Solutions – Chapter 7
Chapter 7 Prospective Analysis: Valuation Theory and Concepts Question 1. Jonas Borg, an analyst at EMH Securities, Securities , states: "I don't know why anyone would ever try to value val ue earnings. !viously, the arket knows that earnings can !e ani#ulated and only values cash $lows." %iscuss.
Valuing earnings is an alternative way of valuing a company even if earnings can be manipulated. Note that, with an infinite forecast horizon, the valuation based on discounted abnormal earnings delivers exactly the same estimate as DCFbased methods, even if there is earnings manipulation. !he estimated values using accountingbased valuation are not affecte aff ected d by accou accounti nting ng choic choices es becau because se of the the self selfcor correc rectin ting g nature nature of double double entry entry boo""eeping. Current period earnings can be manipulated, but the values estimated with accounting accountingbase based d valuation valuation are not to be manipulate manipulated. d. #owever, #owever, with finite horizons, horizons, earnin earnings gs man manipu ipulat lation ion can aff affect ect value value unles unlesss the ana analys lystt recogn recognize izess and undoe undoess the manipulation. $lso, when accounting data is used to forecast cash flows, even a DCF valuation is potentially vulnerable to accounting manipulation. !here !here are two practi practical cal advant advantage agess to valuin valuing g earnin earnings. gs. First, First, accou accounti nting ng based based valuation %using earnings& frames the valuation tas" differently and can immediately focus the analyst's attention on the "ey measure of performance( )*+ and its components %i.e., value drivers such as profit margins, sales turnover, and leverage&. econd, if it is more natural to thin" about future performance in terms of accounting returns, and if the analyst faces a context where a -bac" ofenvelope- estimate of value would be of use, the accountingbased techniue can be simplified to deliver such an estimate. -hortcut- estimates are useful in a variety of contexts where the cost and time involved in a detailed DCF analysis is not /ustified. 0n this context, the detailed DCF method is analogous to a manual camera for which the distance, light exposure, and shutter speed need to be set before ta"ing a picture whereas the -shortcut- accountingbased valuation is analogous to an automatic camera.
Question 2. E&#lain why terinal values in accounting!ased valuation are signi$icantly less than those $or %() valuation.
DCF termina terminall value valuess includ includee the present present value value of all expected cash flows beyond the forecast horizon. Note that the expected cash flows beyond the forecast horizon can be bro" bro"en en down down into into tw two o part parts( s( noral an and a!noral. inc incee the the term termin inal al valu valuee in the the accountingbased techniue includes only the abnormal earnings %expected earnings minus cost of capital times beginning boo" value of euity&, the terminal values in accounting based valuation are significantly less than those for DCF valuation. !he accountingbased approach recognizes that current boo" value and earnings within the forecast horizon already reflect many of the cash flows expected to t o arrive after the forecast horizon.
Question 3. 1
Solutions – Chapter 7
Manu$actured Earnings is a *darling+ o$ Euro#ean analysts. Its current arket #rice is - #er share, and its !ook value is #er share. /nalysts $orecast that the $ir0s !ook value will grow !y -1 #ercent #er year inde$initely, and the cost o$ e2uity is - #ercent. 3iven these $acts, what is the arket0s e&#ectation o$ the $ir0s longter average 4E5 P
1
ROE r
B
r g
where )*+ is the longterm average )*+, g is the longterm average growth in boo" value, r is the cost of euity, 1 is the stoc" price, and 2 is the boo" value per share. 3sing the information in the uestion, 15 1 ROE 0.15 50.15 0.10
or )*+ 4 5.67 %or 678&.
Question 4. 3iven the in$oration in 6uestion 7, what will !e Manu$actured Earnings' stock #rice i$ the arket revises its e&#ectations o$ longter average 4E to 81 #ercent5
*nce again, using the same formula as in the answer to 9uestion :, we have P 1 0.2 0.15 50.15 0.10
or 1 4 ;<5 2ased on above euation, the =anufactured +arnings' stoc" price will be revised to ;<5.
