company valuation ii: dcf - adrien matray

COMPANY VALUATION II: DCF

Roadmap

1. The method: BDM [Chapter: Valuing Stocks]

2. TV issues

3. Variations on TV

The Method

Step 1. Forecasting FCF

a. Set an explicit forecast period

b. Build financial statement projections for the forecast period

c. Estimate FCF for each year in the forecast periodFCF = (1— t)EBIT + Dep. – CAPX – DNWC

– Color code:– Assumptions are in red/boldface– Calculations are in black

– Assumptions are derived from:– Carlsberg’s business plan (e.g. Sales for next 3 years)– Items’ relationship to sales (e.g. EBIT margin = EBIT/Sales)

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65 536 67 964 70 968 73 856 76 604 79 185 81 577 83 755 85 698 87 386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9 585 10 203 11 005 11 453 11 879 12 279 12 650 12 988 13 289 13 551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1 007 27 33 35 36 37 38 39 40 41

EBIT(1-t) 7 623 8 071 8 639 8 991 9 325 9 639 9 930 10 195 10 432 10 638 + Depreciation 3 932 4 078 4 258 4 505 4 673 4 909 5 058 5 193 5 313 5 418 - CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 - DNWC 1 007 27 33 35 36 37 38 39 40 41 = FCF 4 781 6 344 6 832 7 257 7 604 8 019 8 342 8 649 8 935 9 198

Step 2. Terminal Value (TV)

– Def: value of cash flows beyond the forecast period

– “Growing Perpetuity”

gWACC

FCFg)(1TV 10

-×+

=

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 73,856 76,604 79,185 81,577 83,755 85,698 87,386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 11,453 11,879 12,279 12,650 12,988 13,289 13,551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7,623 8,071 8,639 8,991 9,325 9,639 9,930 10,195 10,432 10,638 + Depreciation 3,932 4,078 4,258 4,505 4,673 4,909 5,058 5,193 5,313 5,418 - CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 - DNWC 1,007 27 33 35 36 37 38 39 40 41 = FCF 4,781 6,344 6,832 7,257 7,604 8,019 8,342 8,649 8,935 9,198 Terminal Value 158,242

158,2421.5%7.4%

9,1981.5%)(1gWACC

FCFg)(1TV 10 =

-×+

=-

×+=

TV estimated using growing perpetuity

Step 3. Enterprise Value (EV)

– Compute the discount factor for each year

– Discount FCFs to the present

– Discount TV to the present: TV is a value in year 10 è Discount 10x

è Enterprise Value PV(TV) PV(FCF) EV +=

WACC)(1

1DF .... WACC)(1

1DF WACC)(11DF 1010221 +

=+

=+

=

DF FCF... DF FCF DF FCF PV(FCF) 10102211 ´++´+´=

DF TVPV(TV) 10´=

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 73,856 76,604 79,185 81,577 83,755 85,698 87,386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 11,453 11,879 12,279 12,650 12,988 13,289 13,551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7,623 8,071 8,639 8,991 9,325 9,639 9,930 10,195 10,432 10,638 + Depreciation 3,932 4,078 4,258 4,505 4,673 4,909 5,058 5,193 5,313 5,418 - CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 - DNWC 1,007 27 33 35 36 37 38 39 40 41 = FCF 4,781 6,344 6,832 7,257 7,604 8,019 8,342 8,649 8,935 9,198 Terminal Value 158,242 Dicount factor 1.00 0.93 0.87 0.81 0.75 0.70 0.65 0.61 0.56 0.53 0.49PV of FCF 4,452 5,500 5,515 5,454 5,321 5,225 5,061 4,886 4,700 4,505 PV of FCFs 50,618 PV of TV 77,496 Enterprise value 128,114

Step 4. Value per share

– Enterprise Value = Value of Operating Assets

– To get (Total) Firm Value à need non-operating asset

– To get Equity Value à take care of debt

– Value Per Share = Equity Value / Number of Shares

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 73,856 76,604 79,185 81,577 83,755 85,698 87,386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 11,453 11,879 12,279 12,650 12,988 13,289 13,551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7,623 8,071 8,639 8,991 9,325 9,639 9,930 10,195 10,432 10,638 + Depreciation 3,932 4,078 4,258 4,505 4,673 4,909 5,058 5,193 5,313 5,418 - CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 - DNWC 1,007 27 33 35 36 37 38 39 40 41 = FCF 4,781 6,344 6,832 7,257 7,604 8,019 8,342 8,649 8,935 9,198 Terminal Value 158,242 Dicount factor 1.00 0.93 0.87 0.81 0.75 0.70 0.65 0.61 0.56 0.53 0.49PV of FCF 4,452 5,500 5,515 5,454 5,321 5,225 5,061 4,886 4,700 4,505 PV of FCFs 50,618 PV of TV 77,496 Enterprise value 128,114 Cash and equivalents 3,714 Debt 54,459 Equity value 77,369 Shares (millions) 153 Value per share (DKK) 506

Step 5. Sensitivity analysis

– Always:– With respect to discount rate– With respect to perpetuity growth rate

– Sometimes:– Alternative assumptions for projections (e.g. sales growth, margins, etc.)

