Intermediate Financial Management (with Thomson One)

804 • Part 6 Working Capital Management
these steady-state assumptions, the firm’s cash position will resemble the situation
shown in Figure 23-1.
If our illustrative firm started at Time 0 with a cash balance of C $300,000,
and if its outflows exceeded its inflows by $100,000 per week, then its cash balance
would drop to zero at the end of Week 3, and its average cash balance would
be C/2 $300,000/2 $150,000. Therefore, at the end of Week 3 the firm
would have to replenish its cash balance, either by selling marketable securities, if
it had any, or by borrowing.
If C were set at a higher level, say, $600,000, then the cash supply would last
longer (six weeks), and the firm would have to sell securities (or borrow) less frequently.
However, its average cash balance would rise from $150,000 to
$300,000. Brokerage or some other type of transactions cost must be incurred to
sell securities (or to borrow), so holding larger cash balances will lower the transactions
costs associated with obtaining cash. On the other hand, cash provides no
income, so the larger the average cash balance, the higher the opportunity cost,
which is the return that could have been earned on securities or other assets held
in lieu of cash. Thus, we have the situation that is graphed in Figure 23-2. The
optimal cash balance is found by using the following variables and equations:
C amount of cash raised by selling marketable securities or by borrowing.
C/2 average cash balance.
C* optimal amount of cash to be raised by selling marketable securities or
by borrowing.
C*/2 optimal average cash balance.
F fixed costs of selling securities or of obtaining a loan.
Figure 23-1
Maximum Cash = C
Average Cash = C/2
Cash Balances under the Baumol Model’s Assumptions
Cash Balances ($)
Ending Cash = 0
0 1 2 3 4 5 6 7 8 9 10 11 12
Weeks