Nglilen ciiu trao iii
C0 sii ly thuyet ciia ky thuat chon m^u thiing ke theo don vj tien te suf dung trong kiem toan hao cao tai chinh
S TS. Dodn Thj Ngoc Trai*
Doi vdi cic kiem toin vien (KTV) dgc lap. vice sH dung k/ thuat chon mau tron^ kiem toan bao da tai chinh (DCfC) la het siic can thiet ke ci chon mau tha^ kc va phi (A<% ^e. Tu/ nhien. vice thieu mot tai lieu hudng din ve mat ly thuyet da khien ho gap kho khin khi van dung ky thuat chon miu trong cac chuong trinh kiem toan do cac Cty kiem toin ldn tren the gidi xay dung. Can chi ra cosS ly thuyet ciia Icy thuat ebon miu thong ke. dac biet la ky thuat chpn miu thong kc theo doa vi tien be daag duoc cac cdng ty kiem toan ddc lap sU dung K>ngm.
K ; thuat thdng ke va cdch tiep c3n kiem toan BCTC dua tren rdi ro
Md hinh rui ro kidm todn A R = a R x C 3 i ) x D R Trong do:
- AR: Rui ro kidm todn (Audit risk)
- IR: Rui ro tidm tang (hiherent risk)
- CR: Rui ro kidm soat (Control risk)
DR: Rui ro phdt hien (Detection risk)
Trong thuc td, g i ^ rui ro ti^m tdng va rui ro kidm sodt cd mdi quan he phu thudc 2 chidu, khi md doanh nghidp (I^^O thudng cd xu hudng thidt lap cdc thu tue kiem sodt ndi bd (KSNB) chat che ndu riii ro tidm tdng duoc ddnh gid la cao, va nguoc lai, ndu cac thd tue KSNB la chktciie, dac bigt Id thili tue kidm sodt ngan chan, thi r6i ro ti^m tdng se thdp hon. VI vay, hai loai rui ro nay diudng duoc ddnh gid kdt hop, vd md hinh tia. ro kidm todn thudng ducfc diSn ta nhu sau:
AR = RMMTiDR
RMM Risk of Material
Misstatement (Rdi ro sai sdt trong yeu)
RMM = JRxCR (Inherent Risk X Control Risk)
DR cung ed Xhi duoc chi tiet thdnh ri^i ro do thu tue phan tich va rui ro do thft nghidm chi tiet nhu sau:
DR=APxTD
WcA AP: Analytical Procedures Risk, TD: Test of DetaUs Risk
Trong dd, TD hen quan true tiep ddn ed mdu trong thi^ nghiSm chi tidt, vdi di^u ki£n lixi ro khdng do chon mdu duoc xem la khdng ddngkd.
Ngudi ta da sit dung cdng thiic Bayes trong xdc sudt thdng kd. Co sd ciua cdng th^c Bayes Id xae sudt dd 2 bidn ed ddng thdi xay ra c6 thd xem Id kdt qua ci^a xac sudt xay ra 1 trong 2 bidn cd vdi xdc sudt cd didu kidn eua bidn cd th£ 2, khi bidn cd thfl nhdt dd xay ra.
Ndu goi H la ti Id sai sdt cd trong 1 thanh phdn ciia' BCTC (ching han nhu 1TK) vd E la bang
chthig da duoc thu thap. Mdt each tdng quat, xdc sudt d^ ti 16 sai sdt dd xay ra, vdi bdng chi5ng da cd, cd the ti'nh lai bang each sd dung cdng thiic Bayes nhu sau:
P(HIE) = P(H)*P(EIH)/P{E) Trong dd, P(H) duoc goi la xac sudt tien nghiem, P(HIE) duoc gpi la xac sudt hau nghiSm cua ti 16 sai sdt, P(E!H) id xdc sudt tim thdy bang chiing E khi H la ti 16 sai sdt that su, va duoc gpi la xac sudt hop ly cua bang chiing.
KTV cd thd thu thap them bdng chiing cho den khi rui ro kiem todn du thdp nhu mong mudn. Nguoc lai, KTV cd thd tfnh todn lupng bang chiing cdn thu thap bd sung di dat dugc miic rui ro kiem todn cd the chdp nhan duoc.