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65 536 67 964 70 968 73 856 76 604 79 185 81 577 83 755 85 698 87 386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9 585 10 203 11 005 11 453 11 879 12 279 12 650 12 988 13 289 13 551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1 007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7 623 8 071 8 639 8 991 9 325 9 639 9 930 10 195 10 432 10 638 + Depreciation 3 932 4 078 4 258 4 505 4 673 4 909 5 058 5 193 5 313 5 418 - CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 - DNWC 1 007 27 33 35 36 37 38 39 40 41 = FCF 4 781 6 344 6 832 7 257 7 604 8 019 8 342 8 649 8 935 9 198 Terminal Value 158 242 Dicount factor 1.00 0.93 0.87 0.81 0.75 0.70 0.65 0.61 0.56 0.53 0.49PV of FCF 4 452 5 500 5 515 5 454 5 321 5 225 5 061 4 886 4 700 4 505 PV of cashflows 50 618 PV of TV 77 496 Enterprise value 128 114 505.68 0.5% 1.0% 1.5% 2.0% 2.5%Cash and equivalents 3 714 6.5% 551 603 665 741 835Debt 54 459 7.0% 478 520 570 629 702Equity value 77 369 7.4% 428 464 506 555 615Shares (millions) 153 8.0% 363 391 424 463 508Value per share (DKK) 506 8.5% 316 340 367 399 436

growth rate g

WAC

C

Value per Share (DKK)

How It’s Done and Used In Practice

Standard TV Issues

TV issues

– How do we determine the perpetual growth rate?

– Can the perpetual growth rate be negative?

– How big can the TV be?

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 73,856 76,604 79,185 81,577 83,755 85,698 87,386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 11,453 11,879 12,279 12,650 12,988 13,289 13,551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7,623 8,071 8,639 8,991 9,325 9,639 9,930 10,195 10,432 10,638 + Depreciation 3,932 4,078 4,258 4,505 4,673 4,909 5,058 5,193 5,313 5,418 - CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 - DNWC 1,007 27 33 35 36 37 38 39 40 41 = FCF 4,781 6,344 6,832 7,257 7,604 8,019 8,342 8,649 8,935 9,198 Terminal Value 158,242 Dicount factor 1.00 0.93 0.87 0.81 0.75 0.70 0.65 0.61 0.56 0.53 0.49PV of FCF 4,452 5,500 5,515 5,454 5,321 5,225 5,061 4,886 4,700 4,505 PV of cashflows 50,618 PV of TV 77,496 Enterprise value 128,114 505.68 0.5% 1.0% 1.5% 2.0% 2.5%Cash and equivalents 3,714 6.5% 551 603 665 741 835Debt 54,459 7.0% 478 520 570 629 702Equity value 77,369 7.4% 428 464 506 555 615Shares (millions) 153 8.0% 363 391 424 463 508Value per share (DKK) 506 8.5% 316 340 367 399 436

growth rate g

WAC

C

Value per Share (DKK)

• TV = 60% of EV• Growth rate 1% higher

è value 20% higher

FYI: Variations on TV

Terminal value estimates

– In practice, terminal value:– always using multiples– often also using growing perpetuity

è but which multiple to choose?

– Growing perpetuity:– Several formulas

– Grow last period’s FCF– Value driver formula– Flat growth

Method 0: Terminal value in liquidation

– A conservative estimate of terminal value assumes the company is liquidated at the end of the forecast period

– Similar to a project’s terminal value

NWCPPEtt)(1SVTV TTT +´+-=

Method 1: Exit multiple

– Take the average EV/EBITDA of a peer group

– Multiply it by EBITDA in the last year of forecast

EBITDA )(EV/EBITDATV Tpeers ´=

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65,536 67,964 70,968 73,856 76,604 79,185 81,577 83,755 85,698 87,386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9,585 10,203 11,005 11,453 11,879 12,279 12,650 12,988 13,289 13,551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1,007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7,623 8,071 8,639 8,991 9,325 9,639 9,930 10,195 10,432 10,638 + Depreciation 3,932 4,078 4,258 4,505 4,673 4,909 5,058 5,193 5,313 5,418 - CAPX 5,767 5,777 6,032 6,204 6,358 6,493 6,608 6,700 6,770 6,816 - DNWC 1,007 27 33 35 36 37 38 39 40 41 = FCF 4,781 6,344 6,832 7,257 7,604 8,019 8,342 8,649 8,935 9,198 EBITDA 18,969 EV/EBITDA multiple 7.5 Terminal Value 142,267

