financial ratios - bwl.uni-mannheim.de · leading ratios, use analysts’ forecasts in the...

Bachelor thesis tutorialFinancial Ratios

Ernst MaugUniversity of Mannheim

http://[email protected]: +49 (621) 181-1951

http://cf.bwl.uni-mannheim.de/mailto:[email protected]

© 2015 E. Maug Corporate Finance I 2

Valuation with multiples

Many practitioners use multiples to value companies. Example: Price-Earnings ratio (P/E) Procedure:

- Select set of comparable companies- Compute average P/E-ratio of comparables- Multiply earnings of company to be valued with average P/E of comparables- Done!

Advantages: easy, no estimation of value drivers Problems: lots!


Popular multiples used for valuation

Ratios for firm value (= debt + equity):- Value-to-sales ratio- Value-to-cash-flow ratio- Value-to-EBIT ratio- Value-to-EBITDA ratio- Market-to-book ratio (value over total assets)- Tobin's q (market value over replacement value)

Ratios for equity value:- P/E ratio (price over net income)- Market-to-book ratio (price over book value of equity)

Numerator and denominator should match!


Valuing a Company Using P/E-Multiples

The three steps of using P/E multiples company valuation:1. Find sample of comparable companies2. Compute average of their P/E ratios3. Multiply earnings by average P/E from step 2

Example: Daimler- Comparables: BMW, VW, Toyota, Renault, Fiat, (PSA)

For calculations see Financial Ratios – Multiples.xls, tab “Valuation”.

Averaging method Average Value ErrorMean 25.48 163.04 € 165%Median 10.74 68.71 € 12%Harmonic mean 12.57 80.44 € 31%Geometric mean 15.85 101.43 € 65%Actual values Daimler 9.61 61.53 € 0%

VorführenderPräsentationsnotizenNote:This practice is called pricing by “comparables.”In order for this to work, consider the following DCF models:

Now, if

then pricing by comparables is the same as the DCF model.

Data

CompanyDaimlerBMWVWToyotaPSARenaultFiat

Market Cap (mil)65,827 €56,956 €80,585 €158,424 €8,027 €17,335 €9,643 €

P/E Ratio9.6110.719.0611.20neg.10.7485.67

Latest earings per share6.40 €8.10 €18.69 €4.14 €neg.5.46 €0.09 €

Latest dividend2.25 €2.60 €4.00 €1.16 €1.10 €1.72 €0.09 €

Date of last dividend4/10/145/16/145/14/14n.a.in 20105/12/14in 2010

Shares outstanding (mil)1,0706564763,4187832961,251

Free float79,42%49,28%12,27%n.a.64,19%62,55%62,07%

Stock price (24.09.2014)61.53 €86.79 €169.40 €46.35 €10.25 €58.62 €7.71 €

Dividend per share (exp.)2.38 €2.89 €4.89 €1.18 €- 0 €1.92 €0.02 €

Dividend yield (exp.)3.87%3.33%2.89%2.55%0.00%3.28%0.26%

Total dividend (mil)2,546 €1,897 €2,326 €4,033 €- 0 €568 €25 €

Valuation

Averaging methodAverageValueError

Mean25.48163.04 €165%

Median10.7468.71 €12%

Harmonic mean12.5780.44 €31%

Geometric mean15.85101.43 €65%

Actual values Daimler9.6161.53 €0%

ComparablePE-ratio

BMW10.71

VW9.06

Toyota11.20

Renault10.74

Fiat85.67

PSAneg.


Lessons for the selection of comparables

Multiples valuation avoids the estimation of cash flows, sales forecasts, margins, growth rates, payout ratios.

Instead uses market assessment of all valuations combined Implicit assumption: comparable companies have:

- Similar growth rates- Similar stage (fast growth / slow growth)- Similar margins- Similar cost of capital or cost of equity (leverage!)- Similar payout ratios


Popular financial ratios used for valuation

Which numbers are used?- Always: current market prices in the numerator- For trailing ratios, use the latest historical number in the denominator.- For leading ratios, use analysts’ forecasts in the denominator.

