Company Valuation – DCF ValuationProf. Ernst Maug, Ph.D.

Overview

Market value balance sheets The dividend discount model Simple discounting models:

Perpetuity models Two-stage models Three-stage models

Why DCF? DCF-WACC versus Flow to equity (FTE)

2

The objective of DCF valuationConstructing a market value balance sheet

Construct a balance sheet: Use same principles as in financial accounting Assess all assets and liabilities at market values

3

Value of existing assets

Non-operating cash

Other non-operating assets

NPV of future investments

Equity

Pension obligations

Debt

DCF value of the company

DCF values operating assets of the company as present value of future cash flows from operations. Do not include other cash flows, e.g. interest earned on financial investments.

DCF does not separate assets in place from NPVs from future investments.

Value company as:DCF-value of operating assets

+ market value of non-operating (financial) assets+ cash

4

DCF value of equity

Value equity as:Value of the company

- market value of debt- market value of pension obligations- market value of other liabilities

This equals:DCF value of operating assets

+ market value of non-operating assets (e.g., financial assets) - net debt (= debt – cash)- market value of pension obligations market value of other liabilities

Note: Taxes are not included implicit in DCF-value of operating assets (accounts for taxes). Otherwise included as separate asset (tax shield) and liabilities

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Dividend discount model

Discount future expected payments with the appropriate discount rate:

6

( ) ( ) ( ) ( )...( ) ( ) ( ) ( )t

tE E E Et

E D E D E D E DEquityr r r r

¥

== + + + =

+ + + +å1 2 30 2 3

11 1 1 1

Equity0 value of equity at time 0Dt random dividend at time trE costs of equity

(return on an investment with similar risk)P0 share price at time 0N number of outstanding shares

Price of a single share: P0 = Equity0 / N.

Dividend discount model (2)

Market value of the firm: V0= Equity0 + Debt0

Value of debt can be calculated in the same way:

7

( ( ) )( )

t tt

Dt

E interest principal repaymentDebtr

¥

=

+=

+å01 1

Market value and book value of debt usually do not differ a lot: Approximate Debt0 by the book value of debt

Constant growth formula

Notes on the application of this formula: g is the long-run growth rate.

It cannot exceed the growth rate of the economy. This calculation can be done in real or nominal terms.

r and g must both be either nominal or real. d1 must be expressed in constant Euros (real) or in current Euros

(nominal).

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( )

( )

( )

( )

( ) ( )( ) ...

( )E E E

E E

E D g E D gE DEquityr r r

E D g Dr g r g

+ += + +

+ + +

+= =

- -

21 11

0 2 3

10

1 11 1 1

1

The formula for a T-year horizon can be written as:

9

( ) ( )0 1 1 1

t T t Tt Tt

E E

D PPr r

=

== +

+ +å

1TT

E

DPr g

+=-

( ) ( )0 1

11 1

t T t Tt Tt EE E

D g DPr gr r

=

=

+= +

-+ +å

Apply the growth model to the price in T:

Then the current value of the share is:

Modify the growth model

Valuing a company: A primerA two-stage model

Sometimes equity analysts have knowledge about the immediate, but not the distant future: Dividend forecasts for immediate future (2-5 years) Assume constant growth for distant future (>5 years) How do you apply the model now?

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**

**

*

year-by-yearforecasts

constant exponential growth

T

Dividends

Time

Discounting free cash flows

Discount free cash flows that are generated by the firm rather than payouts as in the dividend discount model.

Free cash flows differ from dividends: Firms retain and reinvest some of their cash flows.

