The basic financial purpose of an enterprise is maximization of its value. Inventory management should also contribute to realization of this fundamental aim. The enterprise value maximization strategy is executed with a focus on risk and uncertainty. This article presents the consequences for the recipients firm that can result from operating risk that is related to delivery risk generated by the suppliers. The present article offers a method that uses portfolio management theory to chose the suppliersCorporate liquidity, firm value, delivery risk

Michalski, Grzegorz

English

Research Papers in Economics

DECREASING NEGATIVE THE DELIVERY RISK INFLUENCE 
ON THE RECEPIENT'S FIRM VALUE: PORTFOLIO 
APPROACH 
 
Grzegorz Michalski 
Wroclaw University of Economics,  
Department of Corporate Finance and Value Management,  
ul. Komandorska 118/120, p. Z-2, KFPiZW;  
PL53345 Wroclaw, Poland;  
Phone: +48717181717,  
michalskig@ue.wroc.pl;  
http://michalskig.ue.wroc.pl/ 
 
 
 
Abstract: The basic financial purpose of an enterprise is maximization of its 
value.  Inventory  management  should  also  contribute  to  realization  of  this 
fundamental aim. The enterprise value maximization strategy is executed with 
a focus on risk and uncertainty. This article presents the consequences for the 
recipients firm that can result from operating risk that is related to delivery 
risk generated by the suppliers. The present article offers a method that uses 
portfolio management theory to chose the suppliers.  
 
Keywords: Corporate liquidity, firm value, delivery risk 
 
JEL Classifications: G39, G32, G11, M11, D81 
 
1. Introduction 
 
The  basic  financial  purpose  of  an  enterprise  is  maximization  of  its  value. 
Inventory management should also contribute to realization of this fundamental aim. 
Many of the current asset management models that are found in financial management 
literature assume book profit maximization as the basic financial purpose. These book 
profit-based  models  could  be  lacking  in  what  relates  to  another  aim  (i.e., 
maximization  of  enterprise  value).  The  enterprise  value  maximization  strategy  is 
executed with a focus on risk and uncertainty. This article presents the consequences 
for the recipients firm that can result from operating risk that is related to delivery risk 
generated by the suppliers. The present article offers a method that uses portfolio 
management theory to chose the suppliers. 
When entrepreneur chooses the tradesman, should concentrate his attention, 
not only at basic knowledge about the contracting party individual shape parameters 
(i.e.  the  tradesman  financial  situation),  but  also  on  information  from  inventory 
management models.  
The  Economic  Order  Quantity  model  of  inventory  management  is  used  to 
mark the optimum size of delivery and to choose the cheapest deliverer. Both of these 
choices should guarantee minimization of total costs of investments in inventories. 
   
Fig 1. Economic Order Quantity model. 
where: LIL - Low Inventory Level (Precautionary Inventory Level); AIL – Average 
Inventory Level; HIL – High Inventory Level; Q – Order Quantity (Q = HIL – LIL).   
source: [2, p. 538]. 
 
On fig 1. is shown the way the EOQ (and VBEOQ) model works. Q could be 
calculated as: 
u
z
a
z
opt K
K P
v C
K P
Q EOQ
 


 
 
2 2
, 
(1) 
where:   EOQ  –  target  (optimal)  order  quantity  (economic  order 
quantity), P – yearly demand for optimized inventories, Kz – creating inventories costs 
(fixed cost of one order), Ku – operating costs of maintaining inventories (without 
costs of maintaining safety/precautionary inventories LIL), Ca – percentage rate of 
operating costs of maintaining inventories (with financial/alternative costs of capital 
and without costs of maintaining safety/precautionary inventories LIL), v – unit price 
(cost) of ordered inventories. 
 
The percentage share of retaining the reserves comes from the fact that the 
costs of retaining the reserves increase proportionally to the level of reserves In the 
enterprise. Its share is a sum of the following costs: alternative (resulting from the 
possibility of their potential use somewhere else but without cost of capital financing 
firm),  storage,  logistics  and  internal  transport  within  the  factory  of  the  reserves, 
insurance, decay. 
 
a b z C v z
Q
K
Q
P
TCI   




    
2
, 
(2) 
where: TCI – total reserves costs, Q – magnitude of the part of delivery, zb – 
the level of safety margin. 
From the point of view of maximizing the enterprise value a part of delivery 
can be determined based on the formula for VBEOQ: 
 
    T C k v
P K T
VBEOQ
Z
   
   

1
1 2
 
(3) 
where: k – alternative cost (equal to the enterprise financing capital), VBEOQ 
–  optimal  magnitude  of  single  order  from  the  point  of  view  of  maximizing  the 
enterprise value, C – percentage rate of operating costs of maintaining inventories (without  financial/alternative  costs  of  capital  and  without  costs  of  maintaining 
safety/precautionary inventories LIL). 
 