Cac qui tudt phan phdi xac sudt sJjT dung trong chon mau kiem todn thdng ke
Cdc ky hieu duoc sii dung trong phdn nay nhu sau:
T: Miic sai sdt cd th^ bd qua a : Rui ro tU chdi sai, nghTa ia xdc sudt ket qud mdu lam cho KTV ddnh gid sai id tdng sai sdt hoac ti li sai sot VMOT qud mOc co thi bo qua, do do tU chdi sai tdng the
P : Rui ro chdp nhdn sai, nghia Id xdc sudt kdt qud mdu ldm cho KTV ddnh gid sai id tdng sai sdt hodc ti 14 sai sot nho hcfn mite CO the bo qua, do do chdp nhdn sai tdng thi
M: tdng sdtiin cua tdng the
" Khoa Ke todn, Dai hoc Kinh te - Dai hoc Da Nang
i eAe^o^.^imi W ^Uem lomt id^mta H/2042
Nghien cihi trao dtfl
N. sfypfidn id cua iSng th^
L: sd phdn tii sai sdt Irong tdng Ihi. vd Lj- Id sd sai sot c6 thC'bd qua cm tSng the
n cd mdu
p: ti 1^ sai sol ciia tStig thi. do vdy, pg, pj, vd py ldn lum Id ti U sai sdl dukieh, ti li sai sdl cd thi bd qua vd gidi iiqn Iren cua li li sai sdt
k sd luong sai sdl Irong mdu, do vdy, k£ Id sd limjg sai sdl difkiih irong mdu.vd cung cd the Id ky hieu long sai sdt Irong ky thudt chon mdu iheo dm vi lien le
R • sd li/mg sai sdt trung binh Irong cdc mdu cd n.
do vay, rj vd rjj Idn luot Id sd lUOng sai .sdl trung binh cd tiii bo qua vd gidi iian Iren cua ti li sai sdt Irung binh.
MUS: Monetary unit sampling - Ky thuat ehpn mdu theo don vi u^n 16.
Trong kidm todn tdi chinh, KTV thudng sir dung ky thuat chon mdu ddi vdi thir nghiem ki^m sodt (khi thu tue ksNB di lai ddu vdt v6 su thuc hien thii luc tr6n chiing tCt, sd sdch) vd thd nghi6m chi tidt sd du va nghiep vu. Ddi vdi thii nghiem kidm sodt, KTV se ap dung ky thuat chon mdu thudc linh, cdn ddi vdi ihir nghiem chi tidt sd du vd nghiep vu, KTV se sii dung ky thuat chpn mdu theo bidn sd ed didn, vdi cdc cdch udc luong tmng binh don vi, udc luong ti sd va udc lupng sai bidt, hoac sii dung ky thuat chpn mdu theo don vi ti^n te (Monetary unit sam- pling - MUS). Ndu sii dung ky thuSt chon mdu thdng ke, KTV se phdi lua chpn cdc phdn tCr vdo mdu theo phuong phdp chpn mdu ngdu nhien, bao gdm cdch chpn theo bang sd ngdu nhien, sii dung chutmg trinh chpn sd ngdu nhien tren mdy tCnh vd chpn mdu hd thdng, sau dd van dung cdc qui luat phdn phdi xdc sudt phii hop dd tinh cd mdu cdn thidt cung nhu ddnh gid kdt qud tdr mdu.
Iheo tdi lieu thuydt minh ky thudt sii dung trong Hudng ddn kidm todn Audit Sampling cfia AICPA, cdc qui luat phan phdi xdc su^t cd thd sCr dung trong chpn mdu kidm t c ^ thdng ke Id phan ph^t sifiu bdi, phan phdi nhi thiic (hay phan ph^i Beta A6i vdi bidn ngdu nhidn Udn tue) vd jMn phdi Poisson (phdn phdi Ganuna ddi vdi bidn ngdu nhidn lidn tue).
Hdm phan phdi xdc sudt sidu bdi diln td xdc sudt md k sai sdt se dupc chpn ra tCt 1 mdu ngdu nhidn kich thudc n, dupc chpn theo phuong thiic khdng hoan lai, tir tdng thd gdm N phdn tix c6 chlia L sai sdt.