Generates higher cash flows in the future

Three versions of discounted (free) cash flows: DCF-WACC: unlevered (free) cash flows to the firm APV: levered (free) cash flows to the firm Flow To Equity (FTE): levered (free) cash flows to shareholders

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Free cash flows differ from earnings: Do not include:

Depreciation or amortization of assets (add those back) Realized capital gains or losses

Do subtract investments that are capitalized

Otherwise use same analytic approach as DDM: Discount FCF to all security holders to obtain value of the firm as a whole

V0 (= debt + equity)

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( ) ( )0 1

11 1

t T t Tt Tt

FCF g FCFVr gr r

=

=

+= +

-+ +å

Valuing a companyA primer

Recall: The free cash flows to the unlevered firm are all cash flows the firm could pay out if it had no debt. Combines cash flows to all security holders Does not include tax shields We refer to these shortly as free cash flows (unlevered) or FCFU:

Consider a company with cash flows from operations of €1 million for the most recent year. The company’s cash flows are expected to grow at a rate of 20% for the next 5

years and at a constant rate of 5% thereafter. To generate this increase in cash flows, the company is required to reinvest

50% of its cash flows for the first 5 years and 40% of its cash flows thereafter. Given the risk of the business, the required rate of return is 15%.

What is the value of the business?

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Period 1 2 3 4 5EBITDA 1.20€ 1.44€ 1.73€ 2.07€ 2.49€ Investment 0.60€ 0.72€ 0.86€ 1.04€ 1.24€ Cash Flow 0.60€ 0.72€ 0.86€ 1.04€ 1.24€ Present value = PV(CF(1) + ... + CF(5))

= € 0.52 + € 0.54 + € 0.57 + € 0.59 + € 0.62= € 2.85

We use free cash flows (FCF) and company value (V)

Same as dividends (D) and value of equity (P) if company has no debt

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For calculations see DCF Valuation.xls tab “Simple valuation model”.

A very simply DCF model

Value of dividends over the first 5 years is € 2.85. Value of business at the end of the 5th year:

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( )65

€2.49 1 0.4 1.05 €15.680.15 0.05E

FCFVr g

-= = =

- -

0 5€15.68€2.85 €2.85 €7.791.15

€10.64

V = + = +

=

Value of the Business:

PV(years 1-5) = 27%, PV(years 6-) = 73% Most of the value comes from the distant future:

Estimation problem!

A very simply DCF model (2)

Reconsider the example from lecture 1 (value drivers)

Assumptions and results: FCF2009: € 4.77 Nominal growth rate: 4.55% Cost of capital (assumed): 7.00%

See spreadsheets on website: Value Drivers - PerpetuityModel.xls

20092008

€4.77 €194.670.07 0.0455U

FCFVr G

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A perpetuity model

Sometimes it is practical to extend the model to three stages:1. Detailed forecasts of cash flows, earnings, dividends for periods 1…T1

2. Transition period where growth and margins from T1 to terminal values at T2

3. Perpetuity model for periods after T2

Example: Growth from 2009 – 2013: 9% Growth from 2016 onwards: 3% Margin from 2009 – 2013: 20% Margin from 2016 onwards: 16% Interpolate values for 2014 and 2015:

Growth is 7% (2014) and 5% (2015). Margin is 18.67% (2014) and 17.33% (2015).

Mechanics same as before, see spreadsheet „DCF Valuation - ThreeStageModel.xls“

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Three-stage models

Why DCF?

We have used the general formula:

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0 1 1

t ttt

FCFVr

Why is this formula right? Investors compare:

Price of the company (buy liabilities combined) V0 Value of expected future cash flows CF1, CF2,...,CFT,...

Consider strategy of a typical private equity investor: Buy company for some price X today, sell it after T years Compare this with an alternative investment that generates a return r

1 1 1

t T t Tt Tt

FCF Vr r

Buy company, sell after T years: What is the portfolio worth in year T? Invest cash flow in year 1 for T-1 years at rate r:

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11 1 TFCF r

Invest cash flow in year 2 for T-2 years at rate r:

22 1 TFCF r

Continue until year T, then receive cash flow in year T, sell company:

... 1 ...T tt T TFCF r FCF V

Account balance after T years:

1

1T T tT tt

V FCF r

Why DCF?Strategy 1: Buy company, sell after T years

Invest price X0 in investment with expected return r What is this alternative portfolio worth in year T?

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0 1 TX r In a functioning asset market, both values have to be the same:

As funds are always invested in assets with the same risk they should have the same return.

Set both equal:

0 1

1 1TT T tT tt

X r V FCF r

Then the result for X0 is:

0 1

1 1TT tT tt

X V r FCF r

...which is just the DCF-formula with X0 = V0!

