Finance Assignment - Treasury Management
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ch.-4.docx4.1 Operating Cycle and Cash Cycle
Short-term finance is about the current or day-to-day financial management of a company. These operations create short-term cash fluctuations for a company that are generally uncertain. The financial manager at a corporation has to make sure that there is adequate amount of cash available at all times. It is also desirable to keep the cash flows synchronous and predictable.
Figure 4.1 illustrates in a schematic way the flow of goods and funds through a corporation. We can assume the company to be a furniture maker. It buys raw material, which is various types of wood, fabrics, finishing products, and other material. It gets the raw material throughout the year from different manufacturers. The company sells the finished furniture to various large retail chains, such as Sears, or Macy’s in that year.
When the firm receives the raw material, it does not pay the invoice immediately. Instead, it takes advantage of the trade credit and pays the bill after an agreed upon delay. We define the time difference between receiving the invoice and paying it, the accounts payable period, payables period, or days payable outstanding .
1. Firm buys raw material
61
A. Places order
B. Stock arrives
4. Firm sells finished goods
5. Firm receives cash for the sales
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Inventory period Accounts receivable period Operating cycle |
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Accounts payable period |
Cash |
cycle |
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2. Firm receives invoice
3. Firm pays cash for raw material
Fig. 4.1: Inventory period, accounts receivable period, accounts payable period, cash cycle, and operating cycle
Converting the raw material into furniture also takes time. The firms try to minimize this time but it is impossible to reduce it beyond a certain point. Eventually, the firm sells the finished goods, but it does not get cash for the sales immediately. The time interval
between getting the raw material and converting it into finished goods is the inventory period, or days in inventory.
The furniture maker sells the furniture at a certain time and waits for the payment to arrive. This waiting period between the delivery of the furniture and the receipt of its payment is known as the receivables period, or days sales outstanding . It could be several weeks. The companies have to manage their receivables period carefully and keep it reasonably short.
The sum of the inventory period and the receivables period is equal to one operating cycle. During this period, the manufacturer converts raw material into finished goods and converts finished goods into cash. Of course, the company needs cash to pay its workers, its suppliers, its interest payments, and its taxes. It is essential to have a steady flow of funds to run the business smoothly and efficiently.
The cash cycle, or cash conversion cycle is the time interval between the point when the company pays cash for the raw materials and finally receives cash for the finished goods.
In Fig. (4.1) we note the following:
1. Inventory period = time between arrival of raw material and the finished products sold.
2. Accounts receivable period = time between finished goods sold and cash received.
3. Accounts payable period = time between receipt for invoice for raw material and the payment of this invoice.
4. Cash cycle = time between cash paid for raw materials and cash received for finished goods sold.
5. Operating cycle = time between the firm receives invoice for raw materials and the firm receives cash for finished goods sold.
The relationship between these periods is as follows:
Treasury Management
4. Financial Planning and Control
Inventory period + Accounts
receivable period
= Accounts payable period
+ Cash cycle = Operating cycle
It is important to keep track of the cash flow in a corporation and make sure that cash is available whenever it is needed. One useful analysis depends on the length of the operating cycle and the cash cycle at a firm.
It is possible to find the length of various periods in the operations of a corporation by analyzing its accounting data. The following example will help understand the procedure for calculating these values. Consider the accounting data for Asquith Company, namely its balance sheet and its income statement, as shown in Table 4.1 and Table 4.2.
