Valuao Mehods of a Lfe Isurace Comay
ISORY...3 2 PRODUC ASSESSMEN : PROFI ESING...4 2. E PROFI ESING IN 3 SEPS...5 2.. Equalece Prcle...5 2..2 radoal Marg...6 2..3 Prof esg...6 2.2 COMMON CRIERIA O EVALUAE E PROFIABILIY...7 2.2. Ne Prese Value...7 2.2.2 Ieral Rae of Reur...7 2.2.3 Relao bewee IRR ad...7 3 COMPANY ASSESSMEN : MEODS...8 3. EMBEDDED VALUE...8 3.. Numercal eamle... 0 3..2 Embedded Value adaages... 2 3..3 Embedded Value dsadaages... 2 3.2 APPRAISAL VALUE... 2 3.3 VALUE ADDED... 2 3.3. Numercal eamle... 3 3.3.2 Value Added comoes... 4 3.4 OAL RAE OF REURN... 6 3.4. Numercal eamle... 7 4 CRIICAL APPROAC... 7 4. E PROBLEM... 7 4.2 REE KINDS OF VALUAION... 2 4.2. Value of a comay... 2 4.2.2 Icrease he alue of a comay... 2 4.2.3 Profably of a comay... 2 4.3 FINAL REMARKS ABOU CRIICAL APPROAC... 22 5 SENSIIVIY ANALYSIS... 22 5. APPROAC... 22 5.2 SENSIIVIY ESIMAION... 23 5.3 INERDEPENDENCE BEWEEN PARAMEERS... 23 5.4 APPLICAION... 24 5.4. Edowme wh aual remums... 24 5.4.2 Edowme wh sgle remum... 26 5.4.3 erm surace wh aual remums... 27 5.4.4 emorary mmedae lfe auy... 28 5.5 SIMULANEOUS SENSIIVIY... 29 5.6 CONCLUSION ON E SENSIIVIY ANALYSIS... 29 6 CONCLUSION... 3 7 ANNEXE... 32 7. BASIC ACUARIAL FORMULAE... 32 7.2 NUMERICAL APPLICAION... 33 7.3 NUMERICAL EXAMPLE 2... 35 7.4 NUMERICAL APPLICAION 3... 38 7.5 BONUS FORMULA... 42 8 REFERENCES... 44 2
sory radoally lfe assurace comaes hae reored facal resuls o shareholders o he bass of he sauory requremes of he surace comaes' legslao. So he mos commo measure of a lfe surace comay's facal year was he sauory eargs from oerao. hs has bee a coee measure sce also rereses he amou of moey whch ca be ad o olcyholder or ad he form of ddeds. he major dsadaage o relyg uo sauory eargs as a measure of how well a comay s dog s ha sauory accoug eds o be desged o roec agas solecy ad herefore by s ery aure suffers from oer coserasm. Sauory eargs do o measure how well a comay s dog o a gog cocer bass. For eamle caal esed acqurg busess acquso eeses ad aluao sra s mmedaely wre off. Successful acquso of rofable ew busess resuls a mmedae loss followed by a subseque ehaced seres of rofs. Alhough suable for solecy esg he sauory aroach by chargg he caal cos of ew busess o reeue ad gorg he fuure surlus sream arbuable o ew busess fals o dslay ay accoug erod a meagful accou of he radg acy of ha erod. For mos roducs a slowdow sales wll resul a mmedae crease sauory eargs ad geerally mos would o regard a slowdow sales as beg a sg of a healhy comay! So s clear ha sauory eargs are he wrog mehod o measure he healh of he comay. Largely as a resul of he adequaces of sauory accoug US surers were requred by he Secures Echage Commsso he early 970 s o beg o reor eargs o shareholders o a Geerally Acceed Accoug Prcles GAAP bass. he major adaage o GAAP accoug s ha does aem o roduce eargs ha reflec how well or how badly he surace comay had erformed a form whch s useful o maageme. Wh GAAP geerally a crease sales wll o deress GAAP eargs o he same degree as would sauory eargs. Uforuaely because 00% of acquso coss are o deferred creased sales wll sll deress GAAP eargs o some ee. Addoally margs for coserasm are ormally roduced o he assumos ad GAAP mgh suffer from he loc- rcle. Oce assumos are se for a arcular geerao or brach of busess he assumos cao be chaged uless fuure losses are lely. Aoher major dsadaage o GAAP s ha GAAP eargs may ary sgfcaly bewee wo decal comaes deedg o he objeceess of maageme esablshg assumos. herefore oerall GAAP s o a good rogoscaor for how well a comay s dog. Durg he erods of flucuao eres raes whch occurred he US durg he md-970 s ad early 980 s some US comaes bega o loo a cash flows as a measure of how well her comaes were dog. he real adaage o usg cash flows as a measureme ool s ha s he oly bass ha loos a real moey. Bu s really oly a mmedae solecy es. Cash flow s o a measure of how well a comay s dog. 3