Question 5. /nalysts reassess Manu$actured Earnings0 $uture #er$orance as $ollows: growth in !ook value increases to -8 #ercent #er year, !ut the 4E o$ the increental !ook value is only - #ercent. 9hat is the i#act on the arketto!ook ratio5
ince the )*+ from the incremental growth value is eual to cost of euity, there is no increase in value.
Question .
2
Solutions – Chapter 7
How can a co#any with a high 4E have a low E ratio5
$ccountingbased valuation suggests that the stoc" price %a numerator of the 1+ ratio& can be viewed as the sum of the current boo" value per share plus the discounted expected future abnormal earnings per share. 1rice per share 4 2oo" value per share x E 1 ROE t 1
1
r E
E t ROE t 1
1 r E
r E 1 g t 1
E t ROE t 1
1 r 2
r E 1 g t 1 3
1 r
E
2
E
$ company with a high %current period& )*+ may have a low price and 1+ ratio when <. cost of euity capital %r+ & is high> 6. expected growth of boo" value is low> and :. expected future )*+ is low %relative to current period )*+&.
Question 7. 9hat ty#e o$ co#anies have: a. a high E ratio and a low arketto!ook ratio5
)ecovering firms, li"e $pple in
-)ising stars- which are expected to grow uic"ly and en/oy high )*+s during the growth period and@or after the growth occurs. c. a low E ratio and a high arketto!ook ratio5
-Falling stars- that en/oy high )*+s on existing investments but are no longer growing fast. 1+ ratio is low due to relatively high earnings in current year. d. a low E ratio and a low arketto!ook ratio5
-Dogs- which have little prospect for either growth or high )*+s.
Question !. 9hich o$ the $ollowing ites a$$ect $ree cash $lows to de!t and e2uity holders5 9hich a$$ect $ree cash $lows to e2uity alone5 E&#lain why and how.
$ll answers assume a tax rate A 5. 3
Solutions – Chapter 7
/n increase in trade receiva!les will cause both FCF+ and FCFDB+ to decrease, since it increases the firm's cash reuired for wor"ing capital. / decrease in gross argins will cause both FCF+ and FCFDB+, to decrease by lowering both +20! %< tax rate& and N0. /n increase in #ro#erty, #lant, e2ui#ent will decrease both FCF+ and FCFDB+ due to an increase in capital expenditures. /n increase in inventories will decrease both FCF+ and FCFDB+ through an increase in cash reuired for wor"ing capital. Interest e&#ense will decrease FCF+ only. For calculating free cash flows to debt, additional interest expense does not change +20! %< tax rate&. /n increase in #re#aid e&#enses will cause both FCF+ and FCFDB+ to decrease through an increase in wor"ing capital. /n increase in notes #aya!le to the !ank will increase FCF+ only. !he increase in notes payable will increase debt, increasing the FCF+ by the same amount.
Question ". Starite (o#any is valued at 81 #er share. /nalysts e&#ect that it will generate $ree cash $lows to e2uity o$ ; #er share $or the $oreseea!le $uture. 9hat is the $ir's i#lied cost o$ e2uity ca#ital5
ith a single, unchanging free cash flow to euity for the foreseeable future, we can calculate the implied cost of euity capital using the following formula(
Value per share Free cash flow to equity Cost of equity capital 3sing a value per share 4 65 and a free cash flow to euity 4 , solving the euation for cost of euity capital yields, r+ 4 658.
Question 1#. Janet Stringer argues that "the %() valuation ethod has increased anagers' $ocus on shortter rather than longter #er$orance, since the discounting #rocess #laces uch heavier weight on shortter cash $lows than longter ones." (oent.