XAc sudt dd 1 mdu cd n cd chlia ddng k sai sdt dupe xdc dinh bang hdm phan ph^i xdc sudt sidu b$i nhusau:
Hyp(k.n.L,N) = -
C
k.n.L.N-0,1,2,...;L£ N;k£L;
n'(N-L)^kSn£N
(Johnson, Kemp, and Kotz 2005. 251).
Tdng xdc sudt (xdc sudt tfch luy) dd sd sai sdt trong mdu ft hon hoac bdng k dupe tinh theo cdng thiic
CHyp(k,n.L.N)= ^l^Hyp(i,n,L,N)
Cd mdu cdn thidt se dupc tfnh tit cdng thiic i^y, khi xdc sudt tfch luj 6i sd sai sdl du kidn trong miu ft hon hoac bdng sd sai i^iam cd thd bd qua phdi nhd hon hoac bdng 3 (rui ro ehdp nhdn sai).
CHyp(kE,n.LT,N) i P
Hdm phan phdi xdc sud^t nhi thtic didn td xdc sudt md k sai sdt se dupc chpn ra tii I mdu ngdu nhien kich thudc n, dupc chpn theo phuong thi^ hodn lai, tii tdng thd gdm N phdn tir cd chlia L sai sdL Trong trudng hpp ndy, xdc sudt dd 1 phdn t& sai sdt dupc chpn ra Id ddc lap vdi nhau, vd ddu bdng p=L /N.Do vay, cdng thiic tfnh xdc sudt tfch luy dd sd sai sdt trong mdu it hon hoac bdng k Id don gian hem.
Bin(k.n.p)=&yi}-py~^
CBin(k.n.p) = J,]^Bin{i,n,p)= ^'^Ctp'il-pT' trong dd k = 0,1,..., n
Cd mdu cdn thidt cung dupc tfnh theo edch nhu tren, dd Id cd mdu n \6i thidu thoa man b& ddng tfilic
CBin(ks.n,pr)^^
Cd thd sir dung cdc hdm dupc xdy dung san trong Excel dd tfnh cd mdu cdn thidt ndy (sit dung hdm BinomSampIe, sau dd cd mdu tfnh dupc se dupc lam trdn ddn sd nguydn gdn nhdt).
n=BinomSam[de(P Jt£ ,pj-)
Phan phdi nhi thiic dupc xem Id phan ^Si xdp xi vd than trpng hon jhOn phdi sidu bdi, vl cd mdu cdn thidt tfnh dupc ldn hon. Cd thd sii dung [didn ^Si nhi thtic dd thay thd cho phdn phdi sidu bdi khi &od n ^ didu kidn n< 0,1N (Johnson. Kemp, and Kotz 2005, 269), vi khi dd xdc sudt dd 1 phdn t^ dupc chpn ra ^ phdn tut sai sdt theo cdch chpn cd hodn lai va khdng hodn lai khdc biet khdng ddng kd. Do cdng thiic tinh todn cd mdu cdn thidt. gidi h ^ trdn ciia tii Id sai pham don gidn hon vd cd thd sii dung Excel dd t ^ , nen trong lt$ thudt chon mdu thudc tfnh. KTV thudng sii
( M^'lomi W ^U^ iodn id'4^d*i^ H/^f^X
Nghign curu trao d^l
dung phan phdi nhi thiic.
Phan phdi nhi thiic cd mdi quan hd vdi phan phdi beta, mdt phan phdi xdc sudt lifin tue. Phan phdi beta dien ta xac sudt ma ti le sai sdt cua tdng th^ (k^ hidu Id p) cd thd nhd hon hoac bang 1 ti 16 da cho trong khoang til 0 ddn 1, vdi cd mdu da cho va sd sai sdt da dupc chon ra.