Machinery
1,500
800
Intangibles
100
100
Table 4.1: Balance Sheet of Asquith Corporation
Asquith Corporation
12/31/09
12/31/08
Assets $ ,000 $ ,000
Current Assets
Cash $ 610 $ 500
Marketable securities (at cost) 500 450
Accounts receivable (less allowance for bad debts) 2,000 1,600
Inventories 3,000 2,000
Total current assets $6,110 $4,550
Fixed Assets
Land $ 450 $ 450
Building 4,000 4,000
Office equipment 50 50
Less accumulated depreciation -2,000 -1,700
Net fixed assets 4,000 3,600
Prepayments and deferred charges 400 300
Total assets 10,610 8,550
Asquith Corporation 12/31/09 12/31/08
Liabilities $ ,000 $ ,000
Current liabilities
Accounts payable 1,000 750
Notes payable 1,500 500
Accrued expenses payable 250 225
Taxes payable 250 225
Total current liabilities 3,000 1,700
Long-term liabilities
First mortgage bonds, 5%, due 2025 3,000 3,000
Deferred taxes 600 600
Total Liabilities 6,600 5,300
Common stock, $5 par value, 300,000 shares 1,500 1,500
Capital surplus 500 500
Accumulated retained earnings 2,010 1,250
Total stockholders’ equity 4,010 3,250
Total liabilities and stockholders’ equity 10,610 8,550
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Asquith Corporation Consolidated Income Statement Net sales Cost of sales and operating expenses: Cost of goods sold Depreciation Selling and administrative expenses Operating profit Other income Dividends and interest Total income from operations Less, interest on bonds and other liabilities Income before provision for taxes Provision for income taxes (40%) Net income Dividends paid out Retained earnings |
2009 $ ,000 11,500
-8,200 -300 -1400 1,600
50 1,650 -300 1,350 -540 810 -50 760 |
2008 $ ,000 10,700
-7,680 -275 -1325 1,420
50 1,470 -150 1,320 -528 792 -42 750 |
Table 4.2: Income statement of Asquith Corporation
The cash cycle and the operating cycle for Asquith are found as follows: Average inventory = ½($3 million + $2 million) = $2.5 million
Cost of goods sold in a year
$8.2 million
Inventory turnover ratio =
Average inventory = $2.5 million = 3.28
Days in inventory =
365 days
3.28 = 111.3 days ♥
Another way to calculate the inventory period is to find the ratio between the average inventory during a given year (in dollars) and the cost of goods sold (in dollars). This will give the fraction of the year that the goods remain in inventory (in years). In this problem, it is
$2.5 million
Inventory period = $8.2 million = .3049 years = .3049(365) days = 111.3 days ♥
Next, we have to find the accounts receivable period. We can do this as follows. Average accounts receivable = ½($2 million + $1.6 million) = $1.8 million
Credit sales in a year Accounts receivable turnover = Average accounts receivable =
$11.5 million
$1.8 million = 6.389
Days in receivable =
365 days
6.389 = 57.13 days ♥
One can find the accounts receivable period by calculating the ratio between the average amount of receivable during a year (in dollars) and the total credit sales in that year (in dollars). The result is in years. For instance, we can do the previous calculation as
$1.8 million
Receivables period = $11.5 million years = .1565 years = .1565(365) = 57.13 days ♥
Next, we have to find the accounts payable period. One can do it as follows. Average accounts payable = ½($1 million + $0.75 million) = $0.875 million
Cost of goods sold
$8.2 million
Accounts payable turnover =
Average payables = $0.875 million = 9.371
Days in payable =
365 days
9.371 = 38.95 days ♥
The other way to calculate the payables period is to find the ratio between the average amount of payables during a year (in dollars) and the cost of goods sold during that year
(in dollars). This gives the payables period in years. You can change it to days by multiplying the result by 365. Following this procedure, we get
Payables period =
$0.875 million
$8.2 million = .1067 years = .1067 (365) days = 38.95 days ♥
The operating cycle is the inventory period and the account receivable period. This gives Operating cycle = days in inventory + days in receivable = 111.3 + 57.13 = 168.4 days ♥
Similarly, the cash cycle is defined as the difference between an operating cycle and the payables period. This gives the result,
Cash cycle = Operating cycle − days in payable = 168.4 − 38.95 = 129.5 days ♥
4.2 Net Present Value of Operations
In chapter 2, we learned one of the most powerful tools in finance, the net present value. We may use it to evaluate and compare a variety of investment proposals. It is also helpful in optimizing the working capital management of a corporation. Formally, we define the net present value as
n C
NPV = – I0 + (1 + r)i (2.8)
i=1
Increasing the NPV of an investment, or an operation, will increase the profitability of the firm. Let us consider the operating cycle and the cash cycle of a firm again.