hile it is true that DCF valuation places more weight on earlier cash flows than on later ones, this reflects the time value of money. $ euro in one year is more valuable than a euro in five year's time. #owever, this does not imply that the longterm is less important than the short term. !ypical DCF valuations show that the value of cash flows beyond, say, five years is a substantial fraction of the overall firm value. 0f managers believe that longterm performance of the firm is the most significant driver of value, they will certainly focus appropriately on ma"ing sure that they do not underemphasize the longterm. 4
Solutions – Chapter 7
DCF valuation helps a manager understand the tradeoffs between short term and longterm actions. Consider management's decision if it has a choice between two mutually exclusive investments that generate euivalent cash flows, one with a short horizon and the other with a long horizon. DCF analysis implies that firm value will increase more if the management ta"es the shortterm pro/ect. 0n this sense, DCF helps managers trade off how much they should focus on shortterm versus longterm considerations. *ne concern often raised about DCF analysis is that it focuses attention on uantifiable costs and benefits from investing. 0t is probably more difficult to uantify long term costs and benefits than shortterm ones. 0f management ignores these types of costs and benefits, they may end up ma"ing decisions that have a shortterm focus. #owever, this is really not the fault of DCF as a method. 0t is simply an indication of the difficulty in ma"ing decisions with highly uncertain payoffs.
Pro$le% 1. &sti%atin' (u'o )oss* e+uity value ,updated 1-2#11 -. (alculate $ree cash $lows to e2uity, a!noral earnings, and a!noral earnings growth $or the years 811< = 81--. 8. /ssue that in 81-8 Hugo Boss /3 li2uidates all its assets at their !ook values, uses the #roceeds to #ay o$$ de!t and #ays out the reainder to its e2uity holders. 9hat does this assu#tion i#ly a!out the co#any0s: a. )ree cash $low to e2uity holders in 81-8 and !eyond5 !. /!noral earnings in 81-8 and !eyond5 c. /!noral earnings growth in 81-8 and !eyond5 7. Estiate the value o$ Hugo Boss0 e2uity on /#ril -, 811< using the a!ove $orecasts and assu#tions. (heck that the discounted cash $low odel, the a!noral earnings odel and the a!noral earnings growth odel yield the sae outcoe. ;. >he analyst estiates a target #rice o$ 81 #er share. 9hat is the e&#ected value o$ Hugo Boss0 e2uity at the end o$ 81-- that is i#licit in the analysts0 $orecasts and target #rice5 . ?nder the assu#tion that the historical trends in the co#any0s 4E @i.e., a##ro&iately -A #ercent, #ayout ratio @C1 #ercent and !ook value growth @. #ercent continue in the $uture, what would !e your estiate o$ Hugo Boss0 e2uity valueto!ook ratio !e$ore the co#any #aid out its s#ecial dividend5 How does the s#ecial dividend #ayent change your estiate o$ the e2uity valueto!ook ratio5
<. !he calculations are( 2##!/ E?5.: ?<.:
2##"& EE.7 E.: 655.6 ?G.< ?E.:
2#1#& EGE.7 7.? 66<. GE.7 ??.?
2#11& E?<.5 :6.5 67? E5.: <
Change in net assets B Change in net debt 0ree cash lo to e+uity Net profit
B6<.E 6:.5 "7.1 ?E.:
<5.5 <<<. 7!.5 ??.?
<6.7 6.? !#.3 <
2eginning 2+ x <68 A$nor%al proit
6:.EE 74.42
6.56 75.!7
6.7?6 "1.1#!
Net assets Net debt +uity 0mplied dividends Net profit
5
Solutions – Chapter 7
Change in net profit %1rofit t< Dividends t<& x <68 A$nor%al earnin's 'roth
<. 5.< 1.45
6. 0f #ugo 2oss liuidates all its assets at their boo" values in 65<6, the companyHs 65<6 net profit is zero and a. 65<6 free cash flow to euity, defined as net profit minus the change in net assets plus the change in net debt, is eual to( 5 I %E?<.5& B %:6.5& 4 67? %i.e., expected euity at the end of 65<<&. b. 65<6 abnormal earnings, defined as net profit minus <6 percent of 65<< ending euity, is eual to( 5 I 5.<6 x 67? 4 :<.5E. c. 65<6 abnormal earnings growth, defined as the change in abnormal earnings, is eual to( :<.5E ?<.<5E 4 <66.
Free cash flow to euity $bnormal profit $bnormal earnings growth
2#1#& GE.7 G7.EG <.7
2#11& E5.: ?<.<5E <7.6:6
2#12& 67? :<.5E <66.