I he 80 s here were ew roducs for eamle u led roducs he crease comeo mergers ad resrucurg decrease rof margs due o creased comeo ec. he resul has bee a greaer eed o be able o maage ad corol surace oeraos he face of creasg flucuaos ad uceray. I s eresg o oe ha solecy ad rofably cao be showed by he same mehod. Solecy s a cosra whch deermes he secury margs ad mehods o use. Profably res o show how well a comay s dog elmag he cos effec of he frs year ad ag he fuure rofs o accou. I shor we ca say ha four os hae corbued o he adoo of aluao mehods ard comeo bewee surers Iesors' ressure o hae comrehese resuls Producs' eoluo owards greaer flebly Deregulao facal corol of solecy ad o more arff aroal such as sadard moraly ables 2 Produc assessme : Prof esg We ow ha he acquso of rofable ew busess resuls a mmedae loss due o he acquso eeses ad he frs ayme o echcal resere. Aferwards we hoe ha a seres of rofs wll follow. he Prof esg aes fuure rofs o accou ad he decreases he effec of he esme of he frs year. o calculae or o esmae hese fuure rofs we use eeced alues. I fac hese fuure rofs come from he rof ad loss accou. ere s a eamle of a surace accou. We hae o he lef he charges ad o he rgh he come. Prof ad loss accou Deah clams ad Release of reseres Amous ad o maury Premums receed Surreder alues ad Ieres ad gas receed Eeses curred ad commssos ad Bous ad Icrease reseres aes Prof durg he year ycally we hae he followg cure for he Prof esg whch rereses he eeced rofs of he rof ad loss accou each year. 4
Prof esg 00 50 0-50 -00-50 -200-250 -300-350 -400 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 I s ery commo o hae a loss followed by a seres of rofs. Bu where does come from? Is he Prof esg relaed wh he acuaral rules? Yes s ad we wll see hs he e chaer. 2. he Prof esg 3 ses We wll see he relaosh bewee he Equalece Prcle ad he Prof esg 3 ses. Sarg from he Equalece Prcle we oba he radoal Marg ad he afer some modfcaos we oba he Prof esg. 2.. Equalece Prcle Equalece Prcle has he followg defo: Acuaral Prese Value APV of Premums equals o APV of Beefs lus APV of Charges. Usg a radoal edowme for a male aged of durao years we hae he followg alcao P'' ä A α γ ä Where ä he e sgle remum for a -year emorary lfe auy-due whch rodes for aual aymes of u as log as he beefcary les. A he e sgle remum for a edowme whch rodes for a ayme of a he ed of he year of deah f occurs wh he frs years oherwse a he ed of he h year. 5
6 α acquso eeses γ admsrao eeses he we hae our eamle ha he oal remum equals o he edowme beef lus he acquso eeses oly he frs year lus he oal admsrao eeses. We suose ha he colleco eeses are egraed he admsrao eeses. 2..2 radoal Marg Usg he bes esmae sead of rude assumos we ca rewre he formula as follows we symbolse he bes esmae bass wh he sar. 0 0 '' B u L ä A M ä P γ α Where Bous Lase beef robably o lase Marg radoal B L u M he wo las eressos are he surreder beef ad he bous. hs s radoally how he rof s calculaed. he Prof s o recogsed yearly bu a he begg of he corac for he whole durao. 2..3 Prof esg Iserg reseres rewrg he formula wh sums o he me ad regroug we oba 0 '' 0 α γ G I V V B u L q P Where eres eared Reseres Prof I V G I he sum we ca see he rof from he accoug G. he surace rofs are dscoued wh he facor.