In the previous section, we calculated the operating cycle and cash cycle of Asquith Corporation to be 168.4 days and 129.5 days, respectively. The total sales of the company in 1999 were $11.5 million, Table 4.2. Thus at the end of each 168-day operating cycle, the company was able to sell, on the average, 11.5(168.4/365) = $5.306 million of goods. The cost of goods sold for this period was 8.2(168.4/365) = $3.783 million. The payment for these goods was made after 38.95 days, the days in payables. Let us assume that the cost of capital for the company is 11%. The NPV of this operation is
3.783
5.306
NPV = − 1.1138.95/365 + 1.11168.4/365 = $1.315 million
The NPV of the operation consists of two terms, the first one being a negative one. The negative term represents the PV of cost of the operations for one cycle, while the second one is the PV of revenues for that cycle. To improve the profitability of the firm, we must reduce the negative term, and increase the positive one. The firm may do it by the following actions:
1. Increase the amount of sales, $5.306 million at present,
2. Reduce the cost of goods sold, $3.783 million at present,
3. Reduce the cost of capital for the firm, presently at 11%.
4. Delay the payment for the goods purchased, presently 38.95 days,
5. Shorten the length of the operating cycle, currently 168.4 days,
The most obvious way to make the company earn more is to have higher sales coupled with lower costs. Just having higher sales, while the costs are rising faster, will not make the company more profitable. In some cases, it is not possible to increase the sales beyond a certain point possibly due to the capacity of the production line. In other cases, it is possible that the company has much higher production costs, such as overtime pay, and that may limit the total sales. In any case, there is an optimal point where the firm can maximize its profits.
We have already seen in chapter 2 that the cost of capital is an important cost for any firm. The firms try to minimize the weighted average cost of capital. Suppose the company is able to reduce its cost of capital from 11% to 10%, while everything else remains constant. This could be the result of the action of the Federal Reserve Board deciding to lower the interest rates. The NPV now is
3.783
5.306
NPV = − 1.138.95/365 + 1.1168.4/365 = $1.333 million
We note that the NPV for one cycle increases from $1.315 to $1.333 million for one operating cycle when the cost of capital drops from 11% to 10%.
That leaves us with points 4 and 5 in the above list. They are related to the management of the working capital of the corporation.
Suppose the company is somehow able to delay the payables by 2 days, and at the same time, speed up its receivables by 2 days. The length of the operating cycle will then become 166.4 days, while the days in payables will be 40.95 days. The sales during the shorter operating cycle will be 11.5(166.4/365) = $5.243 million, while the cost of goods sold during this period will be 8.2(166.4/365) = $3.738 million. The NPV of this operation will become
3.738
5.243
NPV = − 1.1140.95/365 + 1.11166.4/365 = $1.305 million
The NPV for one cycle has decreased from $1.315 million to $1.305 million. On closer inspection, we will find that it actually increases the value of the company. To increase the NPV of their operations, the companies are constantly looking for ways to speed up the cash collection procedure, and to slow down the payment process.
We may summarize the above discussion by writing a formula for calculating the NPV of an operating cycle as follows:
Cd Sd
NPV(operating cycle) = − (1 + r)p + (1 + r)d (4.2)
where we define the symbols as follows
C = cost of goods sold in one year
S = sales in one year
r = cost of capital to the firm, per annum
p = payable period, in years
d = operating cycle, in years
Note that all times are measured in years in equation (4.2), while the cost of capital is expressed as per year. This makes the equation internally consistent.
4.3 Valuation of a Company Based on its Operating Cycle
Consider the following example of the valuation of a company. The sales of this company during the next year are $50 million, and the cost of goods sold is $40 million. The firm makes $10 million in profits. Then it pays $3 million in taxes, at their 30% tax rate. The after-tax income is thus $7 million. Suppose the cost of capital for the firm is 12%. Let us assume that the company will continue to operate in this manner forever. Using (3.2) with discount rate, r = .12 for a perpetuity, and the cash flow, C = $7 million, we get the value of the firm to be
V = 7/.12 = $58.333 million.