C v z
Q
K
Q
P
TCI b z   




    
2
, 
(4) 
And: 
   
    T C C k v
P K K T
VBEOQ
Z Z
    
    

1
1 2
# *
* #
*#  
(5) 
where: K
#
z – tax-deductible creating inventories costs (fixed cost of one order), 
K
*
z – non- tax-deductible creating inventories costs (fixed cost of one order), C
# – 
percentage rate of tax-deductible operating costs of maintaining inventories (without 
financial/alternative  costs  of  capital  and  without  costs  of  maintaining 
safety/precautionary  inventories  LIL),  C
*  –  percentage  rate  of  non-tax-deductible 
operating  costs  of  maintaining  inventories  (without  financial/alternative  costs  of 
capital and without costs of maintaining safety/precautionary inventories LIL).    
And: 
* # * #
2 2
C v z
Q
C v z
Q
K
Q
P
K
Q
P
TCI b b z z   




     




        
(6) 
 
The problem, we are going to deal with in this paper is to select a counterpart 
amongst the suppliers in a situation where the parameters we know carry the risk 
resulting from deliveries out of schedule.  
 
Example  1.  Enterprise  X  producing  special  fireproof  curtains  uses  raw 
material D-18. The annual demand for this raw material is  8000 m
3. There are two 
suppliers (A and B) on the market offering similar delivery terms. The price of the 
material  for  both  of  them  is  3000$  for  m
3,  the  lead-time  is  20  days,  the  cost  of 
inventory retaining is 38%, the cost of enterprise financing capital  is 30%, effective 
tax rate is 19%, the costs of ordering is 200$ and the cost of  lack of reserves is 
5000 000$. The analysis of recommendation given by the companies showed that both 
suppliers were not equally reliable. Supplier A was nearly perfect, supplier B often 
did not deliver on time, he happened to show up 4 days before the agreed date , but 
equally often used to come 8 days later. 
Based  on  the  gathered  data  it  was  estimated  the  standard  deviation  of  the 
delivery time in case of supplier A was 4 days, and for supplier B 6 days. In order to 
evaluate  who  is  more  reliable  it  is  necessary  to  determine  the  safety  margin  for 
supplier A and then for supplier B. The next step is to check the impact of suppliers 
risk on the enterprise value. We assume that the enterprise in order to estimate the 
optimal order magnitude uses the VBEOQ. model 
 
   
7 , 37
19 , 0 1 38 , 0 3 , 0 3000
8000 200 19 , 0 1 2

   
   
  B A VBEOQ VBEOQ m
3 
Differences in reliability of deliveries have a great impact on different levels 
of safety margins required for suppliers A and B. For this purpose the following 
formula is used [3, p. 57]: 
bz
b K P
v s Q C
s Z

    
   
2
ln 2
2  
(7) where: s  –  standard  deviation  for  reserves  usage,  Kbz  –  cost  of  lack  of 
inventory reserves. 
 
In order to use the formula it is necessary to exchange the deviation of delivery 
time  to  deviation  of  raw  material  use.  It  is  known  average  daily  use  is 
8000/360 = 22,2 m
3. Therefore 4 days deviation for delivery date is equal to deviation 
of use equal to  88,8 m
3. Therefore, for such a situation the safety margin will be 
equal to : 
63 , 362
000 5000 8000
1416 , 3 2 3000 8 , 88 7 , 37 38 , 0
ln 8 , 88 2
2 

    
    A Z m
3. 
In this case the level of  resources tied in the reserves is: 
440 1144 63 , 362
2
7 , 37
3000  




    A ZAP $, 
Next case reflects a situation in which the entrepreneur uses the services from 
company B. So the standard deviation will be 6×(8000/360) = 133,3 m
3. 
Therefore reserves safety margin will be: 
531
000 5000 8000
1416 , 3 2 3000 3 , 133 7 , 37 38 , 0
ln 3 , 133 2
2 

    
    B Z m
3. 
In this case the level of  resources tied in the reserves is: 
550 1649 531
2
7 , 37
3000  