:. *n Lanuary <, 655?, the value of #ugo 2oss’ equity equals: FCFE FCFE Equity value end 2008 FCFE2011 200 2010 1 r e
1 r e
2
1 r e
FCFE2012
3
1 r e
7.1 78.5 80.3 25.0 371.03 1.12 1.12 1.12 3 1.12 4 Or
#E
!"E
Equity valueend 2008
#E 200
end 2008
1
74.42
75.87$
1 r e 2 1.108
1.12
1.12 2
1.12 3
3
2
#E 2010
1 r e
2#13& 5 5 :<.5E
#E 2011
1 r e
3
2012
1 r e
31.08 371.03 1.12 4
4
*r Equity valueend 2008
%ro&it
200
r
1 #E' r
e
e
2010
1 r
#E' 2011
e
8.3
1
0.12
0.12
1.45$ 1.12
2
1 r
#E' 2012 1r
e
3
122.188
1.12 2
1.12 3
4
1 r
e
15.232
#E' 2013 e
31.08 371.03 1.12 4
$n euity value of ;:G<.5: million on Lanuary <, 655?, corresponds with a value of ;:E<.77 million %:G<.5: x <.<6?5@:7&, ;7.6 per share %:E<.77@G5.&, on $pril <, 655?. $
Solutions – Chapter 7
. $ target price of ;65 per share implies a mar"et value %on $pril <, 655?& of ;<,5E million. $ mar"et value of ;<,5E million on $pril <, 655?, corresponds with a mar"et value of ;<,:?.65 million on Lanuary <, 655?. !he discounted value of #ugo 2ossH expected free cash flows in 655?65<< euals( "alue
FCFE200 1 r e
FCFE2010 1 r e
2
FCFE2011
1 r e
3
7.1 78.5 80.3 20$.43 1.12 1.12 1.12 3
2
#ence, with a current euity value of ;<,:?.65 million, the present value of the expected euity value at the end of 65<< must be eual to( <,:?.65 I 65.: 4 <,<6.GG. !he future value of the expected euity value at the end of 65<< is therefore ; <,::.5 million %<,<6.GG x <.<6:&, or ; 6:.65 per share. Note that this future expected mar"et value of euity is substantially higher than the expected future boo" value of euity of %;<,::.5 million versus ;67? million&. 7. $s described in Chapter G, for a firm in steady state, the valuetoboo" multiple formula simplifies to( Equity value ( to ( )oo* +ultiple 1 ,-E 0 r e requity
e
For #ugo 2oss, this would imply that the euity valuetoboo" multiple is( Equity value ( to ( )oo* +ultiple1
0.18 0.12 1.23 0.12 0.055
!he special dividend of ;:7.< million decreases both the mar"et value and the boo" value of euity by the same amount. Conseuently, the expected valuetoboo" multiple would increase from <.?6: to :.76( #d/usted equity value ( to ( )oo* +ultiple
1.23 1 345.1 345.1 3.524 1
!his multiple would imply an euity value of ;G5<.67 million, or ;?.? per share, on Lanuary <, 655?. !his would be euivalent to ;<5.6 per share on $pril <, 655?, when #ugo 2ossH shares traded at ;<<.