To do this calculation algebraically, we see that the future annual gross profit is S − C, and the after-tax income is (S − C)(1 − t). With a discount rate r, the value of the company becomes, with the help of (3.2),
(S −C)(1 −t)
V = r (4.3)
Equation (4.3) assumes that the company does not have any investment in inventory and accounts receivable. If these factors are included, the value of the company will decrease. The company uses part of its income to finance the inventory, making it less profitable, and hence less valuable.
Now let us take a deeper look at the operations of the company. It is possible to calculate the value of a corporation by looking at the net present value of its operating cycle. Consider a more general case and use the discrete time analysis. Suppose the annual sales are S, while the cost of goods sold is C. Then the sales in one operating cycle = Sd, where d is the length of the operating cycle in years. The cost of these goods = Cd. Thus we can calculate the NPV of one cycle, from (4.2), to be
Cd
Sd
NPV of one cycle = − (1 + r)p + (1 + r)d = N, say.
The value of firm is the sum of the NPV of the first cycle, plus the NPV of the second cycle discounted by time d, plus the NPV of the third cycle discounted by the time 2d, and so on. Thus the value of these NPV's as a perpetuity is
N
N
N
V = N + (1 + r)d + (1 + r)2d + (1 + r)3d + ...
This is a geometric series with the first term a = N, and the ratio between the terms x = 1/(1 + r)d. Using the following equation to sum an infinite geometric series,
S = a + ax + ax2 + ax3 + ... ∞ = a
1 − x
N
Thus, V = 1 − 1/(1 + r)d
Substituting the value of N, write (4.4), as
Cd
p +
Sd 1
d d
V = − (1 + r)
(1 + r) 1 − 1/(1 + r)
Including the effect of taxes, and considering after-tax cash flows, the value becomes
− Cd
p +
Sd
d
1
d(1 − t) (4.4)
V = (1 + r)
(1 + r) 1 − 1/(1 + r)
In this expression, we define
p = payables period (in years) d = operating cycle (in years) S = sales in one year
C = cost of goods for one year
r = cost of capital of the firm.
If we let p = d = 1 in (4.6), we can reduce it to the simpler equation (4.3).
Let us consider another example. Suppose we have the following information about a company.
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Annual sales, S |
$50 million |
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Cost of goods sold, C $40 million |
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Income-tax rate, t 30% |
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Cost of capital, r 12% |
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Payables period, p 30 days |
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Operating cycle, d 120 days |
Use (4.4) to find the value of the company as
−40(120/365)
50(120/365) 1
30/365 +
120/365
120/365(1 − .3)
V =
1.12
1.12
1 − 1/1.12
Or, V = $53.752 million
Suppose the company is able to delay its payments by 3 days, so that the payables period becomes 33 days. This will not change the length of its operating cycle, d. Then its value will become
−40(120/365)
50(120/365) 1
33/365 +
120/365
120/365(1 − .3)
V =
1.12
1.12
1 − 1/1.12
Or, V = $53.984 million
This increases the value of a company by more than $230,000. Suppose the company is able to reduce its receivables period by 3 days, making its operating cycle 3 days shorter to 117 days, while the payables period is still 30 days, then
−40(117/365)
50(117/365) 1
30/365 +
117/365
117/365(1 − .3)
V =
1.12
1.12
1 − 1/1.12
Or, V = $54.009 million
This action increases the value of the company by more than $250,000. Now suppose the company manages to increase the payable period by 3 days to 33 days and decrease the operating cycle by 3 days to 117 days, then
−40(117/365)
50(117/365) 1
33/365 +
117/365
117/365(1 − .3)
V =
1.12
1.12
1 − 1/1.12
Or, V = $54.241 million
This combination of belt tightening on both ends creates a value 54.241 – 53.752 = .489, which is $489,000. The companies try to increase their value by such measures.
4.4 The Sources-and-Uses-of-Cash Statement
Another useful tool in keeping track of the cash flow in a company is its sources-and- uses-of-cash statement. This enables the managers to spot any undesirable trends in the cash flows and fix them in time. In case of a shortage of cash, one can focus on the sources of cash and see if there is a slowdown in any one of them; or the uses of cash, and see if there is an excessive flow in them.