he eleme braces a he ed of he sum s he dfferece bewee he resere a he ed of he year ad he oher a he begg of he year. I fac each erm of he sum s a le of he Prof ad Loss accou. So he Prof esg uses he radoal elemes of he acuaral scece. Of course ay ew eleme ca be sered le for eamle a resurace remum. We ca see ha he Prof esg ca be used as rofably ool or as a rcg ool. 2.2 Commo crera o ealuae he rofably 2.2. Ne Prese Value he Ne Prese Value wh Rs Dscou Rae s defed as follows: 0 G NPV If he Ne Prese Value s ose he roduc s rofable. Profably occurs whe he roduc geeraes a leas o he frs year sra. Rs Dscou Rae he Rs Dscou Rae s defed as he rae of reur led o busess rs of he surace comay. I realy hs rae s ery subjece. I deeds o he maageme he shareholders ad he esors. 2.2.2 Ieral Rae of Reur he Ieral Rae of Reur s defed as he rae whch ges a Ne Prese Value of zero. 0 G IRR 0 If he Ieral Rae of Reur s hgher ha he Rs Dscou Rae he he roduc s rofable. 2.2.3 Relao bewee IRR ad 7
NPV IRR NPV 0 IRR 3 Comay assessme : Mehods We wll sudy fe mehods whch ealuae a surace comay. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao ". 3. Embedded Value Embedded Value rereses a he aluao dae a esmae of he asse alue ad he soc of he surace comay. More recsely he Embedded Value of a lfe offce a a arcular aluao dae s ae o be he sum of he shareholders e asses ad he alue of he busess force a he aluao dae. he alue of -force busess a he aluao dae s he rese alue of fuure rofs eeced o emerge from olces already wre. Where Embedded Value Shareholders Ne Asses he Soc: he alue of he busess -force a he aluao dae Ne Asses share caal solecy caal rof hdde reseres 4444444 24444444 3 surlus Le us see ow hs formula more deal. If we deoe aluao year EV EV a he ed of he year NA Ne Asses a he ed of he year S Soc ealuaes a me year of rof 8
for > sauory rof eeced for he year ealuaed for he whole force busess a he me for sauory rof realsed for he year z- dscou facor wh he Rs Dscou Rae We hae he followg formula for Embedded Value EV NA z z z 44 2443 soc We ow ha z rereses he fuure rof eeced o be geeraed resec of resely force busess ad o be rasferable afer allowg for all relea aes o he rof ad loss accou. I he sum we use o ae oly he fuure rofs o accou. Bu we ca wre more elcly. s ew busess year aluao year sauory rof year for s < sauory rof eeced for he year for he busess wre he year s ealuaed G s for s < e sauory rof realsed he year for he buses wre he year s forr s sauory rof realsed he year for he ew busess Summg he G s o he whole years s we oba he sauory rof of he rof ad loss accou: G s s for If we roduce a a rae ha s ad whe he sauory rofs are ose ad a rae f > 0 0 oherwse We ge he followg formula for Embedded Value 9
[ ] EV > where s called dsrbuable rof of he year. hs s he sauory rof afer aes. 3.. Numercal eamle Le us ae he followg eamle order o llusrae he Embedded Value. Edowme surace 30 20 C 00'000 α 4% o Caal β.5% o Premum γ 0.3% o Caal SM978/83 4% P 3970 α 3.8% β % 6% 8% Ieres o e asses.5% γ 0.2% ae rae 0% he eres o e asses s he afer a esme reur eared by he asses ha suor shareholders e asses. I s o uusual for hs rae of reur o be subsaally below he reur eared o asses suorg surace lables because of asses allocao echques used by comaes. I s commo o assg o-eresbearg asses or lower-yeldg asses o suor shareholders e asses ad o allow he hgher-yeldg asses o bac olcyholder lables. Before showg he chars we hae o oce ha we wll rese a rojeco of he aluao mehods. I realy hese mehods are calculaed each year wh he daa of ha year ad used o comare wh fgures of reous years. I our eamle we are eresed he deelome of he resuls hrough me ad he we suose ha we do o chage he assumos ha he assumos mach wh he realy ad ha here s o ew busess. Wh hese assumos he real rof equals he eeced rof. Soc rofle 0
450 400 8% 350 300 250 200 50 00 50 0 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 We oce ha he rofle s decreasg. hs s because he aual rofs are early cosa ad he each year he soc has oe rof less because here s o ew busess. Embedded Value rofle 000 900 8% 800 700 600 500 400 300 200 00 0 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 Each year he Embedded Value creases because of he eres eared o e asses ad he aual rof.
