Solutions to Problems: Chapter 12
1. Developing a simple cash-forecasting template.
ASSUMPTIONS:
Item
Cash receipts
- Cash disbursements
= Cash flow
+ Beginning cash
= Ending cash
June
July
August
$375.00 $345.00 $450.00
$295.00 $425.00 $535.00
$80.00 ($80.00) ($85.00)
$35.00 $115.00
$35.00
$115.00 $35.00 ($50.00)
Cash flow is the difference between cash receipts and
disbursements for a given period.
Beginning cash in one period is last period's ending cash. Ending cash is beginning cash
plus that period's cash flow (recognize that you could be adding a negative flow).
The forecast indicates that cash receipts will not cover disbursements in July and August,
that the cash balance will be drawn down to
become negative in August. The company will need to borrow
just to have a zero cash balance at the end of August, assuming the forecast is accurate.
$35.00
in July and will even
$50.00
2. Omega, Inc. - using the normal distribution table in forecasting.
ASSUMPTIONS:
Average cash position has been
Standard deviation of cash has been
Distribution of cash positions is approximately normal.
Minimum cash balance is
The Z for zero cash would be
standard deviations below the expected cash position
$300,000
$275,000
$0
1.0909
Probability of running short of cash:
0.1377
The normal probability approximation shows that there is a probability of
13.77%
in the left tail of the distribution. The company has almost a
14%
probability of running out of cash in any month. On the other hand, the
. If the manager
probability of not running out of cash is
86.23%
wants
to reduce the probability of running short on cash, she needs to increase the
expected cash position by borrowing or by having a prearranged line of credit.
3. Beach Top Boats - sales forecast for upcoming year.
ASSUMPTIONS:
Cash Collections
30 day Collections
60 day Collections
Purchases/Forecasted current month sales
Purchases/Forecasted next month sales
Required minimum cash
balance
Percent cash
purchases
Beginning Cash:
Memo: Sales
Cash
Lag 1 Mth
Lag 2 Mth
Interest income
Asset sales
Cash Receipts (CR)
Memo: Purchases (.35*St + .35*St-1)
Cash Purchases
Lag 1-Month Purchases (1*Pt-1)
Jul
Aug
75.00
3.75
63.00
3.15
33.75
0.05
0.45
0.47
0.5
0.5
$100
0%
Cash Budget
Sep
Oct
165.00
57.00
40.00
2.85
2.00
28.35
25.65
35.25
29.61
0.00
35.00
92.26
48.50
36.00
0.00
0.00
48.50
Nov
Dec
208.76 159.15
32.00 45.00
1.60
2.25
18.00 14.40
26.79 18.80
15.00
0.00
0.00
0.00
61.39 35.45
38.50 42.50
0.00
0.00
36.00 38.50
Jan
40
Principal repayment
Interest payment
Tax payment
Assets acquired
Cash Disbursements (CD)
Net cash flow (CR - CD)
Ending cash balance (Beg.+NCF)
- Minimum cash balance
= Surplus / (Shortage)
165.00
0.00
0.00
0.00
0.00
48.50
43.76
208.76
100.00
108.76
0.00
0.00
0.00
75.00
111.00
-49.61
159.15
100.00
59.15
165.00
20.00
40.00
0.00
263.50
-228.05
-68.90
100.00
-168.90
Interpretation: Beach Top has a surplus (invested balance)
of $89 in October,
which drops to $39 in November. In December, cash
disbursements far exceed cash
receipts (NCF = -$228) so the company must sell off the remaining $39 of investments
and draw down their credit line in the amount of $189. Historical cash flow studies
generally forewarn the cash manager of this type of seasonal effect.
If arranging a credit line, be sure to look at earlier parts of the year, but also make
sure that somewhat more than the anticipated need of $189 be arranged in negotiations
with the bank or other financing source. If only $189 in credit is established, one
would be assuming perfect forecast accuracy, which is clearly an heroic assumption.
4. Cash collection forecast.
ASSUMPTIONS:
Cash Sales
Credit Sales:
Lag 1 Month (.55*70%)
Lag 2 Months (.30*70%)
Lag 3 Months (.15*70%)
Total
55%
30%
15%
30.00%
70.00%
38.50%
21.00%
10.50%
100.00%
June cash collection forecast is based on June sales (cash sales), May sales (Lag 1-month),
January - June sales (actual)
Jan
220,000
Feb
140,000
Mar
150,000
Apr
140,000
May
170,000
June
150,000
April sales (Lag 2-Months), and March sales (Lag 3-Months).
Cash collected in June =
$155,600
5. Using the distribution method to forecast
payroll clearings.
ASSUMPTIONS:
1. Amount of payroll checks issued on Monday, April 30:
2. Historical check clearing data (past four payroll check issuances).
$1,750,000
Days after
issuance
Payroll #1
1
2
3
4
5+
65%
32%
2%
1%
0%
Proportion clearing:
Payroll Payroll
Payroll
#2
#3
#4
60%
58%
66%
33%
33%
32%
6%
5%
2%
1%
3%
0%
0%
1%
0%
First, determine the average for each day (fill in far right column, as shown above).
Then, distribute the $1,750,000 check issue across those days:
Day
Tues.
Wed.
Thurs.
Fri.
Clearing
$1,089,375
$568,750
$65,625
$21,875
$1,745,625
Notice the slight difference -- due to the fact that Payroll #3 did not fully
clear within four days. We could subjectively increase each day's clearing by an
adjustment factor ($1,750,000 / $1,745,625), but since the reason for the
Average
Proportion:
0.62
0.33
0.04
0.01
0.00
1.00
difference is a late clearing, we'll add the $4,375 to the Friday clearing, giving us
$26,250 for Friday.