    B ZAP $, 
Comparing this magnitude to the level of reserves in situation where one 
would have used supplier A it is obvious that the increase of money resources tied in 
the reserves will be: 
110 505 440 1144 550 1649     B A ZAP $. 
The last stage is to compare what impact the risk generated by the counterparts 
– suppliers has on the value of the enterprise. Therefore we estimate the level of total 
costs of reserves: 
328 477 38 , 0 3000 63 , 362
2
7 , 37
200
7 , 37
8000
   




     A TCI $, 
269 669 38 , 0 3000 531
2
7 , 37
200
7 , 37
8000
   




     B TCI $, 
941 191 328 477 269 669     B A TCI $. 
Obtained results will be used for estimation of fluctuations in the enterprise 
value: 
   
351 1023
3 , 0
19 , 0 1 941 191
110 505  
  
    B A V $. 
It is apparent that it is better to select counterpart – supplier A because selection of 
supplier B may result in destruction of enterprise value.  
 
2. Suppliers` portfolio 
 
Usually  the  enterprise’s  suppliers  have  materials  and  stock  from  the  same 
source. It happens though, that their sources of supply are different and therefore the 
risk of deliveries related to individual suppliers is different. f such a thing occurs, it 
may  be  possible  to  use  elements  taken  from  the  portfolio  theory  for  supplier’s evaluation.  Sometimes  the  counterparts  ,  who  although  may  be  have  virtues  who 
exclude them from being suppliers of services in the beginning (like supplier B in 
example B), it may be possible that having considered the risk of the buyer it may turn 
out that on the contrary they decrease or stabilize the risk level [4, p. 48-52].  
 
Portfolio is a set of assets (for example in a non accountant sense : suppliers). 
The theory of portfolio management is based on the rate of advantages drawn from 
buying from particular supplier, informing about the relation of advantage generated 
by such a purchase to the outlay related to such a purchase.  
The measure allowing the measurement of risk connected to costs from 
particular buyer may be defined as this variation:  
  

  
m
i
i i R R p V
1
2
  

   
m
i
i i R R p V s
1
2
 
(8) 
where: pi – probability of occurrence of the given situation estimated from 
historical data.  
In connection to the information about what potential advantages might be 
brought by giving a loan to a particular buyer, it is possible to estimate the variation 
coefficient: : 
R
s
c 
 
(9) 
The next element is a correlation of benefits from purchase from particular 
supplier  with  benefits  from  this  purchase  from  other  suppliers.  The  correlation 
coefficient is usually the measure of such a correlation:  
   
2 1
1
2 2 1 1
2 . 1 s s
R R R R p
m
i
i i i

   


 
 
(10) 
where:  2 . 1   - correlation coefficient of benefits from purchase from the first 
and  second  supplier;  R1  –  expected  rate  of  benefits  from  purchasing  from  first 
supplier; R2 – o expected rate of benefits from purchasing from the second supplier; s1 
–  standard  deviation  for  the  first  supplier  s2  –  standard  deviation  for  the  second 
supplier; R1i – possible rates of benefits from the purchases from the first supplier; R2i 
–  possible  rates  of  benefits  from  the  purchases  from  the  second  supplier;  pi  – 
probability of occurrence of possible rates of benefits from supplies. 
 
3. Portfolio of two suppliers (groups of suppliers).  
 
Example 2. The enterprise uses two suppliers. On of them operates in sector 
A,  the  other  represents  sector  B.  The  use  of  portfolio  idea  is  useful  when  the 
correlation between the benefits from purchases from these suppliers is negative. We 
can follow this in the picture below.  
Fig. 2. Relation between benefit and risk for portfolio of two suppliers at 
different correlation coefficients (equal to 1, (-1) or 0).  
source: own study. 
 
Case  1.  The  correlation  coefficient  between  benefits  from  purchases  from 
supplier A and B equals to 1. The picture shows that at positive correlation  near to 1 
there is no possibility to seek advantages resulting from diversification.  
Case  2.  Correlation  coefficient  equal  to  –1.  Ideal  negative  correlation.  All 
possible portfolios  at correlation coefficient equal to –1 are contained on the broken 
line A-A/B1-A/B2-B. Points “A” and “B” represent single-components portfolios (eg. 
Using only supplier A). As we see, when we move away from point “A” and increase 
the share of deliveries performed by “B” the risk S decreases and benefits R increases. 
This happens until point A/B1 . If this share is exceeded the risk of portfolio will 
increase together with the increase of income. As we see it is no substantiated to have 
only supplier A in the portfolio because at identical risk portfolio A/B2 offers greater 
benefits.    
Case 3. Correlation coefficient equals 0. It is a situation in which the benefits 
from supplier A and supplier B are not connected to each other. In this situation only 
partial risk reduction is possible. Reasonable entrepreneur should not select any of the 
portfolios  of  dues  lying  on  A-A/B3  arc,  because  it  always  possible  to  find  more 
advantageous complement on  A/B3 – A/B4 arc which at the same risk s yields higher 
benefits R.  
 
