On the Determination of Capital Charges in a Discounted Cash Flow Model. Eric R. Ulm Georgia State University

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1 On h Dmnaon o Capal Chags n a Dscound Cash Flow Modl c R. Ulm Goga Sa Unvs

2 Movaon Solvnc II Rqud sss dmnd on a consoldad bass sss allocad o h lns o busnss on a magnal bass Dvson no Rsvs and Capal s ln b ln Do Capal Chags on capal and chang n svs cancl o pomanc analss o ln manags?

3 Movaon Mulpl Canddas o Rsvs: U.S. Sauo Rsvs; U.S. GP Rsvs; U.S. a Rsvs; Fa alu o abls; sss a a somwha consvav solvnc sandad Solvnc II uss 75%; pcd oss und h alsc masu dscound a h sk- a.

4 Pomanc valuaon Incom lss Capal Chags a Rsvs valuaon Rsvs Ya

5 Dscound Cash Flow Modl Ms and Cohn 987 Cummns 990 alo 994 ssums svs a chncal svs.. dscound valu o pcd losss F paam s capal.. asss capal chncal svs. Ovvw n Cummns and Phllps 000

6 ampls Sngl Pmum / Sngl oss CF0 CF CF CF CF 0 - CF 0 P 0 CF P CF CF 0 0

7 ampls Sngl Pmum / Sngl oss 0 P Δ Δ 0 P quvalnl Δ Δ

8 ampls Sngl Pmum / Sngl oss valuaon Rsvs and capal solvs o b nducon 0 0 P 0

9 ampls Sngl Pmum / Sngl oss Mo nuvl... Δ Δ Δ

10 ampls Mulpl Pmum / Mulpl oss Nonsochasc P and.. losss a uncolad and pmums pad wh can... P 0 0 Ohws plac wh n h pmum quaons and wh I n h sv quaon. Mak smla subsuons o P

11 ampls Mulpl Pmum / Mulpl oss Mo nuvl... Dnng Paccall h and on dpnd on h pmums. Δ Δ Δ 0 0 P P Δ P Δ Δ

12 ampls Mulpl Pmum / Mulpl oss P 0 P P P P Δ Δ Δ

13 Solvnc II Con On Pod In on a asss a and labls a 0. Solv P P o nd 0 Pmum s R 0 ξ P P ξ R wh P

14 Solvnc II Con Mulpl Pod as pod s smla: ξ Oh pods qu h dmnaon o M M ~ 0 K nsgh: P h pmum whch would b chagd a m o cov h loss a m mus b M and hs pmum can b ound om h pvous analss. Fnd h mak valus cusvl.

15 Solvnc II Con Mulpl Pod M M M 0 R M P ξ P R ξ 0 sss om

16 Solvnc II Con Mulpl Pod ξ R sss

17 Solvnc II Con Mulpl Pod ann s R R ann Rs R ξ Rs ann valuaon Rsvs ann

18 a Rsvs a q. Pncpl svs a 7%. Guss sss a ampls wo Pod oss 400 ξ ξ 700 6% 0% P 0 P Π ξ P M

19 ampls wo Pod oss Mak alu o abls a ss M P Π 0 M 0

20 ampls wo Pod oss Balanc Sh Ims o wo Pmum wo oss ampl m Δ Δ Capal M Incom Samn Ims o wo Pmum wo oss ampl Cash Flow CF Incom Cash Chang n Capal Chags

21 ampls wo Ya m $00000 ac 000 dncal ndvduals q 0.00 q P0 000Π N ξ N P 980Π N s bnomal wh pobabl 0.05 N s bnomal wh pobabl 0.0 N Π Π

22 ampls wo Ya m M 0 000Π *000 N M N N NΠ 99.5% solvnc a N Π Dmn Π

23 ampls wo Ya m Δ Balanc Sh Ims o m ampl Δ pcd M Capal Incom Samn Ims o m ampl Cash Flow Chang n CF pcd Cash Incom pcd Capal Chags

24 W nd D N ssum Solv o N k 00000ξ N ampls Whol ξ P N N M D N N d N Π N c d N ξd N ~ ~ N ξ D N N c N ξ D N Π a N b N Π N P N N N N N Π k 000 N 0 k k k k k

25 ampls Whol Fnall whw... hn gvs N q p N N M Π ~ p N N p N Π N d N c M d c Π

26 ampls Whol 980 CSO on 40 a old. ssumpons Pmum quvalnc Pncpl $03.30 Sol 99.5% a P 6% $34.95 Sol 99.5% a P 6.5% $7.80 Sol 99.5% a CRM 6.5% $30.37 Sol 99% a P 6% $33.50 Sol 95% a P 6% $9.8

27 ampls Whol Cash Flow pcd Cash CF Incom Chang n pcd Capal Chags Chang n pcd Cash Incom 0 dusd pcd Capal Chags dusd Incom

28 ampls Whol pcd Balanc Sh Ims a Rsvs valuaon Rsvs Mak alus Rqud sss

29 ampls Whol Pomanc valuaon Incom lss Capal Chags a Rsvs valuaon Rsvs Ya

30 ampls GMDB d N S d N q q S M Π λ Π Π 0 S q λ S d σ σ Π ln S d σ σ Π ln

31 ampls GMDB Π N s S σ µ ξ 0 ξ ξ λ s s qma M q S Solvnc con gvs ~ ~ ξ λ Π s S q S

32 ssum ampls GMDB 6% 34% q % λ 0% om opon pcng ho. Π s h paam and quaons gv:.07%

33 ampls GMDB alu sss val Rsv Capal M Sock

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