments (replacement investments are included in NOPAT ). The growth rate g

equals ROIC x IR. This formula is mostly used only for the forecast period. In the residual period

formula 1a mostly applies.

NOPAT calculation

Turnover- costs

= EBITDA

- depreciation

= EBIT

- taxation (as if the company is financed with 100% equity, tax advantage is in the WACC)

= NOPAT

2a Equity value (direct method)

The dividend Gordon formula for the value of equity equals

1

00 )1(

)1(

)(

t DE

D

t

E

t

gk

gD

k

DEE (2)

ONLY if the (expected) return on reinvestment equals the expectations of investors the dividend

policy is irrelevant, formula 2 can be replaced by the following formula 3


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)0()1(

)(

1

00

E

t E

t

E

t gifk

E

k

EEE (3)

2b Equity value (indirect method)

E = V(company) market value debt D (4)

Market value of debt is equal to

D

B

tt

D

t

k

Bk

k

repaymenterestD

1 )1(

int(5)

D is the market value of debt, B is face value of debt, kD is the market rate and kB is the coupon

rate by contract. If kD is close to kB the market value of debt D is close to the face (book) value B.

3 WACC

ED

DTk

ED

EkWACC DEV

)1( (6)

The tax advantage of debt financing shows up in the WACC formula. T is the corporate tax rate.

4a Costs of equity

Costs of equity from a MM perspective (with corporate tax) equals to

)1()( TkE

Dk DE (7)

With this formula the WACC equals

)1( TED

DWACC

(8)

In practice the formula for the costs of equity equals to

mSizepremiuemiumdistressprTkE

Dk DE )1()( (9)


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4b Calculation of kE for private companies with CAPM formula

Step 1: Calculate the values ofL

E for a number of peer listed companies.

Step 2: Calculate for each peer listed companyU

E ( ) with the Hamada formula (which looks

alike formula 7). UE is unknown, LE , D, E, T and LD are known.

)1())(()()( TpeerE

Dpeerpeer

U

E

U

E

L

E (10)

Calculate the average ofU

E ( ) for all peers. The D is for simplicity reasons - equal to 0.

Step 3: CalculateL

E and kE for the private company by using the average ofU

E ( ) for all peers.

)1())()(()(

)(

TcompanyprivatepeersE

Dpeers

companyprivate

D

U

E

U

E

L

E

(11)

))(()( fmL

EfE rrcompanyprivatercompanyprivatek (12)

5 Costs of debt

Costs of debt from a banking perspective

%15

cos

cosexpexp

cos

capitaleeconomicpremiumrisk

tsloperationapremiumriskLGDPDspread

tsloperationalossesectedUNlossesectedspread

spreadtsfundingkD

(13)


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I Valuation of a company with reinvestment

Free cash flows (to investors) are in year 1 equal to NOPAT1 I1. I1 is the reinvestment for

growth. If the return on the reinvestment equals r1 the free cash flow in year 2 equals to

NOPAT2 I2 + r1 I1. Reinvestment of I generates each year a return of rI.

The time series of free cash flows will look as follows.

year 1: NOPAT1 -I1

year 2: NOPAT1 + r1 I1 -I2year 3: NOPAT1 + r1 I1 + r2 I2 -I3

etc.

The net present value of these cash flows equals to the value of the company

1 11 )1()1()1()(

t t

tt

t

t

tt

t

WACC

Ir

WACC

I

WACC

NOPATcompanyV

(14)

with

t

tt

t

tt

WACCWACC

Ir

WACC

Ir

)1(

1

)1(1

(15)

Formula 14 can be rewritten as follows

11

)1()1()1(

)(t

t

t

t

t t

t

WACC

r

WACC

I

WACC

NOPATcompanyV (16)

Which can be further reshaped to

1

)()1(

)(t

tt

tt WACCrWACCWACC

I

WACC

NOPATcompanyV (17)

The first component equals to formula 1a with no growth and the second component is only

positive when rt is larger than WACC, in other words when the reinvestment rate is larger than

the expected return by investors.


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II Equity valuation with EVA

The value of equity equals to (formula 4)

DcompanyVE )(

For a non-growth company the value of equity is (by using formula 1a)

DWACC

NOPATD

WACC

CEE

tt

t

tt

t

11

0

)1()1(

)((19)

Adding invested capital and subtracting IC gives

ICICDWACC

NOPATE

tt

t

1 )1((20)

with

1 )1(

11

tt

WACCWACC

formula 20 can be rewritten as follows

DICWACC

ICWACCNOPATE

tt

t

1 )1((21)

which is

capitalequityinvestednetWACC

EVAE

tt

t

1 )1((22)

So the value of equity (in net present value) increases after a net investment of equity capital of

IC- D only when EVA is larger than 0, so when earnings (NOPAT) are larger than expected

(WACCxIC).


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III Splitting value creation in a realization component and a future component

The value of a company on t = 0 equals to the sum () of the present value of all expected futurefree cash flows E0(Ct)

1

0

0)1(

)(

tt

t

k

CEV (23)

Formula 23 is equal to

2

0100

)1(

)(

)1(

)(

tt

t

k

CE

k

CEV (24)

Investors who have invested VO at t = 0 expect a return of k, so their expectations about the value

of the company at t = 1 equals

)()()1(

)()(

)1()(

1010

21

0

10

010

TECEk

CECE

VkVE

tt

t

(25)

T1 is the present value of all expected free cash flows aftert = 1

On t = 1 the value of a company equals

)()1(

)(111

21

011 TEC

k

CECV

tt

t

(26)

It is the sum of the realized cash flow C1 in past period (0,1) and the present value of all expected

free cash flows aftert = 1

Value creation is the difference in value between the realized value V1 and the EXPECTED value

of V1 at t = 0, E0(V1)

componentfuturecomponentnrealisatio

TETECEC

VEVV

)}()({)}({

)(

1011101

101

(27)

Important note: the discount rate is expected to be constant.

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Valuation Formulas