4. Using the elements of portfolio theory for selection of suppliers   
 
Skilful construction of portfolio of two (groups) of suppliers may lead to a 
considerable reduction of risk. Inclusion of second component into single-component 
portfolio (which like in example 1 so far consisted of only one better supplier A and 
accepting deliveries from less risky supplier) nearly always leads to reduction of risk, 
sometimes even at simultaneous increase of benefit rate of portfolio. 
Example  3.  (continuation  of  the  previous  example)  After  assessment  of 
supplier A and B , the entrepreneur noticed that  the delays  connected to services 
provided by suppliers A and B are negatively correlated with each other, because their 
sources of supply are different when troubles with deliveries from first source can be 
expected, the other source does not pose a risk of such difficulties.  Thanks to that we 
can expect a decrease of risk of non forward deliveries . Both suppliers acquire the 
material  D-18  based  on  different  technologies.  Therefore  one  can  expect  that  the 
impact of deliveries risk on the receiver can be decreased due suing the service of 
both  suppliers,  because  the  correlation  of  distribution  of  forward  deliveries  of 
suppliers A and B is negative and is equal to –0.56. The orders will be placed in 
quantities and frequency resulting from VBEOQ model. The orders will be realized 
by both suppliers: A and B equal shares of 18,85 m
3. . In order to estimate new level of safety margin it is necessary to use the equation determining the total standard 
deviation [3, p. 60]: 
B A B A B A T s s s s s &
2 2 2          (11) 
where: sT  –  total  standard  deviation,  sA  –  standard  deviation  of  the  first 
distribution, sB – standard deviation of the second distribution,  B A&   – correlation 
coefficient between the first and second distribution.  
 
Assuming that one-day deviation is equal to deviation of use equal to 11,1 m
3; 
the safety margin is:: 
6 , 55 ) 56 , 0 ( 6 , 66 4 , 44 2 6 , 66 4 , 44
2 2         T s  
3 , 233
000 5000 8000
1416 , 3 2 3000 6 , 55 7 , 37 38 , 0
ln 6 , 55 2
2
& 

    
    B A Z m
3. 
In this case the level of money resources tied in the reserves will be: 
450 756 3 , 233
2
7 , 37
3000 &  




    B A ZAP $, 
comparing this magnitude to the level of reserves in a situation where we 
would have used supplier A only it is obvious that the increase of money tied in the 
reserves will be equal to: 
) 990 387 ( 440 1144 450 756 &       B A A ZAP $. 
The last stage is to compare what impact the risk generated by the 
counterparts-suppliers has on the enterprise value. Therefore we estimate the total 
level of costs of reserves: 
891 329 38 , 0 3000 3 , 233
2
7 , 37
200
7 , 37
8000
&    




     B A TCI $, 
) 437 147 ( 328 477 891 329 &       B A A TCI $. 
Obtained results are used for estimation of changes of the enterprise value.  
   
070 786
3 , 0
19 , 0 1 437 147
990 387 & 
 
     B A A V $. 
As we see in particular conditions it is possible to get benefits from using both 
suppliers (better A and worse B). Such a choice may result in increase of enterprise 
value.  
 
BIBLIOGRAPHY 
 
[1]  Fabozzi  F.  J.,  G.  Fong,  Zarządzanie  portfelem  inwestycji  finansowych 
przynoszących stały dochód, WN PWN, Warszawa 2000. 
[2]  Kalberg  J.  G.,  K.  L.  Parkinson,  Corporate  liquidity:  Management  and 
Measurment, IRWIN, Homewood 1993. 
[3]  Piotrowska  M.,  Finanse  spółek.  Krótkoterminowe  decyzje  finansowe, 
Wydawnictwo AE, Wrocław 1997. 
[4] Pritchard C.L., Zarządzanie ryzykiem w projektach. Teoria i praktyka, MT&DC, 
Wig-Press, Warszawa 2001. 

Decreasing negative the delivery risk influence on the recepient's firm value: Portfolio approach

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