Pro$le% 2. &sti%atin' Adidas* e+uity value -. (heck whether all changes in the !ook value o$ e2uity that the analyst #redicts can !e $ully e&#lained through earnings and dividends. 9hy is this an i#ortant #ro#erty o$ the analyst0s e2uity estiates5 8. 9hen using these $orecasts to estiate the value o$ e2uity, the analyst can deal with inority interests in the $ollowing ways: a. @- (lassi$y inority interests on the !alance sheet as a noninterest!earing lia!ility @and hence as a negative o#erating asset and @8 e&clude incoe $ro inority interests $ro earnings @i.e., $ocus on net #ro$itD
7
Solutions – Chapter 7
!. @- (lassi$y inority interests on the !alance sheet as @grou# e2uity, @8 include incoe $ro inority interests in earnings @i.e., $ocus on grou# #ro$it, and @7 su!tract the !ook value o$ inority interests $ro the estiated value o$ grou# e2uity to arrive at the value o$ shareholders0 e2uity. >hese a##roaches ay yield di$$erent values. %iscuss #otential draw!acks o$ !oth a##roaches. 7. Based on a arket value o$ ;,A;< illion on March 7-, 811< and the analyst0s estiates, /didas0 leading arket valuetoearnings ratio is -1.<. 9hat does this ratio suggest a!out the analyst0s e&#ectations a!out $uture a!noral earnings growth5 ;. (alculate a!noral earnings $or the years 811< = 81--. . /ssue that a!noral earnings in 81-8 and !eyond are ero. Estiate the value o$ /didas0 grou# e2uity @grou# e2uity is the su o$ shareholders0 e2uity and inority interests. 9hat ight e&#lain the di$$erence !etween your e2uity value estiate and /didas0 actual arket value @o$ ;,A;< illion5
<. 0f all changes in the boo" value of euity can be explained through earnings and dividends, this means that the analystsH predictions are consistent with the clean surplus assumption. !his is a necessary reuirement for the euivalence of the dividend discount model and the abnormal earnings valuation model. 2##!/
2eginning shareholders' euity Net profit Dividends +nding shareholders' euity
::E.5
2##"& ::E.5
2#1#& :G:7.7
2#11&
B.: ?.E :G:7.7
B77G.? <<6.6
B5G.5 <6<.? .:
6. !he first approach implicitly assumes that the investors holding the minority interest hold a claim on noncurrent assets only and that none of the consolidated liabilities Mbelongs to these investors. $lthough these assumptions do not affect the valuation analysis directly they do affect the ratios in the financial analysis and, as such, may indirectly affect the analystHs predictions. !he second approach implicitly assumes that the value of minority interests euals its boo" value, which is typically lower than the value of other euity components. :. !he leading mar"et valuetoearnings ratio is calculated as follows( eadin equity value ( to ( earnins ratio 1 1 2 pro&it d1 1 r e d2 1 r e pro&it pro&it
1 2
r e
1 r e
r e
3
1
pro&it 2
2
1 r
1 r
e
1
pro&it
1 .3
pro&it
.4
d3
1 r e
3 e
1 Su+ o& &uture saled a)nor+al earnins roth
.12 .12 8.33 1 Su+ o& &uture saled a)nor+al earnins ro4th 10. .12
#ence, the analyst expects that the sum of future abnormal earnings growth is positive. . hen focusing on group euity and group profit, the calculations are( 2##"& :55.5
%a& 2eginning group euity 8
2#1#& :G6.7
2#11&
Solutions – Chapter 7
%b& -Normal- profit 4 %a& x 5.<6 %c& Oroup profit %d& $bnormal earnings 4 %c& I %b&
5E.5 E.E 5.E
?.< 7<.6 <<6.<
756.6 <5.7 <5E.:
$lternatively, when focusing on shareholdersH euity and net profit, the calculations are( 2##"& ::E.5 5.: .: 5.5
%a& 2eginning shareholders' euity %b& -Normal- profit 4 %a& x 5.<6 %c& Net profit %d& $bnormal earnings 4 %c& I %b&
2#1#& :G:7.7 E.: 77G.? <5?.
2#11&
7. !he calculations are( 2##!/
%a& 2eginning group euity %b& $bnormal %group& earnings %c& Discount factor %r 4 <68& %d& Discounted abnormal %group& earnings 1resent value of future abnormal %group& earnings Oroup value
2##"&
2#1#&
2#11&
:55.5 5.E 5.E?6? :.
<<6.< 5.G?G6 E?.
<5E.: 5.G<
656.?
:56.?
*ur estimate is much lower than $didasH current mar"et value, primarily because our assumption that abnormal earnings is zero after 65<<. $lthough it is reasonable to expect that competition will drive down $didasH abnormal earnings in the future, it is not li"ely that this will happen overnight. #ence, it is necessary to include an estimate of the value of $didasH post 65<< abnormal earnings in our calculations, i.e., the terminal value. !erminal value calculations will be the topic in Chapter E.