Why DCF?Strategy 2: Invest in securities with the same risk

A variant of DCF: Flow to equity

Recall: Flows to equity (FTE) are free cash flows that accrue to equity holders.CFE = Free cash flow to the levered firm

+ Payments by debtholders to the firm (issues)- Payments from the firm to debtholders (interest

+ principal) These are discounted with the costs of equity, re:

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01

( )(1 )

tt

t E

E CFEEquityr

¥

==

+å

Get firm value as V0 = Equity0 + Debt0

Looks much easier than DCF-WACC but there are hidden problems...

FTE versus DCF-WACC (1)An example

Assume that EBIT = 100 (million €) depreciation equals capital expenditure no working capital investment no capital gains or losses FCFU = 100 (million €) debt is 266.7 (million €) rE = 20% and rD = 7.5% all these numbers are constant for all future years

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For calculations see DCF Valuation.xls, tab “Flow to equity”.

FTE versus DCF-WACC (2)An example

Use DCF with pre-tax weighted average cost of capital : Start the calculation by assuming that leverage is 40% Unlevered cash flow is 100. r = 40% 7.5% + 60% 20% = 15%

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Equity0 = 60% 666.7 = 400 Debt0 = 40% 666.7 = 266.7

So leverage of 40% is correct.

0100 666.70.15

UFCFVr

= = =

FTE versus DCF-WACC (3)An example

Use Flow To Equity (FTE): Levered cash-flow is 100 – 7.5% 266.7 = 80

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080 4000.2E

CFEEquityr

= = =

V0 = Equity0 + Debt0 = 400 + 266.7 = 666.7

Both approaches arrive at the same result.

FTE versus DCF-WACC (4)An example

New assumption: EBIT grows with 2% per year. Leverage remains constant.

Use DCF with pre-tax weighted average cost of capital: Assume that leverage is 36% rOA = 36% 7.5% + 64% 20% = 15.5%.

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Debt0 = 36% 740.74 = 266.7 So leverage of 36% is correct.

0100 740.70.155 0.02

UFCFVr g

= = =- -

FTE versus DCF-WACC (5)An example

Use FTE: Levered cash-flow is 100 – 7.5% 266.7 = 80

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080 444.40.2 0.02E

CFEEquityr g

= = =- -

V0 = Equity0 + Debt0 = 444.4 + 266.7 = 711.1

Why do the two methods yield different results under identical assumptions? Flow to equity used incorrectly here! Does not take into account that equityholders receive cash from debtholders

as value grows with constant leverage.

FTE versus DCF-WACC (6)An example

Use FTE correctly: Levered cash flow: 100 – 7.5% 266.7 + 2% 266.7 = 85.33

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085.33 4740.2 0.02E

CFEEquityr g

= = =- -

V0 = Equity0 + Debt0 = 474 + 266.7 = 740.7

Consistent forecasts are easier for unlevered cash flows.

DCF-WACC is easier to apply than FTE.

We have two models for the value of equity: The dividend discount model:

01

( )(1 )

tt

t E

E DEquityr

¥

==

+å

01

( )(1 )

tt

t E

E CFEEquityr

¥

==

+å

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The (cash) flow to equity model:

DDM and payout policy

1

( ) 0(1 )

t tt

t E

E D CFEr

¥

=

-=

+å

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They are consistent only if:

This does not imply that Dt=CFEt. Equivalence is in present value terms.

If the firm pays out the present value of future cash flows, then payout policy is irrelevant. Example 1: put retained cash flows into financial securities and other zero-

NPV investments: Value of firm increases by NPV of financial investments = 0. Cash flow valuation and dividend valuation are the same.

Example 2: borrow against future cash flows to pay dividends today: Borrowing is also a zero-NPV transaction.

Modigliani-Miller dividend irrelevance

The value of a company‘s equity is the present discounted value of all future dividends even if shareholders have short investment horizons.

The value of an (unlevered) company can be expressed as the present discounted value of all future free cash flows.

Flow to equity is equivalent if applied correctly.

Open Questions: What do you do if the tax system discriminates between dividends and

interest payments? How do you account for leverage?

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Conclusion