Phan phdi beta cd th^ dupc xac dinh v^ mat toan hpc bang hdm mat dd xac sudt:
b(p.I+k,n-k)=(n-k)( l)p*{l~ pJ'"'' 0 <p <1, n= 0,1,2.3 ,- i!:-0,;,2 «
(Degroot 2002, 303) Day la phan phdi beta
b(p,0,X) khi 6,= 1+k va A = n-k (k Id sd nguyen) va xdc sudt tfch luy la
B(p,l+k,n-k) = j''b{t,l + j,n~k)}t'Si< p<\
"Xdc sudt nhi thiic tich luy cd the duoc vie't dudi dqng cua phdn phdi beta
Cbin(k,n,p)= }'B(p,l+k.n-k)
Khi sir dung ky thuat chpn mdu theo don vi tien te, KTV cd th^ six dung phan phdi beta dd lap ke hoach chpn mdu va ddnh gia kdt qua mdu, vi each tinh don gian hon la sii dung true tidp phan phdi nhi thlie.
Rian phdi Poisson la 1 phan phdi xac sudt quan trpng nay sinh trong nhieu qud trinh ngdu nhien cd xac sudt xay ra nhd, thudng dupc gpi la qua trinh PoissoiL Day la trudng hpp gidi han cua phan phdi nhi thiic, khi
n-*oo va /7-*0 dinp = r dupc giii cd dinh, vdi r Id sd sai pham tmng binh trong mdu va r > 0, k=0,1,2.. .IL
Taed:Bm(k,n,p)= C * / 7 * ( l - ; ? ) " " * Khi n->" va /?->0 dinp = r dupc giii cd dinh thi:
Hdm phan phdi xdc sudt Poisson md td xdc sudt ma it sai sdt se dupc chpn ra trong mdu c3 o khi sd lupng sai sdt trung binh trong mdu ed n la r.
Poi(k,r)= —e"^ r>0,k=O,l,2...ii. r*
Xdc sudt tich luj dd sd sai sdt trong mdu Id ft hon hoac bang k Id:
Phan phdi Poisson cung edp 1 xdp xi kha tdt cho phan phdi nhi thiic khi
n > 20 vd p <0,05
(Freund 1972, 83). Do tinh don gian trong viec xac dinh cd mdu va danh gia kdt qud mdu, nSn phan phdi ndy dupc sii dung rdng rai trong chpn mdu kiem toan, nhdt Id trong ky thuat chon mdu theo don vi tien te, khi di^u kien trSn dupc dap ling de dang.
Phan phdi Poisson cd mdi quan he vdi 1 phan phdi xdc sudt lien tue la phan phdi Gamma. Phan phdi nay md td xac sudt ma /•, sd trong binh sai sdt trong mdu cd «, cd the' nhd hon hoac bdng 1 gia iri da cho, vdi sd lupng sai sdl da dupc chpn ra.
Phan phdi Gamma dupc xac dinh bdng ham mat dd xac sudt
g(x,Q,X), cd cdng thiic tdng quat nhu sau:
g(x;e,X.): : -^^ -^ . . ,X>
xr(e)
0;9,X>0 Trong dd, 6 la tham sd dang va X la tham sd ti 16.
Khi X =1, tham sd ti 16 bidn mdt va phan phdi nay dupc gpi la phan phdi Gamma tieu chudn. Fhfai phdi Gamma don gian nhdt chfnh la phan phdi mu, cd tham sd dang 6 =1.
Khi tham sd ti 16 X =lva tham sd dang 9 = 1+k, vdi k la sd sai sdt xudt hien trong mdu, bidn sd la r, hdm mat dd xdc sudt cua phan ph^i nay trd thdnh g(r,l+k) =
r(l + it)' Vdir(l+k)= JfVfift
(Johnson, Kotz, and Balakrishnan 1994,337) Ndu tdt ca sai sdt ddu la 100%, ham xac sudt tich luy se la
G(r,l+k)=£^
C P o i ( k j ) = X o ^ ^ ' ( ' ' ' ' )
Mdi quan he chii ydu giQa phan phdi Poisson vk phan phdi Gamma la d ch6 xdc sudt tfch luy Poisson cd thd dupc vidt dudi dang phan p h ^ Gamma. Vdi k la sd sai sdt trong mdu, ta cd
CPoi(k,r)=l- G(r,l+k) (Raiffa and Schlaifer 2000, 224).
Ddng thiic tr6n rdt hiiu fch trong viec lap kd hoach vd ddnh gia kdt qud mdu trong ky thuat chon mdu thudc tfnh cd chpn mdu theo don vi tidn td.
(CdnnOa)
i cA/tj^'^aem W ^^ietn tomt, A6'ikmt^ H/2042