國立中興大學行銷系
2013.01.16
BUDGET ALLOCATION
FOR CUSTOMER
ACQUISITION AND RETENTION
TO BALANCE
MARKET SHARE GROWTH AND CUSTOMER EQUITY
Hsiu-Yuan Tsao
1
ABSTRACT
• Blattberg and Deighton (1996) used a decisioncalculus approach to construct a simple model, the
BD Model, which helps managers find the optimal
balance between spending on acquisition and
retention to maximize the customer equity.
– Customer Equity v.s Market Value
– Optimal Budget Allocation to Maximized Customer Equity
– Drivers of Customer Equity
• However, little explicit research has simultaneously
addressed the question of dividing spending between
acquisition and retention and balancing the
objectives of short-term market share growth and
long-term customer equity.
.
Blattberg, R. C. and Deighton, J. (1996), “Manage Marketing by the
Customer Equity Test,” Harvard Business Review, 74(4), 136–144.
2
the BD model
(Blattberg and Deighton 1996)
r  CRr 1-exp  kr R  
R  (1/ k r )*ln((CRr  r ) / CRr )
a  CRa 1-exp  ka A  
A  (1/ k a )*ln((CRa  a) / CRa )
Where r=Retention rate
R=Retention spending
CR=Ceiling rate
k= Accelerating rate
Where a=Acquisition rate
A=Acquisition spending
CR=Ceiling rate
k= Accelerating rate
Parameter CR (acquisition or retention ceiling rate) is the
manager’s direct assessment of the maximum proportion
of targeted prospects converted on condition that there
is no limit to spending.
In addition, k and can be determined once the manager
decides the spending levels and rates for retention and
acquisition.
3
CRr=Ceiling rate
250
200
CRa=Ceiling rate
150
R
100
A
kr= Accelerating rate
ka= Accelerating rate
50
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
4
the BD model
(Blattberg and Deighton 1996)
CE  a[CLV ]  A
CE  a[M  (M  R / r )*(r / (1  d  r ))]  A
Where
CE=Customer Equity
a= acquisition rate
M=margin
R=Retention spending
r=Retention rate
d=discounted rate
A=Acquisition spending
5
segment-based market share model
• Thomas (2001) claimed that the BD model ignores the fact that
spending on acquisition may affect the relationship between
spending on retention and the retention rate.
• Thus, the market share of the next period for the th brand is a
compound of retainer, and newly acquired segments as follows:
Mksit  Mksit 1 * g
N
Mksit  Mksit 1 * rit   Mks jt 1 * ait ,(i  j )
j 1
ait  [Mksit  (Mksit 1 * rit )] / (1  Mksit 1 )
Thomas, J. (2001), “A Methodology for Linking Customer Acquisition to
Customer Retention,” Journal of Marketing Research, 38 (May), 262–268.
6
The optimization process
CE  a[ M  ( M  R / r )*(r / (1  d  r ))]  A
Where
CE=Customer Equity -> Objective Function (MAX)
a= acquisition rate
-> the function of SBMS
M=margin
-> Constant (assumed M=$50)
R=Retention spending -> Decision Variable
r=Retention rate
-> the function of R
d=discounted rate
-> Constant (assumed 1.10)
A=Acquisition spending -> the function of a
The preset objective of market share is 0.10 because of
the assumed growth rate of g=1.15.
R->r->a->A
g->Market Share
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The Differential Costs of
Marginal Effect
A common business theory suggests, It costs five times more
to acquire a new customer than to retain a customer”
(Blattberg & Deighton, 1996; Pfeifer, 2005).
Research investigating the effect of the unit cost of
marginal effect for acquisition and retention programs on
consumer profitability and market share growth are rare.
1
Rmc 
kr *(CRr  r )
1
Amc 
kr *(CRr  r )
For details, please refer to Pfeifer (2005).
Pfeifer, P. (2005). The optimal ratio of acquisition and retention costs. Journal
of Targeting, Measurement and Analysis for Marketing, 13(2), 179–188.
8
Data & Method
• We test the model and method developed
in this study on the numerical example
found in the paper in which the BD model
was originally proposed.
• the optimal solution for the objective
function to maximize CE can be obtained
by the nonlinear programming of an
evolutionary algorithm provided by
Microsoft Excel Solver 2011
9
Result
Complete results for the numerical example of BD Model
Item #
1 CR
2K
Acquisition
Retention Common
0.4
0.7
0.13863
0.08473
3M
50
4d
0.1
5g
1.5
6 Mksit–1
0.1
7 Mksit
0.15
R->r->a->A
8 Optimal Spending (A,R) 2.61616612 10.194929
9 Optimal Rate (a,r)
0.12167613 0.4049148
g->Market Share
10 CLV
64.459829
11 CE
5.2270564
10
Result
The ratio of marginal cost, market share growth and CLV at optimality
a
r
Amc
Rmc
m
CLV
CE
1
0.10
0.12
23.85
20.42
1.17
53.93
3.24
1.5
0.12
0.40
25.92
40.00
0.65
64.46
5.23
2
0.17
0.47
31.31
52.07
0.60
66.53
7.31
2.5
0.22
0.50
40.57
59.09
0.69
67.03
9.04
3
0.28
0.52
58.04
65.04
0.89
67.19
10.09
3.16
0.29
0.52
67.32
67.22
1.00
67.20
10.18
3.5
0.33
0.54
101.49
73.62
1.38
67.11
9.61
4
0.38
0.59
342.86
106.66
3.21
65.07
3.42
g
11
Conclusion
Amc=Rmc=CLV
Optimal Budget to Maximized CE
12
Conclusion
High
High
Ceiling Rate
CR
Retention Rate(r)
low
high
g
Market Share Growth
low Customer Equity low
Acquisition Rate (a)
low
Low
high
MC
High
Marginal Cost
Figure 2. Optimal budget allocation.
13
Appreciate for
your kind attention
and
Q & A
14