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, - .., .. (. .) ( , ). . MANAGING LIQUID ASSETS OF A HOLDING: TASKS, ALGORITHMS AND BUSINESS PROCESSES OF CREDIT POLICY SELECTION Balashov V.G., Tokareva G.V. (Dolgoprudnii, Moscow region) Enclosed is conceptual and mathematical of managing liquid assets of a parent company and material flow, accounts payable, accounts attention is focused on decision-making process the most profitable option of borrowed current restitution. problem description and affiliates (funds receivable). Special as to the selection of assets attraction and

. , «» «» : (-, -, 165


2.

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. 1: -

1. . (). 2. (), « » ( ) . () . : 1 ­ , «»; 2 ­ .; 3 ­ «» ( 100% ). 3. : « ?». «», 4. «», 7. 4. (, , .). 5. () . . 5. , 7. 6. . ­ (Cash) ( ). 7. ( , 166


.. . -- -10, 2002, .165-167

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167


2.

- , . , . . 1. . : [0,T]; {Ii(t)} {i(t)} t[0,T]; S (t ) k(t) . {Si*(t)} {Si*(t)} , SAi (T ) CSAi (T ) .
SAi (T ) =
T


t =1

S i (t ) min ; 0
xX

(1) (2)

CSAi (T ) =


t =1

T

CS i (t ) min ; 0
xX

, ­ , . , X s0 = {Si(t);CSi(t)}:
CFSi (t ) = CFi0 +
=1

[(

t

I i ( ) - Ci ( )) + (Si ( ) - CSi ( ))] 0, t [0, T ];
)) ;

(3) (4) (5)


t =1

T

CS i (t ) =



T

t =1

t S i (t ) + ki (t ) ( S i ( ) - CS i ( =1

Si (t ) 0, CS i (t ) 0, t [0, T ] .

(3) ( ), (4) ­
168


.. . -- -10, 2002, .165-169

, [0, T ] , .. . {I (t ), C (t )} . 1: t CF(t)<0. S(t) = -CF(t) {t: CF(t)<0} , S(T) . 2. SA(T) CSA(t) t*, CF (t ) 0, t < t*, t [0, T ], CF (t*) < 0, t [0, T ] CF(t) S(t) {CS(t)} :
0 CF (t ) 0, S (t ) = - CF (t ) CF (t ) < 0, min{CF (t ), KSA(t )} CF (t ) > 0, KSA(t ) - ; CS(t ) = 0 CF (t ) 0.

1. . 1. . 1.1. . : F0, {I(t)}, {C(t)}, t = 1, 2,...,T. 1.2. f(i) = I(1) ­ C(1) CF(1) = CF0 + f(1). 1.3. t. f(t) = I(t) ­ C(t) CF(t) = CF(t-1) + f(t). t = T, , t T, t . 2. . 2.1. . ( ): CF (t ) 0 , t = 1,2,..,T. 2.2. t [0, T ] , .
169


2.

t [0, T ] : CF (t ) < 0 ,

3. 3. . 3.1. t*. CF(t*)< 0,CF(t) 0,t < t*,t [0,T]. 3.2. t = t* S(t*) = -CF(t*). : SA(t) = (1+k(t))S(t*); S(t), I(S(t)) CF. I(S(t*)) = I(t*) + S(t*), F (S (t* ), t* ) = CF(t*) ­ S(t*) = 0. 3.3. t = t+1. t = t*+1 CF(S(t)) = CF(t)+S(t*). 3.4. . CF (S (t ), t ) < 0 , 3.2-3.4 S (t ) = -CF (S (t ), t ) ) KSA(t ) =
=1

(1

t -1

+ k ( ) )S ( ) .

CF (S (t ), t ) = 0, t = t+1 3.1-3.3. CF (S (t ), t ) > 0, CS(t) KSA(t): CS (t ) = min{KSA(t ), CF (S (t ), t ) } KSA(t ) =
=1

(1

t -1

+ k ( ) )(S ( ) - CS ( ) ) .

