Bachelor thesis tutorial Financial Ratios Ernst Maug University of Mannheim http://cf.bwl.uni-mannheim.de [email protected] Tel: +49 (621) 181-1951
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!
© 2015 E. Maug Corporate Finance I 3
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!
© 2015 E. Maug Corporate Finance I 5
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.
© 2015 E. Maug Corporate Finance I 9
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
© 2015 E. Maug Corporate Finance I 10
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.
© 2015 E. Maug Corporate Finance I 13
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.
© 2015 E. Maug Corporate Finance I 14
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.
© 2015 E. Maug Corporate Finance I 15
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.
© 2015 E. Maug Corporate Finance I 16
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
© 2015 E. Maug Corporate Finance I 17
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.
© 2015 E. Maug Corporate Finance I 18
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