3..2 Embedded Value adaages Embedded Value aes he fuure rofs of he Prof esg o accou ad he he alue s o oly flueced by he loss of he frs year. Embedded Value allows comarg facal resuls of dffere ds of aces. Vsual rereseao whch seems o be easy o udersad. 3..3 Embedded Value dsadaages Whou ublshg he assumos he resul of he mehod has o real sese. Rs Dscou Rae s o a geeral coce ad furhermore Embedded Value s esecally sese o Rs Dscou Rae. I radoal boo eeg we eer use hs rae. hs rae s oly used Prof esg ad Embedded Value. Embedded Value s sesy o 420.00 400.00 380.00 360.00 340.00 320.00 Embedded Value 8% Embedded Value 0% Year 0 Embedded Value wh of 8% equals 403.6 Embedded Value wh of 0% equals 35.7 3.2 Arasal Value Arasal Value s he eeso of he Embedded Value o he mare alue. So o oba hs alue we hae o cosder he goodwll. Bu he goodwll s a subjece alue whch rereses he alue of he cles he fuure ew busess ec. So hs alue s ery dffcul o ealuae. Arasal Value Embedded Value Goodwll 3.3 Value Added Value Added s a dyamc alue. I s he crease he Embedded Value bewee wo me erods. VA EV EV 2
We saw ha he Embedded Value s he alue of he comay he Arasal Value s he mare alue of he comay ad ow we see he Value Added whch s a dyamc measure cosdered o show how well he comay s dog durg a secfed erod. We wll use ow oly Embedded Value because Arasal Value s more comlcaed o alue because of he goodwll. Bu of course hs mehod ad he followg ca also be calculaed wh Arasal Value. o llusrae he Value Added we ca ae he followg eamle. Suose ha a comay has 00 of equy ad es eeryhg ew busess we could hae for eamle: Begg of year Ed of year Ne asses 00 0 Busess force 0 5 Value Added 5-00 5 Prof ad loss accou could hae show a loss of 00. hrough hs eamle we oce ha he Value Added seems o be more able o show he rofably ha he sauory rofs. 3.3. Numercal eamle Value Added rofle 60 8% 50 40 30 20 0 0 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 Frs year he Value Added s esecally hgh because he comay sells a rofable roduc a hs me. Aferwards here s o ew busess ad he Value Added decreases. Comarso bewee Value Added ad sauory eargs: 3
00 50 0-50 -00-50 -200 8% 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 Sauory eargs Value Added -250-300 -350-400 hs grah s ery eresg because we ca see he dfferece bewee Value Added ad sauory eargs. I hs eamle he wo mehods behae comleely dfferely. he sauory eargs show frs a loss followed by a seres of gas ad he Value Added shows frs a ga followed by a seres of smaller gas. he Value Added seems much more able o show rofably ha he sauory eargs. 3.3.2 Value Added comoes Sarg wh he defo of he Value Added we wll sl he formula fe comoes VA we oe eres o e asses Rs Dscou Rae a rae dded rae D VA EV EV S S ad we rewre he soc a me - o aoher way order o reare he calculao VA D 44444444444444 2444444444444444 3 S S S 44442 44443 S we use he formula of he soc ad we oba 4
5 > > D S VA ad regroug D S VA We use he formula of sauory rof ad we solae he aes s s D s G s G S VA s D s G s G G S VA we arrage he elemes [ ] s D s G s G G G S VA ad we ge fally hs formula [ ] s D s G s G G G S VA where he fe comoes of he Value Added ca be see
VA 444 44 244444 3 eres o e asses G 4243 sauory rof of year for he ew busess of year S 4243 corbuo from force busess [ G ] 44444444 244444444 3 soc of ew busess of year D 444 24443 G s G s caal adjusemes 4 s 444444 24444444 3 444 24444 3 essseme 44444444444444444 244444444444444444 3 corbuo from ew busess chage of assumos ademergece of acualeerece ae relef We hae foud fe comoes of he Value Added whch are he followg: Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusmes Chage of assumos ad emergece of acual eerece 3.4 oal Rae of Reur oal Rae of Reur eresses he crease of Embedded Value as a erceage. RR VA D C EV where D shareholders ddeds a he ed of me C shareholders corbuos a he ed of me I s ecessary o do correcos for ddeds ad shareholder corbuo because he Embedded Value s chaged by hese alues. Whe dded s ad he e asses decrease ad he Embedded Value oo. he shareholder s ew s ha he recees dded ad he Value Added. he we hae o ae accou of he dded he oal Rae of Reur. Whe shareholders mae corbuos he Embedded Value creases bu he shareholder s ew s ha he recees he Value Added less wha he corbues. 6