CS(t) (S (t ), CS (t ) ,t ) =C(t)+CS(t) CF(t): CF (S (t ), CS (t ), t ) =CF (S (t ), t ) - CS(t). t = t +1 3.4 . t = T . CF(T) 0 , {S(t),CS(t)} ­ 1. CF (T ) < 0 , CF (t ) 0 t [0, T ] 1 : {I(t), C(t), k(t)}. 1 ( 3) 2 ( 3), : 1 1, 170


.. . -- -10, 2002, .165-171

SA(T), 1 . , «» : 1 ; 1 ; ; ; . . ­ . , , ( ). , . . : , 0; r; (24%); ( 0% 24%); . , . , ( - ) . n- . , , . TA ( 4- . 1).

171


2.

TA = = rC


i =1

n

rC

i -1

= rC

0

(1
i =1

n

+ (1 - )r

)

i -1

=

0

(1 + (1 - )r )n (1 + (1 - )r )

-1 [1 + (1 - )r = -1 1 -

(

]n

-1 C

)

0

TA c ( 5- . 1).
TA =


i =1

n-1

rCi -1 + rC




n-1

= rC0

(1
i =1

n-1

+ (1 - )r

)

i -1

+ rC0 (1 + (1 - )r

)

n-1

=

[1 + (1 - )r = 1 -

(

]n

-1

- 1 + r (1 + (1 - )r

)

)

n-1

C 0 =

= + r [1 + (1 - )r 1-
1 1) 2) 3) 4) 5) 6) , 7) 8) 1
0

]n
2

-1

-

C 0 . 1-
... n-1 ... n
-2

n
n-2
n-1

1
0

(1 + r )C

(1 + r )C1

... (1 + r )C ... r
n-2

(1 + r )C
r
n-1

n-1

r

0

r
0

2

rC

rC1 rC1
0

... rC

n-2

rC

n-1

rC0
( - )rC
1 = 1 + (1 - - ) r C
1 = 1 + (1 - - )r C
0

... rC

n-2

rC
-2

n-1

( - )rC1
2 = 1 + (1 - )r - C0
2
2

... ( - )rCn

0



n -1

=
n -1

n = 1 + (1 C0 - ) r - C
n 0

0

... 1 + (1 -

- )r

n -1

2 = 1 + (1 - - )r

=
n -1

n =
C
0

... 1 + (1 - C0 - )r

1 + (1 - - )r

C

n

0

172


.. . -- -10, 2002, .165-173

SA . .1).
SA
-

-

­ , (6-

=


i =1

n -1

( - )rCi -1 = ( - )rC0

(1
i =1

n -1

+ (1 - )r

)

i -1

=
-1

= ( - )rC0

(1 + (1

(1 - )r )n-1 - 1 - [1 + (1 - )r = + (1 - )r ) - 1 1-

(

]n

- 1 C0 .

)

P =

TA + SA TA

-

, -

, , , , . [1 + (1 - )r ]n-1 - 1 + 1- - [1 + (1 - )r ]n-1 - 1 + r (1 + (1 - )r )n-1 + 1- P= = [1 + (1 - )r ]n - 1 1-

(

)

(

)

(

)

-1 . - + (1 - )r - 1 , , max P 0 . =
+ (1 - )r )i -1 = - + (1 - )r ]n - + (1 - )r ]n - 1 i =1 (1 - )r = 1 + (1 + (1 - )r ) + (1 + (1 - )r )2 + ... + (1 + (1 - )r [1 + (1 - )r ]n - 1 P=

(1 (1

- ) [1 + (1 - )r

( )([1

]n ]n

) )

(1 (1

- ) [1 + (1 - )r ]n - 1

( )([1



, P 0 = 0. . 2.
173

(

)(

)= 1) ([1

(1

- )r

)

(1

n

)n

-1

).


2.

. 2.



E=

_ CFn+1

._.

- SA

-

CFn+1

_._.

, -

n+1 n+1 . (1 + (1 - )r )[1 + (1 - )r ]n -1 - - [1 + (1 - )r ]n -1 - 1 1- E= = [1 + (1 - )r ]n 1- [1 + (1 - )r ]n + - 1- 1- = . n [1 + (1 - )r ] , , max E 0 . E

(

)



0 =0. , . : , , 0%, , = 24%. ,
174


.. . -- -10, 2002, .165-175

.3., : 1 ­ ; 2 ­ ; 3 ­ () ; 4 ­ ; 5 ­ . , ) ) , .

. 3.

: 1. ­ . , 50% . 2. : 2.1. () , «» , , , .64-66 . 2.3. () ­ .
175


2.

2.4. ( ) , .. ­ , ( ). 3. () , , . , ().

176