Appendix 27A
DETERMINING THE TARGET CASH BALANCE
SLIDES
CHAPTER ORGANIZATION
27A.1 The Basic Idea
27A.2 The BAT Model
27A.3 The Miller-Orr Model: A More General Approach
27A.4 Implications of the BAT and Miller-Orr Models
27A.5 Other Factors Influencing the Target Cash Balance
ANNOTATED CHAPTER OUTLINE
Lecture Note: In most chapters, the appendixes are not covered in the instructor’s
manual, but rather are available only via the internet. However, given the prevalence of
the content in Appendix 27A, we provide a discussion here, along with accompanying
PowerPoint slides.
Target cash balance – the desired cash balance as determined by
the trade-off between carrying costs and storage costs.
Adjustment costs – costs associated with holding low levels of
cash; shortage costs.
27A.1 Costs of Holding Cash
27A.2 The BAT Model
27A.3 The BAT Model
27A.4 The BAT Model
27A.5 The BAT Model
27A.6 The Miller-Orr Model
27A.7 The Miller-Orr Model Math
27A.8 Implications of the Miller-Orr Model
27A.9 Implications of the Miller-Orr Model
27A.10 Other Factors Influencing the Target Cash Balance
With a flexible working capital policy, the trade-off is between the
opportunity cost of cash balances and the adjustment costs of
buying, selling and managing securities.
A. The Basic Idea
Slide 27A.1 Costs of Holding Cash
B. The BAT (Baumol-Allais-Tobin) Model
Slide 27A.2 –
Slide 27A.5 The BAT Model
Define:
C = optimal cash transfer amount (amount of marketable
securities to sell to raise cash)
F = fixed cost of selling securities
T = cash needed for transactions over entire planning period
R = opportunity cost of cash (interest rate on marketable
securities)
Trading cost = # of transactions*cost per transfer = (T/C)*F
Total cost = opportunity cost + trading cost = (C/2)R + (T/C)F
To find the optimal transfer amount, take a first derivative of
the cost function relative to C and set it equal to zero. You can
also find it by setting opportunity cost = trading cost and
solving for C.
Method 1:
∂TC
∂C=R
2+−FT
C2=0
R
2=FT
C2
C2=2FT
R
2FT
Method 2:
C
2R=T
CF
C2=2TF
R
C=
√
2FT
R
Example: Hermes Co. has cash outflows of $500 per day, the
interest rate is 10% and the fixed transfer cost is $25.
T = 365*500 = 182,500
F = 25
R = .1
C=
√
2(25)(182 ,500 )
.1
C=$9,552 . 49
C. The Miller-Orr Model: A More General Approach
Slide 27A.6 The Miller-Orr Model
Slide 27A.7 The Miller-Orr Model Math
The Miller-Orr model offers a general approach to handling
uncertain cash flows.
The basic idea:
When cash reaches U*, the firm transfers cash (buys securities)
Using the model:
Given the variance (2) of cash flow (“cash flow” refers to both
the amounts that go into and come out of the cash balance) per
period, the interest rate per period (period may be a day, week,
or month as long as the two are consistent), and L, the target
balance and upper limit, are given by:
Example: Suppose F = $25, R = 1% per month, and the
D. Implications of the BAT and Miller-Orr Models
Slide 27A.8 –
Slide 27A.9 Implications of the Miller-Orr Model
From both:
-The higher the interest rate (opportunity cost), the lower the
target balance
-The higher the transaction cost, the higher the target balance
From Miller-Orr:
-The greater the variability of cash flows, the higher the target
balance
E. Other Factors Influencing the Target Cash Balance
-Flexible versus restrictive short-term financing policy
-Compensating balance requirements
-The number and complexity of checking accounts
Slide 27A.10 Other Factors Influencing the Target Cash Balance
You can access Appendix 27B (Adjustable Rate Preferred Stock, Auction Rate Preferred
Stock, and Floating-Rate Certificates of Deposit) at www.mhhe.com/rwj.