Some ratios are heavily influenced by accounting choices:- P/E ratio, EBIT ratio, EBITDA ratio- To get around this problem:

Re-adjust earnings for special items Use ratios based on financial numbers "further up in the income statement",

e.g. value-to-sales ratio.


Empirical evidence: Which ratios are successful?

Liu, Nissim and Thomas (Journal of Accounting Research, 2002) perform a horse-race of different ratios:

- For each firm, they use all firms from the same industry as comparables and calculate the average multiple.

- Then they multiply this average multiple with the corresponding accounting number of the firm to be valued.

- Finally, they compare the obtained value estimate with the firm’s market capitalization.

Their findings are:- Multiples derived from earnings forecasts have the lowest pricing errors.- Multiples with historical earnings come second.- Cash flow and book value of equity are tied for third.- Sales perform worst.


Repeated for - 26,613 firm-year observations between 1982 and 1999 - for 19 different types of multiples.- Measure of accuracy: Absolute difference between estimated value and market

value Their findings are:

- Multiples derived from earnings forecasts have the lowest pricing errors.- Multiples with historical earnings come second.- Cash flow and book value of equity are tied for third.- Sales perform worst.


Empirical evidence: Which ratios are successful?

Other finding: Harmonic mean results in lower errors than arithmetic mean or median.

- Harmonic mean:

( )−

−

=

=

∑1

1

1

n

h ii

m n x

- Arithmetic mean:

=

= ∑1

1 na i

im x

n

- These results are consistent across years and industries.


Dittmann, Maug (WP 2005) also include median and geometric mean:

=

==∏ 1/1

i n ng ii

m x ( ){ }=

=

= =

∑

1

1exp ln exp lni n

i a ii

x m xn

Analyze percentage errors and log errors:

Benchmark against „dummy procedures“:- Set market value = book value, or equal to $1