Asquith Corporation
Sources of Cash:
Cash flow from operations
Net income Depreciation
Total cash flow from operations
Decrease in net working capital
Increase in accounts payable Increase in notes payable Increase in accrued expenses Increase in taxes payable
Total sources of cash Uses of Cash:
Increase in fixed assets
Increase in prepayments Dividends
Increase in net working capital: Increase in inventory
Increase in accounts receivable Increase in marketable securities
Total uses of cash Change in Cash Balance
$ ,000
810
300
1,110
250
1,000
25
25
2,410
700
100
50
1,000
400
50
2,300
110
Table 4.3: The sources-and-uses-of-cash statement for Asquith Corporation.
Let us look at the income statement of Asquith Corporation, given in Table 4.1. The next table, Table 4.3, presents a statement that identifies the sources of cash and the uses of cash for Asquith Corporation. The net income of a company is obviously a source of cash for a company. Depreciation is a non-cash expense, and it is the accounting measure of the decrease in the value of the assets of a firm. The company sets this amount aside for the purchase of new assets.
A decrease in the net working capital represents a source of cash. The net working capital may be thought of as a storage of cash, and thus cash may be released by reducing the net working capital. The decrease in the net working capital is created by the increase in the current liabilities, such as notes and accounts payable, and accrued expenses and taxes due.
A use of cash is the purchase of long-term assets of the firm. This increases the fixed assets of the company. Other cash payments include payment of dividends, and the payment of other expenses. As far as the working capital is concerned, an investment in marketable securities, or inventory, or accounts receivables, will use up cash.
4.5 Working Capital Policy
The working capital policy of a firm generally consists of the following two elements:
1. What is the total investment in the current assets?
2. How is this investment going to be financed?
The total amount of investment in the working capital depends upon the overall size of the company and its revenues. Further, this total investment would also depend upon whether the firm has a liberal or a restrictive working capital policy. If a corporation has a liberal policy, then it will have a large amount of cash and marketable securities on hand; it will have a large inventory of merchandise; and it will give generous credit terms to its customers resulting in large accounts receivable. However, a liberal working capital policy will impose a heavy cost on the corporation. This cost is reflected in the cost of capital of a company. For instance, if the cost of capital for a company is 10%, then to maintain a million dollar inventory will cost the company $100,000 a year.
A restrictive policy requires that the company has low cash balances, no marketable securities, a very small inventory, and no credit sales. This also means that the company has to be careful about the possibility of a cash shortage. A small inventory implies that the company may be out of an item required by a customer. Both the lack of credit sales, and the non-availability of merchandise due to a small inventory, can lead to a severe downturn in the revenues of the firm. The firm cannot afford to have a very restrictive policy.
We are faced with the dilemma of having two opposite costs, the carrying costs , and the shortage costs. Generally, the costs that rise with increasing current assets are called carrying costs, and those that decline with larger current assets are termed shortage costs. We have to minimize the total costs under optimal conditions.
The following diagram, Figure 4.2, illustrates the carrying costs as a function of cost of capital. For instance, if the cost of capital for a firm is 10%, then its carrying cost for a $1 million in current assets is $0.1 million. The declining curve represents shortage costs. These costs are more difficult to determine, and we are assuming an inverse relation between these costs and the level of current assets.
Consider optimization as a calculus problem. In the above case, we have reduced it to an algebraic problem by equating the two types of costs at the optimal point.
If the cost of capital is lower, the firm can afford to have more money invested in the current assets. Thus it can give generous credit terms to its customers. It can also afford to have a higher inventory and cash level.
Next we look at the second main question, how to finance the current assets. In the ideal situation, the current assets are equal to the current liabilities, thus we have zero net working capital. In this situation, the long-term assets are financed by long-term obligations.
In reality, because of safety reasons, one must have much higher current assets compared to current liabilities. The firm can get the short-term financing by using secured and unsecured loans. The banks may issue lines of credit to corporations, which are unsecured. A bank may also give a company a secured loan based upon the accounts receivable, or inventory. We will look at this type of financing in more detail.
