1.
ASSUMPTIONS
(current assets shaded)
Cash & Equivalents
Accounts Receivable
Inventory
Net Fixed Assets
Total Assets
(current liabilities shaded)
Accounts Payable
Notes Payable
Accrued Operating
Exp.
Long-Term Debt
Shareholders Equity
Total Liabilities &
NW
Revenues (Sales)
Cost of Goods Sold
Operating Expenses
Depreciation
Interest
Taxes
Net Profit
Dividends
Cash
Flow
NI
Dep
ChgAR
ChgInv
ChgAP
ChgACC
OCF
Tax
rate =
Balance Sheets
2007
$75
300
150
525
$1,050
2008
$75
400
250
575
$1,300
2009
$90
600
350
610
$1,650
2010
$100
550
250
540
$1,440
2011
$100
500
250
465
$1,315
$125
165
$175
162
$250
178
$225
136
$200
99
60
161
165
89
76
500
200
400
402
300
757.2
100
890.2
50
890.2
$1,050
$1,300
$1,650
$1,440
$1,315
Income Statements
$3,000 $2,000
1,200
800
895
750
65
70
28
25
325
142
487.2
213
132
80
$1,500
600
725
75
10
36
54
54
$1,500
600
600
35
30
94
141
40
$2,250
900
797
50
33
188
282
80
141
35
282
50
100
100
$50
101
283
n/a
n/a
n/a
n/a
Cash-Based Ratios
CCE (decimal)
Cash Ratio (decimal)
Cash Burn Rate (days)
NLB ($)
2008
0.12577778
0.05769231
30.4166667
-87
487.2
65
200
100
$75
4
331.2
213
70
(50)
(100)
($25)
(76)
332
54
75
(50)
0
($25)
(13)
141
2009
2010
2011
0.1104
0.166
0.094
0.0545455 0.06944 0.07605
27.375 45.625 60.8333
-88
-36
1
0.4
Discuss and interpret: Except for the CCE, the ratios suggest increases
in the cash ratio, burn rate, and NLB. Although the firm appears to be less
efficient at converting revenues into cash flow, the overall liquidity
positon has improved over the sample period.
2. a.
b.
3.
A desired cash burn rate of 250 days and no change in COGS implies that
the
firm have cash holdings equal to
411.0
This value implies that cash
holdings would need to increase by
$311.0 from the end of 2011.
Assuming that the firm cannot accumulate the needed cash to achieve a
cash
then management must reduce COGS
BR of
250
to
YEAR
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Exp 2013
Rev 2013
NCF ($M)
15
0
-1
2
4
8
0
2
-1
5
8.1
6.8
Cash holdings & credit lines =
Expected NCF
Std. Dev. NCF
Lambda
Probibility of illiquid
Probibility of liquid
3.4
4.7370877
1.9210115
2.74%
97.26%
Lambda
Probibility of illiquid
Probibility of liquid
1.6465813
4.98%
95.02%
Liquidity Scenario
4.
Cash + Unused Credit lines
Anticipated Net Cash Flow
Standard Deviation of NCF
Lambda (λ)
FIRM
FIRM A
FIRM B
C
$500
$1,000
$100
$3,000
$200 $1,500
$2,127
$729
$972
1.65
1.65
1.65
BR =
$146
1 $M
250
Based on λ, all firms have equal liquidity. Initially, this result may seem surprising
given that Firm B has the smallest liquidity position ($1,200), relative to Firms A and
C. However, further inspection indicates that this lower level of liquidity is warranted
given the less variable nature of Firm B’s net cash flows.
5. a.
b.
Maximum acceptable probability of illiquidity
Cash holdings
Expected next period cash flow
Standard deviation of cash flow
Lambda (λ)
2.25%
$500
$650
$1,400
2.0046545
Minimum available credit line
2.004 = (500 + Credit Line* +
$1,656.52 650)/1,400
Maximum acceptable probability of illiquidity
Cash holdings
Expected next period cash flow
Standard deviation of cash flow
Lambda (λ)
5.00%
$500
$650
$1,400
1.6448536
Minimum available credit line
1.645 = (500 + Credit Line* +
$1,152.80 650)/1,400
ASSUMPTIONS:
annual disbursements, TCN
fixed transaction cost, F
annual opportunity rate, k
minimum cash balance
variance of daily net cash flows
lower control limit
8.
a.
$5,000,000
$75
12.00%
$0
$5,000,000
$0.00
Calculating the cash return level using the Miller-Orr model
Z* = ((3 x $75 x $5,000,000)/(4 x .12/365))^(1/3)
Z* =
$9,493
b.
Calculating the average cash balance using Miller-Orr model
average cash balance = (4 / 3)(Z*) + LCL =
$12,657.27
c.
Explanation and use of findings
Assuming that the LCL = $0, Z* is the dollar return point. When the current cash
balance hits the UCL, the amount of securities to purchase is the dollar amount that
will bring the cash balance down to the Z* level.
d.
Effect of a change in variance of daily net cash flows
annual disbursements, TCN
$5,000,000
fixed transaction cost, F
$75
annual opportunity rate, k
12.00%
minimum cash balance
$0
variance of daily net cash flows
$10,000,000
lower control limit
$0.00
Z* =
$11,960
higher than
The cash return level is only
26%
previously.
e.
Miller-Orr results versus Baumol results
Miller-Orr cash return level =
Baumol cash return level =
Baumol, average cash balance
Miller-Orr, average cash balance
estimated variance of daily cash
flows
standard deviation of cash flows
$9,493
$79,057
$39,528
$12,657
$5,000,000
$2,236