142,2677.518,969 TV =´= 18,9695,41813,551DepEBITEBITDA 101010 =+=+=

Average for Carlsberg peers: EV/EBITDA = 7.5

TV estimated usingEV/EBITDA

Method 2: Standard growing perpetuity formula

– Beyond the forecasting period, FCFs grow at constant rate g

– Terminal value (in year T, the end year of the forecasting period)

gWACCg)(1FCFTV T

T -+´

=

Method 3: “Value drivers” formula

– Assumption:– Net Assets (NA) = PPE + NWC [è what about cash?]– Return on invested capital (ROIC) = EBIT(1−t)/NA– Assume ROIC is stable beyond the forecast period: ROIC = ROICT

– Value created: iif (approx.) ROIC > WACC

gWACC]g/ROICt)[1(1g)EBIT(1

gWACC

]/ROICg)(1

gt)[1(1g)EBIT(1TV

TT

TT

T

---+

»

-+

--+=

Method 4: Flat perpetuity

– The previous formula becomes

WACCt)(1g)EBIT(1TV T

T-+

»

Other Standard Issues

Shares outstanding vs. fully diluted shares

– Other existing items that may become shares:– Stock options– Call warrants– Convertible bonds– Etc.

– “Treasury shares method”: in the money items

Other Methods to Compute Equity Value

– Discounted Dividend Method (DDM):– Equity value = 𝐷!(1 + 𝑔)/(𝑟 − 𝑔)

– Example: Current dividend of Queen Corp. is 0.55. Suppose that g=2.5% and r=7%

§ 𝑃! = 0.55 "#!.!%&!.!'(!.!%&

= 12.53

– Flow to Equity Method:– Equity Value = expected FCF to equity discounted at the cost of equity capital

Appendix:Building a Sensitivity Analysis Table in Excel

35

– Pick a cell which will be the top-left corner of your sensitivity table (here cell C34)

– Refer to the cell where the cell containing the value per share (here cell B30)

36

– On the table’s top side, type in a range of values for the perpetual growth rate, around and including the base case growth rate (here, around and including 1.5%)

– On the table’s left side, type in a range of values for the discount rate, around and including the base case discount rate (here, around and including 7.4%)

37

– Select all cells in the table

38

– In the Menu, go to– Data– What-if Analysis– Data Table

– Dans le menu, aller à:– Données– Analyse scenarios– Table de données

39

– In the “row input cell” (FR: “cellule d’entrée enligne”), refer to (i.e. click on) the cell containing the base case perpetual growth rate (here, cell B13)

ç NB: don’t omit $ signs

40

• In the “column input cell” (FR: “cellule d’entrée en colonne”) refer to (i.e. click on) the cell containing the base case discount rate (here, cell B12)

ç NB: don’t omit $ signs

41

• Press OK

• The table will fill itself up with values per share corresponding to the different growth rate and discount rate scenarios

42

– Clean up the presentation

Carlsberg (in DKKm) Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10Sales 65 536 67 964 70 968 73 856 76 604 79 185 81 577 83 755 85 698 87 386 Sales growth 1.80% 3.70% 4.42% 4.07% 3.72% 3.37% 3.02% 2.67% 2.32% 1.97%EBIT 9 585 10 203 11 005 11 453 11 879 12 279 12 650 12 988 13 289 13 551 EBIT margin 14.6% 15.0% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5%Tax rate 20.47% 20.90% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50% 21.50%Depreciation as % sales 6.0% 6.0% 6.0% 6.1% 6.1% 6.2% 6.2% 6.2% 6.2% 6.2%CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 CAPX as % sales 8.8% 8.5% 8.5% 8.4% 8.3% 8.2% 8.1% 8.0% 7.9% 7.8%DNWC 1 007 27 33 35 36 37 38 39 40 41

Discount rate 7.4%Perpetual growth 1.5%EBIT(1-t) 7 623 8 071 8 639 8 991 9 325 9 639 9 930 10 195 10 432 10 638 + Depreciation 3 932 4 078 4 258 4 505 4 673 4 909 5 058 5 193 5 313 5 418 - CAPX 5 767 5 777 6 032 6 204 6 358 6 493 6 608 6 700 6 770 6 816 - DNWC 1 007 27 33 35 36 37 38 39 40 41 = FCF 4 781 6 344 6 832 7 257 7 604 8 019 8 342 8 649 8 935 9 198 Terminal Value 158 242 Dicount factor 1.00 0.93 0.87 0.81 0.75 0.70 0.65 0.61 0.56 0.53 0.49PV of FCF 4 452 5 500 5 515 5 454 5 321 5 225 5 061 4 886 4 700 4 505 PV of cashflows 50 618 PV of TV 77 496 Enterprise value 128 114 505.68 0.5% 1.0% 1.5% 2.0% 2.5%Cash and equivalents 3 714 6.5% 551 603 665 741 835Debt 54 459 7.0% 478 520 570 629 702Equity value 77 369 7.4% 428 464 506 555 615Shares (millions) 153 8.0% 363 391 424 463 508Value per share (DKK) 506 8.5% 316 340 367 399 436

growth rate g

WAC

C

Value per Share (DKK)