Fig. 4.2: The diagram shows the carrying costs (rising straight line), the shortage costs (falling curve), and the total costs with a minimum, representing the optimal level of current assets.
Key Terms
Accounts-receivable period, 50
Carrying costs, 57
Cash cycle, 50
Inventory period, 50 Net working capital, 49 Operating cycle, 50
Shortage costs, 57
Examples
4.1. Attlee Furniture Company has the following information.
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Annual sales |
$22 million |
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Variable cost ratio 65% |
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Number of days sales outstanding 75 days |
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Number of days in payables 35 days |
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Inventory turnover ratio 3.21 |
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Cost of capital 13% |
Find the following information about Attlee:
A. Inventory period
B. Receivables period
C. Operating cycle
D. Payables period
E. Cash cycle
F. Sales in one operating cycle
G. NPV of its operating cycle.
We calculate various values as follows:
Working Capital Management
4. Financial Planning and Control
Number of days in a year
365
A. Inventory period =
Inventory turnover ratio = 3.21 = 113.7 days
B. Receivables period = Days sales outstanding = 75 days
C. Operating cycle = Inventory period + Receivables period
= 113.7 + 75 = 188.7 days
D. Payables period = 35 days
E. Cash cycle = Operating cycle – Payables period = 188.7 – 35 = 153.7 days
F. Sales in one operating cycle =
188.7
365 * $22 million = $11.374 million
.65*11.374
11.374
G. NPV of operating cycle = −
1.1335/365 + 1.13188.7/365 = $3.371 million ♥
In the above calculation, the initial payment is delayed by 35 days and the final payment is received after 188.7 days. Examining the above calculation, we infer that we can increase the profitability of the firm if we do the following:
(a) ecrease the variable cost ratio, 65%,
(b) Increase the sales in one operating cycle, $11.374 million,
(c) Lengthen the payables period, 35 days,
(d) Decrease the length of the operating cycle, 188.7 days.
4.2. The income statement of Baldwin Company for 2008 shows the cost of goods sold to be $100 million, while the credit sales are $120 million. We also have the following information about the company from its balance sheet, in $million.
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12/31/08 |
12/31/07 |
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Inventory 30 20 |
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Accounts receivable 25 15 |
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Accounts payable 15 5 |
A. Find the length of operating cycle for Baldwin.
B. Find how many days are in its cash cycle.
Cost of goods sold
100
Inventory turnover ratio = Average inventory = ½(30 + 20) = 4
365 days Days in inventory = Inventory turnover ratio =
365
4 = 91.25 days
Average accounts receivable = ½(15 + 25) = $20 million
Credit sales Accounts receivable turnover = Average accounts receivable =
120
20 = 6
365 Days in receivable = Accounts receivable turnover =
365
6 = 60.83 days
Operating cycle = days in inventory + days in receivable
= 91.25 + 60.83 = 152.08 days ♥
Average accounts payable = ½(5 + 15) = $10 million
Accounts payable turnover =
Cost of goods sold Average payables =
100
10 = 10
365 days Days in payables = Accounts payable turnover =
365
10 = 36.5 days
Cash cycle = Operating cycle − days in payable = 152.08 − 36.5 = 115.58 days ♥
4.3. We have the following information about the operations of Balfour Company:
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Annual sales |
$8 million |
|
Variable cost ratio 73% |
|
|
Number of days sales outstanding 45 days |
|
|
Number of days in payables 35 days |
|
|
Inventory turnover ratio 7.22 |
|
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Cost of capital 12% |
Find the NPV of its operating cycle.
First, find the number of days in the inventory period. Since the inventory is turned over
7.22 times in a year, it takes 365/7.22 = 50.55 days to turn it over once. The inventory period is 50.55 days.