3.4. Numercal eamle oal Rae of Reur rofle 8% 6% 8% 4% 2% 0% 8% 6% 4% 2% 0% 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 hs rofle seems o be easy o udersad ad allow fg a smle objece. For eamle oe could say e year we hae o reach a oal Rae of Reur equal o he. 4 Crcal Aroach Ul ow we hae see he aluao mehods. Eeryhg seems o be smle ad we are able o show he rofably of a comay. Bu some asecs of hese mehods could be crcsed. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao 2". 4. he roblem he resuls of he aluao mehods deed o he model ad he arameers le he reur o esme he bes esmae moraly ec. hese mehods use always he mea of fuure rss. So he adaage s o oba a uque alue bu he dsadaage s o hde he flucuaos. I realy he flucuaos are due o he model he radomess ad he uceray. o choose a model wh a ew o coceualsg real heomea s a smle aroach whch cao reflec eacly he realy. he radomess s he uforeseeably of ees whch follow a robably fuco. Ee whe we erfecly ow he robably law he effece realsao of he ees cao be deermed. I our model arcular he radomess corresods 7
o he flucuaos of he reur o esme ad he flucuaos of he real umber of deahs. he esmaos we calculae oday are oly mea alue of fuure realsao. he uceray comes from he merfec owledge of he arameers ad her ossble eoluo hrough he me. For eamle we do o ow eacly he real amou of eeses ad hs amou ca follow a fuure ueeced eoluo. Besdes hese flucuaos roblems here s a erreao roblem. he Value Added ad he oal Rae of Reur are ofe cosdered as rofably ools ee hough hese mehods ca ge a false sgal o he rofably of he comay. o dscuss hs erreao roblem we ae he followg umercal eamle Edowme surace 40 25 Caal 00'000 α 5% o Caal γ 0.4% o Caal β cluded γ SM988/93 4% P 332 α 5800 Muao eeses 333 8% Ieres o e asses.5% γ 80 6% ae rae 0% We wll use wo secal cases as follows: A rofable case: Prooro of rof reaed 3% A o rofable case: Prooro of rof reaed 5% he rooro of rof reaed s he erceage of rof ha he surace comay was o ee. hs meas he ar whch s o dsrbued o he sured. Le us see ow he chars hese wo cases. 8
Value Added Profable case No-rofable case 350 350 250 250 50 50 50 50-50 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24-50 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24-50 -50-250 -250 he frs year loos sesble here s o erreao roblem. he surace comay sells a rofable corac whch creases he alue of he comay he frs case. I he secod case he corac s o-rofable ad he alue of he comay decreases. Secod year ad laer. For he frs case we do o oce ay roblem. he Value Added decreases because he comay does o sell ay oher corac. I he secod case he comay does o sell ay oher corac ad he Value Added s ose alhough had sold reously a o-rofable corac. he se esecally bewee he frs ad he secod year s o easy o udersad for he urose of rofably. 9% 8% 7% 6% 5% 4% 3% 2% % 0% -% -2% -3% -4% -5% -6% Profable case 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 oal Rae of Reur 9% 8% 7% 6% 5% 4% 3% 2% % 0% -% -2% -3% -4% -5% -6% No-rofable case 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 We hae eacly he same erreao roblem wh he oal Rae of Reur. I order o udersad wha haes le us aalyse he fgures of he Value Added. 9