-2

-1.5

-1

-0.5

0

0.5

1

-100

%-9

3%-8

6%-7

9%-7

2%-6

5%-5

8%-5

1%-4

4%-3

7%-3

0%-2

3%-1

6% -9%

-2% 5% 12%

19%

26%

33%

40%

47%

Percentage error

Loga

rithm

ic e

rror

i

i

i

iiP MV

MVeMV

MVMVe^

ln,^

log =−

=

Diagramm1

-1

-0.99

-0.98

-0.97

-0.96

-0.95

-0.94

-0.93

-0.92

-0.91

-0.9

-0.89

-0.88

-0.87

-0.86

-0.85

-0.84

-0.83

-0.82

-0.81

-0.8

-0.79

-0.78

-0.77

-0.76

-0.75

-0.74

-0.73

-0.72

-0.71

-0.7

-0.69

-0.68

-0.67

-0.66

-0.65

-0.64

-0.63

-0.62

-0.61

-0.6

-0.59

-0.58

-0.57

-0.56

-0.55

-0.54

-0.53

-0.52

-0.51

-0.5

-0.49

-0.48

-0.47

-0.46

-0.45

-0.44

-0.43

-0.42

-0.41

-0.4

-0.39

-0.38

-0.37

-0.36

-0.35

-0.34

-0.33

-0.32

-0.31

-0.3

-0.29

-0.28

-0.27

-0.26

-0.25

-0.24

-0.23

-0.22

-0.21

-0.2

-0.19

-0.18

-0.17

-0.16

-0.15

-0.14

-0.13

-0.12

-0.11

-0.1

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

7.52869988573934E-16

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.4

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

Percentage error

Logarithmic error

-13.815510558

-4.605070191

-3.9119730067

-3.5065245645

-3.2188508252

-2.9957122738

-2.8133940502

-2.6592457513

-2.5257161444

-2.4079344976

-2.302575093

-2.2072658223

-2.1202552029

-2.0402131362

-1.9661057135

-1.8971133182

-1.8325752138

-1.7719509596

-1.7147928726

-1.6607259437

-1.6094329124

-1.5606429864

-1.5141231872

-1.4696716222

-1.427112189

-1.3862903611

-1.3470698018

-1.3093296163

-1.2729621044

-1.2378709077

-1.203969471

-1.1711797557

-1.1394311582

-1.1086595942

-1.0788067202

-1.0498192674

-1.0216484698

-0.9942495706

-0.9675813947

-0.9416059758

-0.9162882319

-0.8915956803

-0.8674981868

-0.8439677447

-0.8209782793

-0.798505474

-0.7765266156

-0.7550204566

-0.7339670917

-0.7133478471

-0.6931451806

-0.6733425925

-0.6539245443

-0.6348763856

-0.6161842876

-0.5978351826

-0.5798167095

-0.5621171638

-0.5447254513

-0.5276310472

-0.5108239571

-0.4942946825

-0.478034188

-0.4620338723

-0.4462855401

-0.4307813776

-0.4155139288

-0.4004760741

-0.3856610102

-0.3710622321

-0.3566735154

-0.3424889005

-0.3285026781

-0.314709375

-0.3011037414

-0.2876807391

-0.2744355299

-0.2613634654

-0.2484600772

-0.2357210677

-0.2231423013

-0.2107197967

-0.1984497192

-0.1863283734

-0.1743521967

-0.162517753

-0.1508217269

-0.1392609179

-0.1278322351

-0.1165326927

-0.1053594045

-0.0943095806

-0.083380522

-0.0725696176

-0.0618743399

-0.0512922418

-0.0408209529

-0.0304581766

-0.0202016869

-0.0100493258

0.000001

0.009951321

0.0198036077

0.0295597731

0.0392216747

0.0487911165

0.0582698515

0.0676595831

0.0769619671

0.0861786137

0.0953110889

0.1043609162

0.1133295782

0.1222185177

0.1310291396

0.1397628119

0.1484208672

0.1570046035

0.1655152859

0.1739541475

0.1823223901

0.1906211861

0.1988516784

0.2070149824

0.2151121861

0.2231443513

0.2311125146

0.2390176879

0.2468608592

0.2546429936

0.2623650337

0.2700279006

0.2776324942

0.2851796941

0.2926703602

0.3001053332

0.307485435

0.3148114698

0.3220842238

0.3293044666

0.3364729509

0.3435904136

0.3506575758

0.3576751436

0.364643808

0.3715642461

0.3784371207

0.3852630811

0.3920427635

0.3987767911

0.4054657748

Tabelle1

No.TagInhaltAnwendungenQuelle

1MontagValue drivers36Who is who, cash flow calculationsCF1 - 02

2Cost of capital3268CF1 - 03

3DienstagDCF31Warren BuffetCF1 - 04

4Capital structure & APV3667CF1 - 12

5MittwochResidual income27Excel Übung: NetscapeCF1 - 06Alternative: BHP-Rio

6Financial ratios15CF1 - 06Additionally: Case on financial ratios

7International valuation2769CF3 - 12

8DonnerstagEvent studies34Rexford StudiosCF1 - 10

9Leasing1549KM - 9

10FreitagRisk management23Thyssen KruppCF3 - 11

11IPOs2548CF1 - 08

30118.8125

AssignmentGreat Eastern Toys