Days in operating cycle = inventory period + accounts receivable period
= 50.55 + 45 = 95.55 days
Accounts payable period = 35 days
Amount of sales in one operating cycle =
95.55
365 * $8 million = $2.094 million
Cost of these sales = .73(2.094) = $1.529 million
Now we use (4.2)
Cd
Sd
and we get
NPV(operating cycle) = − (1 + r)p + (1 + r)d (4.2)
1.529
2.094
NPV (operating cycle) = − 1.1235/365 + 1.1295.55/365 = $0.5203 million ♥
4.4. The following information is available about Canning Company.
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Annual sales (on credit) |
$85 million |
|
Variable cost ratio 65% |
|
|
Average accounts receivable $22 million |
|
|
Average accounts payable $15 million |
|
|
Average inventory $18 million |
|
|
Cost of capital 14% |
Find the NPV of one operating cycle.
Cost of goods sold = 65% of sales = .65(85) = $55.25 million = C
Inventory period =
Average inventory
COGS = 18/55.25 = .3258 years
Average receivables
Receivables period =
Annaul sales = 22/85 = .2588 years
Length of the operating cycle = Inventory period + Receivables period
= .3258 + .2588 = 0.5846 years = d
Payables period =
Average payables
COGS = 15/55.25 = .2715 years = p
NPV of one cycle =
−55.25(.5846) 1.14.2715 +
85(.5846)
1.14.5846 = $14.86 million ♥
4.5. We have the following information about Churchill Company.
n n n
Cost of capital
12%
Inventory turnover ratio 6.55
Days sales outstanding 68
Annual sales (on credit) $23 millio
Cost of goods sold $15 millio
Accounts payable $4 millio
Income tax rate 32%
Calculate the following:
A. Inventory period = 1/6.55 = .1527 year = 365(.1527) = 55.73 days ♥
B. Receivables period = 68 days ♥
C. The operating cycle = 68/365 + .1527 = .3390 year = 123.73 days ♥
Accounts payable
4
D. Payables period = Cost of goods sold = 15 = .2667 year = 97.33 days ♥
E. Cash cycle = 123.73 − 97.33 = 26.4 days ♥
15
23
F. NPV(operating cycle) = .3390 − 1.12.2667 + 1.12.3390= $2.569 million ♥
15
23
G. NPV(whole year) = − 1.12.2667 + 1.12.3390 = $7.580 million ♥
H. The value of the company based on (4.6),
−Cd
Sd
p + d
(1 + r)d
d
(1 − t) (4.6)
V = (1 + r)
(1 + r) (1 + r)
− 1
It is easier to calculate the value of the three factors in the above expression separately and then multiply them. This gives
−Cd
Sd
p +
d= $2.569 million
(1 + r)
(1 + r)
(1 + r)d
d =
1.12.3390
.3390
= 26.53
(1 + r)
− 1
1.12 − 1
(1 − t) = 1 − .32 = .68
V = (2.569)(26.53)(.68) = $46.36 million ♥
4.6. Based on the above calculation, list some ways to improve the profitability of the firm.
First we look at the operating cycle. It should be as short as possible, because of two reasons. First, there will be more cycles per year, and that will increase its annual revenues and profits. Second, within a cycle, the present value of the cash flows is higher because the cash is available sooner.
The operating cycle consists of two elements: the inventory period and the receivables period. To make the operating cycle shorter, the firm should try to shorten both these elements.
Consider the inventory period. To make it short, the firm tries to move the goods faster through its operations, whether it is manufacturing or selling. However, there is a limit how fast you can manufacture a car, or sell a pair of shoes. The inventory level should be kept at an optimal point, and thus the inventory period has an optimal value.
The same is true for the receivables period. A firm would like to keep it as short as possible, by offering discounts to early payers, and charging interest to slow payers. The receivables period cannot be made too short because they have to balance it against the possibility of reduced sales due to a restrictive credit policy. Thus there is an optimal level of accounts receivable.
The operating cycle is also the sum of accounts payable period and the cash cycle. The firm should have a short cash cycle to maximize its present value. The cash cycle may be shortened by lengthening the accounts payable period. The firms do that by delaying the payment of bills that are due. The firms try to work out a deal with their suppliers to get favorable payment schedules.
Finally, the firm should do something about its cost of capital. The weighted average cost of capital should be kept at a minimum level by using a judicious mix of debt and equity. A lower discount rate will increase the present value of the cash flows, and hence the profitability of the firm.