Profable case Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusme dded Value Added 0 5400 000 29294 000 34694 228 27499 5287 23440 No-rofable case Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusme dded Value Added 0 5400 000-27304 000-2904 228 2297 5287 892 For he frs year here s o erreao roblem. he dfferece comes from he ew busess ose for he rofable case ad egae for he o-rofable case. For he secod year we hae a erreao roblem. Le us aalyse each comoe of he Value Added: -Ieres o e asses s he same because bous begs oly he hrd year our eamle. -Corbuo from ew busess s he same because we do o sell ay ew coracs. -Caal adjusme s he same because we do o ge ay bous before he hrd year. -he dfferece comes from he corbuo from force busess. Wha s surrsg s ha he o-rofable case hs corbuo s ose ad hs s le a reur effecely he calculao. ha s why he Value Added s ose he orofable case. Fally he roblem of erreao s due o he corbuo from force busess ad more esecally o he Rs Dscou Rae. Le us see ow he fluece of Rs Dscou Rae o Value Added. 700 650 600 550 500 450 400 350 300 250 200 50 00 50 0 Profable case wh 8% 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 700 650 600 550 500 450 400 350 300 250 200 50 00 50 0 Profable case wh 9% 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 he Rs Dscou Rae s a requreme of reur he frs year bu aferwards hs rae becomes a reur o he soc. Afer he frs year he Value Added calculaed wh a of 9% s hgher ha wh a of 8%. hs s really he source of he erreao roblem. 20
4.2 hree ds of aluao We hae o adm ha he Value Added ad he oal Rae of Reur are o able o show drecly he rofably of he comay. Bu he erreao roblem dsaears f we use he aluao mehods he correc coe. Value of a surace comay Icrease of he alue of a comay Profably of a comay 4.2. Value of a comay Of course he alue of a comay s drecly ge by Embedded Value or Arasal Value. 4.2.2 Icrease he alue of a comay For measurg he crease he alue of a comay we hae o aalyse he Value Added ad s comoes eres o e asses corbuo from force busess corbuo from ew busess caal adjusmes chage of assumos ad emergece of acual eerece ad he oal Rae of Reur. We ca aalyse each o o see f s ose or egae. Ad he we ow whch comoe crease decrease or sagae he alue of he comay. he Value Added ges he real crease. he oal Rae of Reur ges he relae crease ad he comoes of he Value Added allow searao of he comoso of he crease. I our reous eamle dese he fac ha he coracs sold do o mee he crera of Ieral Rae of Reur he reur s ose bu smaller ha he. ha s why he comay creases s alue wh hs roduc. 4.2.3 Profably of a comay he roblem of erreao comes also because we do o hae a clear defo of rofably. We wll use he followg defo of rofably. I our coe he rofably s he measure of he acy of a comay coeco wh he ew busess ealuaed hrough he fuure rofs eeced o emerge from he ew busess durg a secfed erod of me. Whe we are eresed he rofably of a surace comay seems o be logcal o be esecally eresed he ew busess creaed durg he secfed erod of me. I our coe we ca aalyse he Ieral Rae of Reur of he ew busess ad s NPV. We ca he hae he followg coclusos: 2
IRR NPV of ew busess Cocluso > >0 Am of reur reached 0<IRR< <0 Am o reached bu ose reur <0 <0 Loss New busess has also a fluece o he admsrae eeses o he ddeds ec bu we cocerae o he aes. 4.3 Fal remars abou crcal aroach We hae see ha he Value Added ad he oal Rae of Reur cao be drecly cosdered as ools for measurg he rofably. We hae see ha he aluao mehods mus be used he rgh coe. We hae o use he comoes of he Value Added. hs s why we hae defed wha we call alue crease of he alue ad rofably of a surace comay or a rof cere. I our coe we ge a defo of rofably. We hae o foud ay ew mehod we jus ela ha he aluao mehods do o always drecly ge he rgh aswer ad ha we hae o use he rgh coe. 5 Sesy Aalyss As we hae already see he resuls of he aluao mehods deed o he model ad he arameers le he reur o esme he bes esmae moraly ec. hese mehods use always he mea of fuure rss. So he adaage s o oba a uque alue bu he dsadaage s o hde he flucuaos. I realy he flucuaos are due o he model he radomess ad he uceray. he uceray comes from he merfec owledge of he arameers ad her ossble eoluo hrough he me. For eamle we do o ow eacly he real amou of eeses ad hs amou ca follow a ueeced fuure eoluo. 