Yell group

Tabelle2

ErrorLog error

-100%-13.815510558

-99%-4.605070191

-98%-3.9119730067

-97%-3.5065245645

-96%-3.2188508252

-95%-2.9957122738

-94%-2.8133940502

-93%-2.6592457513

-92%-2.5257161444

-91%-2.4079344976

-90%-2.302575093

-89%-2.2072658223

-88%-2.1202552029

-87%-2.0402131362

-86%-1.9661057135

-85%-1.8971133182

-84%-1.8325752138

-83%-1.7719509596

-82%-1.7147928726

-81%-1.6607259437

-80%-1.6094329124

-79%-1.5606429864

-78%-1.5141231872

-77%-1.4696716222

-76%-1.427112189

-75%-1.3862903611

-74%-1.3470698018

-73%-1.3093296163

-72%-1.2729621044

-71%-1.2378709077

-70%-1.203969471

-69%-1.1711797557

-68%-1.1394311582

-67%-1.1086595942

-66%-1.0788067202

-65%-1.0498192674

-64%-1.0216484698

-63%-0.9942495706

-62%-0.9675813947

-61%-0.9416059758

-60%-0.9162882319

-59%-0.8915956803

-58%-0.8674981868

-57%-0.8439677447

-56%-0.8209782793

-55%-0.798505474

-54%-0.7765266156

-53%-0.7550204566

-52%-0.7339670917

-51%-0.7133478471

-50%-0.6931451806

-49%-0.6733425925

-48%-0.6539245443

-47%-0.6348763856

-46%-0.6161842876

-45%-0.5978351826

-44%-0.5798167095

-43%-0.5621171638

-42%-0.5447254513

-41%-0.5276310472

-40%-0.5108239571

-39%-0.4942946825

-38%-0.478034188

-37%-0.4620338723

-36%-0.4462855401

-35%-0.4307813776

-34%-0.4155139288

-33%-0.4004760741

-32%-0.3856610102

-31%-0.3710622321

-30%-0.3566735154

-29%-0.3424889005

-28%-0.3285026781

-27%-0.314709375

-26%-0.3011037414

-25%-0.2876807391

-24%-0.2744355299

-23%-0.2613634654

-22%-0.2484600772

-21%-0.2357210677

-20%-0.2231423013

-19%-0.2107197967

-18%-0.1984497192

-17%-0.1863283734

-16%-0.1743521967

-15%-0.162517753

-14%-0.1508217269

-13%-0.1392609179

-12%-0.1278322351

-11%-0.1165326927

-10%-0.1053594045

-9%-0.0943095806

-8%-0.083380522

-7%-0.0725696176

-6%-0.0618743399

-5%-0.0512922418

-4%-0.0408209529

-3%-0.0304581766

-2%-0.0202016869

-1%-0.0100493258

0%0.000001

1%0.009951321

2%0.0198036077

3%0.0295597731

4%0.0392216747

5%0.0487911165

6%0.0582698515

7%0.0676595831

8%0.0769619671

9%0.0861786137

10%0.0953110889

11%0.1043609162

12%0.1133295782

13%0.1222185177

14%0.1310291396

15%0.1397628119

16%0.1484208672

17%0.1570046035

18%0.1655152859

19%0.1739541475

20%0.1823223901

21%0.1906211861

22%0.1988516784

23%0.2070149824

24%0.2151121861

25%0.2231443513

26%0.2311125146

27%0.2390176879

28%0.2468608592

29%0.2546429936

30%0.2623650337

31%0.2700279006

32%0.2776324942

33%0.2851796941

34%0.2926703602

35%0.3001053332

36%0.307485435

37%0.3148114698

38%0.3220842238

39%0.3293044666

40%0.3364729509

41%0.3435904136

42%0.3506575758

43%0.3576751436

44%0.364643808

45%0.3715642461

46%0.3784371207

47%0.3852630811

48%0.3920427635

49%0.3987767911

50%0.4054657748

Tabelle2

Percentage error

Logarithmic error

Tabelle3


Empirical evidence (2):

Results of empirical analysis and simulations of Dittmann, Maug (WP 2005):- Harmonic mean is biased downward, about as much as arithmetic mean is biased

upward.- Geometric mean and median are both good.


Conclusion

Multiples provide a short-cut. Rely on comparability:

- Companies from the same industry- Really companies with similar value drivers!

Averaging methods matter! Recommended reading: Titman and Martin, Valuation: the Art and Science of

Corporate Investment Decisions, Chapter 6.

Bachelor thesis tutorial�Financial RatiosValuation with multiplesPopular multiples used for valuationValuing a Company Using P/E-MultiplesLessons for the selection of comparablesPopular financial ratios used for valuationEmpirical evidence: �Which ratios are successful?Foliennummer 14Empirical evidence: �Which ratios are successful?Foliennummer 16Empirical evidence (2):Conclusion

financial ratios - bwl.uni-mannheim.de · leading ratios, use analysts’ forecasts in the...

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