Cash Budgeting Teaching Notes
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Cash Budgeting
The cash budget is a primary tool of short-term financial planning. It allows managers to identify short-term financing needs. It helps identify when short-term borrowing will be needed. The cash budget basically records estimates of cash receipts and disbursements.
1.1
Cash Budgeting: An Example
Fun Toys’ cash inflows during the coming year are expected to be as follows: Quarter
Sales (in millions of $) 1.1.1
First
Second
Third
Fourth
100
200
150
100
Cash Budgeting: An Example (Cash Inflows)
Fun Toys sells to department stores on credit, and has a 90-day collection policy: Collections = Last quarter’s sales Receivables at the end of a quarter = Quarter’s sales 1.1.2
Cash Budgeting: An Example (Cash Inflows)
Assume sales of $100 million during the quarter before First. 1
Quarter
1.1.3
First
Second
Third
Fourth
Sales (in millions of $)
100
200
150
100
Collections
100
100
200
150
Beginning receivables
100
100
200
150
Ending receivables
100
200
150
100
Cash Budgeting: An Example (Cash Outflows)
Assume Payments = Last quarter’s purchases Purchases = 1/2 of next quarter’s sales forecast Wages and other expenses: Normal costs of doing business (e.g. 1/5 of sales) Capital expenditures: $100M in the last quarter Long-term financing: Interest and dividend payments, $10M each quarter Quarter First
Second
Third
Fourth
Sales (in millions of $)
100
200
150
100
Purchases
100
75
50
50
A/P payments
50
100
75
50
Wages and other
20
40
30
20
0
0
0
100
L-T financing
10
10
10
10
Total uses of cash
80
150
115
180
Uses of cash
Capital expenditures
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1.1.4
Cash Budgeting: An Example (The Cash Balance) Quarter First
Second
Third
Fourth
100
100
200
150
80
150
115
180
20
(50)
85
(30)
20
(30)
55
25
5
5
5
5
15
(35)
50
20
Total cash receipts Total cash disbursements Net cash flow Cumulative excess cash flow Minimum cash balance Cumulative surplus
1.2
Short-Term Financial Plan
The plan previously described is nothing more than a “ best guess”. One can go further than the best guess by making a “what-if”, or “scenario”, analysis. A scenario analysis investigates more than one scenarios. Sensitivity analysis can also be used in financial planning. Simulation analysis combines both scenario analysis and sensitivity analysis.
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Chapter 28: Cash Management
Most large Canadian corporations hold around 3 percent of their assets in highly liquid form: Cash and marketable securities. What are the costs and benefits of holding cash? How to determine the appropriate target cash balance?
2.1
Reasons for Holding Cash
Cash is needed to pay wages, bills, taxes, etc. Cash inflows and outflows are not perfectly synchronized and thus some level of cash holdings is necessary to serve as a buffer.
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When the firm runs out of cash, it has to sell marketable securities, which involves trading costs.
2.2
Costs of Holding Cash
The main cost of holding cash is the loss in return had the money been invested in either securities or profitable projects. This is an opportunity cost. The greater the cash balance, the greater the opportunity costs.
2.3
The Baumol Model
C ≡ cash balance when cash is replenished. D ≡ net cash disbursements during a period (1 week, say). n ≡ number of periods within a year. F ≡ fixed cost of selling securities to replenish cash. K ≡ opportunity cost per dollar of cash held.
Cash is replenished when the cash balance is zero. Total cash disbursements during the year: nD Number of times cash has to be replenished during a year: Cost of selling securities during the year:
nD C
×F
Average amount of cash held throughout the year: Opportunity cost of cash during the year:
C 2
nD C
C 2
×K
Total costs of holding cash: CK nDF + . 2 C The optimal cash balance minimizes costs of holding cash: d CK nDF K nDF + = − = 0. dC 2 C 2 (C ∗ )2 ∗ C=C
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This gives us r C∗ = 2.3.1
2nDF . K
The Baumol Model: An Example
D = $600 per week, K = 0.10, F = $1 Opportunity costs: C
C/2
CK/2
$4,800
$2,400
$240
2,400
1,200
120
1,200
600
60
600
300
30
300
150
15
nD = 52 × 600 = $31, 200. Trading costs: nD
C
nDF/C
$31,200 $4,800
$6.50
31,200
2,400
13.00
31,200
1,200
26.00
31,200
600
52.00
31,200
300
104.00
Total costs: C
Total costs
$4,800
$246.50
2,400
133.00
1,200
86.00
600
82.00
300
119.00 5
Optimal cash balance: r C∗ =
2nDF = K
r
2 × 52 × 600 × 1 = $789.94. 0.10
Limitations of the model: • Constant disbursement rate. • No cash receipts. • No safety stock.
2.4
The Miller-Orr Model
Z ≡ target cash balance. H ≡ upper limit to the cash balance. L ≡ lower limit to the cash balance. As long as the cash balance is between H and L, the firm makes no transaction. If the cash balance reaches H, a dollar amount H − Z of marketable securities is purchased. If the cash balance reaches L, a dollar amount Z − L of marketable securities is sold. F ≡ fixed cost of buying or selling marketable securities. K ≡ period interest rate on marketable securities. Net cash flows per period are random, with expectation zero and variance σ 2 . L is taken as given, and the values of Z and H are chosen to minimize expected total costs of holding cash. This gives r Z
∗
= L +
3
3F σ 2 4K
and
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H ∗ = 3Z ∗ − 2L.
2.4.1
The Miller-Orr Model: An Example
Suppose F = $1, L = 0, σ = $2, the annual interest rate on marketable securities is 10% and a period is one day. (1 + K)365 = 1.1
⇒
K = 0.0002612,
σ 2 = 22 = 4, Z∗ = 0 +
q 3
3×1×4 4×0.0002612
= $22.57,
H ∗ = 3Z ∗ − 2L = 3 × 22.57 = $67.71. 2.4.2
The Miller-Orr Model: Empirical Evidence
Miller-Orr test: The daily cash balances predicted by the model were much lower than what firms actually held. Other tests have provided support to the theory. However, simple rules of thumb do as good as the model itself.
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