5. Aroach he sesy aalyss s used o aalyse he fluece of he uceray he arameers' alues. For hs urose we creae some scearos wh omsc ad essmsc alues of arameers. We suose ha cera rages of arameer alue are ossble ad we es he reacos of he resul of he mehod wh hose modfcaos of arameer alue. wo ways are ossble he successe sesy aalyss ad he smulaeous sesy aalyss. 22
I he successe sesy aalyss he alue of a uque arameer s chaged. he alue of he oher arameers does o chage. he am of hs aalyss s o erac he more flue arameers o he resul of he aluao mehod. I he smulaeous sesy aalyss he alue of he whole arameers s chaged. he am of hs aalyss s o aalyse he wors ad he bes ossble suao ag resecely he essmsc alue of seeral arameers ad ag he omsc alue of seeral arameers. Bu we hae o oce ha some erdeedeces are ossble bewee he arameers. So we hae o model whe s ossble ad relea. I s rue ha he leel of arao of he arameers alue wll fluece he arao he resul of he aluao mehod. Bu o hae a homogeeous comarso we ca ae a cosa erceage of arao for each arameer alue. Of course hs erceage s eerheless arbrary. 5.2 Sesy esmao We wll use curre ecoomc oo: he elascy heorec elascy E R R R Emrcal aromao ˆ E R R R hs s he elascy of he resul R of he aluao mehod eeg wh he arameer. Aferwards we wll oly use he emrcal aromao of he elascy bu o smlfy he erm we wll oly sea abou elascy ad o more abou emrcal aromao of he elascy. We say ha he arameer s elasc f he resul of hs formula s hgher ha ad resecely elasc f he resul of hs formula s lower ha. hs elascy formula s used he successe sesy aalyss bu s ossble o show ha we ca geeralse hs formula for successe sesy aalyss. 5.3 Ierdeedece bewee arameers I our model we hae ae he followg erdeedeces bewee arameers. - We suose ha he eeses deed o he flao ad are erdeede. - he eres rae deeds o flao. - he Rs Dscou Rae ad he eres o e asses deed o he eres rae. - he bous deeds o he bes esmae bass. he followg able shows he arameers whch are chaged he scearos. 23
Parameer Symbol Ierdeedace formula Rs Dscou Rae λ Ieres o e asses Prooro of rof reaed Acquso eeses a me Admsrao eeses a me Muao eeses a me Surreder alue a he ed of year ρ R R J CP CP a&& c FA δ MFA CA FA I FG FG δ MFG I FM S ae rae Dded rae D Bes esmae moraly Aual flao rae I Surreder rae u q FM δ MFM I 5.4 Alcao A sesy aalyss s aled o he Prof esg Embedded Value ad s crease wh four ds of roducs a edowme wh aual remums a edowme wh oe sgle remum a erm surace wh aual remums ad a emorary mmedae lfe auy. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao 3". A successe ad a smulaeous sesy aalyss are doe wh araos of arameer alue of ± 0%. 5.4. Edowme wh aual remums 400 Prof esg for all scearos -00 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24-600 -00-600 -200-2600 Frsly we cao see ay sgfca arao hs char. hs s he radoal rofle of a edowme wh aual remums. he oly scearo whch s clearly 24
dffere from he ohers s he eese scearo. he ohers seem o be close o he referece scearo. Bu f we aalyse he NPV we hae aoher suao. NPV NPV Elascy IRR IRR Elascy Referece scearo 462.2% Omsc eeses 743-6.06 6.2% -4.38 Pessmsc eeses 82-6.06 8.9% -2.06 Omsc Rs Dscou Rae 328-2.9.2% 0.00 Pessmsc Rs Dscou Rae 64-3.27.2% 0.00 Omsc rooro of rof reaed 558 2.06.8% 0.48 Pessmsc rooro of rof reaed 367 2.06 0.7% 0.5 Omsc moraly rae 55 -.4.7% -0.45 Pessmsc moraly rae 40 -.3 0.8% -0.42 Omsc aes 489-0.57.4% -0.626 Pessmsc aes 436-0.57.% -0.628 Omsc flao 438 0.53 0.8% 0.37 Pessmsc flao 483 0.45.6% 0.35 Omsc surreder alue 486 0.50.4% -0.368 Pessms surreder aluec 439-0.50.% -0.373 Omsc surreder rae 47-0.8.3% -0.0435 Pessmsc surreder rae 454-0.7.2% -0.0433 hs elascy of eeses meas ha for eamle a arao of 0% he eeses causes a arao of -60.6% he NPV! I hs able he eeses are clearly he arameer o whch he NPV s mos sese he case of a edowme wh aual remums. As he acquso eeses are mora he frs year ad because oly a ar of s zllmersed he dfferece s arcularly relea for he frs year. Aferwards he dfferece s smaller bu s becomes greaer hrough me. A he ed of he corac he dfferece s aga hgher because flao creases he eeses ad a he same me he aual remums remas always he same. he Rs Dscou Rae he rooro of rof reaed ad he moraly are also cosdered elasc arameers. 25
5.4.2 Edowme wh sgle remum 700 Prof esg for all scéaros 500 300 00 900 700 500 300 00-00 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 he rofle of hs sgle remum edowme roduc s uusual. We do o hae ay al esme ad we hae some losses a he ed of he corac. As before we cao see ay hgh dfferece hs char. he oly scearo ha s clearly dffere from he ohers s he eese scearo. he ohers seem o be closed o he referece scearo. NPV NPV Elascy Referece scearo 2452 Omsc eeses 266-0.85 Pessmsc eeses 2240-0.87 Omsc rooro of rof reaed 265 0.8 Pessmsc rooro of rof reaed 2252 0.82 Omsc flao 2282 0.69 Pessmsc flao 266 0.67 Omsc surreder alue 2532-0.3235 Pessms surreder aluec 2373-0.3240 Omsc Rs Dscou Rae 2395-0.23 Pessmsc Rs Dscou Rae 253-0.25 Omsc aes 2480-0.28 Pessmsc aes 2425-0.28 Omsc moraly rae 248-0.48 Pessmsc moraly rae 2424-0.43 Omsc surreder rae 2457-0.0208 Pessmsc surreder rae 2448-0.0207 26
I hs case we see ha o arameer ca be cosdered elasc. hs s because he NPV s ery hgh he referece scearo. Furhermore he rofle of he sauory eargs are for eamle o sese o he because we hae a hgh ga a he begg ad less hgh amous aferwards. 5.4.3 erm surace wh aual remums 000 Prof esg for all scéaros 500 0 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24-500 -000-500 -2000-2500 -3000-3500 -4000-4500 -5000 I hs case we hae aga a radoal rofle of sauory eargs. he eese scearo s aga he mos flueal. NPV NPV Elascy IRR IRR Elascy Referece scearo 49 2.% Omsc eeses 787-5.54 5.4% -2.67 Pessmsc eeses 52-5.54 9.6% -2.06 Omsc Rs Dscou Rae 873-2.40 2.% 0.00 Pessmsc Rs Dscou Rae 462-2.72 2.% 0.00 Omsc rooro of rof reaed 354.78 2.8% 0.5 Pessmsc rooro of rof reaed 945.78.5% 0.54 Omsc moraly rae 347 -.72 2.7% -0.48 Pessmsc moraly rae 953 -.7.5% -0.50 Omsc flao 264 -.00 2.2% -0.026 Pessmsc flao 039-0.96 2.% -0.028 Omsc aes 205-0.49 2.3% -0.6562 Pessmsc aes 093-0.49.9% -0.6557 Omsc surreder rae 78-0.25 2.2% -0.06944 Pessmsc surreder rae 22 -.024 2.0% -0.06937 Omsc surreder alue 54-0.04 2.% -0.00996 Pessms surreder aluec 45-0.04 2.% -0.00998 27
We hae eacly he same elasc arameers ha he edowme roduc wh aual remums. 5.4.4 emorary mmedae lfe auy 4600 4300 Prof esg for all scéaros 4000 3700 3400 300 2800 2500 2200 900 600 300 000 700 400 00-200 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24-500 -800-00 -400 he rofle of sauory eargs s oce aga dffere. A hgh ga he frs year follows by a seres of losses ad he a seres of gas. hs s rcally due o he bous whch decreases. he eese scearo s always he remarable oe. NPV NPV Elascy Referece scearo 643 Omsc rooro of rof reaed 2046 2.453 Pessmsc rooro of rof reaed 239 2.455 Omsc Rs Dscou Rae 494-0.90 Pessmsc Rs Dscou Rae 825 -. Omsc flao 508 0.82 Pessmsc flao 77 0.78 Omsc eeses 740-0.60 Pessmsc eeses 543-0.6 Omsc aes 700-0.35 Pessmsc aes 585-0.35 Omsc moraly rae 640-0.08 Pessmsc moraly rae 646-0.022 28