18.2 Working Capital: Receivables, Inventory, and Short-Term Financing

Working Capital Management: Receivables, Inventory, and Short-Term Financing

This section continues working capital management with the two largest operating current assets, accounts receivable and inventory, and with the short-term financing sources that fund them. It covers credit standards and the cost of trade discounts, economic order quantity and reorder points, effective interest rates on bank loans, and a comprehensive worked example of the cash conversion cycle, EOQ, and discount decision.

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1. Accounts Receivable Management

Credit policy governs trade credit granting, discount structures, and collection administration to maximize net operating profits while controlling bad debt exposure and carrying costs.

The 5 Cs of Credit

1. Character: The applicant's historical reputation and integrity in honoring contractual obligations.
2. Capacity: The borrower's operating cash generation ability to service obligations from recurring revenues.
3. Capital: The borrower's net worth and financial equity base.
4. Collateral: Specific asset pledges available to secure credit extensions.
5. Conditions: Macroeconomic and industry-specific economic headwinds affecting the debtor's business.

The Economics of Cash Discounts: Nominal Cost of Trade Credit

When a seller quotes terms such as "$2/10, n/30$", a buyer who pays on Day 30 rather than Day 10 foregoes a $2\%$ discount to hold trade credit for an extra 20 days.

$\text{Nominal Annual Cost of Forgoing Discount} = \frac{\text{Discount \%}}{100 - \text{Discount \%}} \times \frac{360}{\text{Credit Period} - \text{Discount Period}}$

$\text{Effective Annual Rate (EAR)} = \left(1 + \frac{\text{Discount \%}}{100 - \text{Discount \%}}\right)^{\frac{360}{\text{Credit Period} - \text{Discount Period}}} - 1$

For credit terms $2/10, n/30$: $\text{Nominal Rate} = \frac{2}{98} \times \frac{360}{20} = 2.0408\% \times 18 = 36.73\%$ $\text{Effective Rate (EAR)} = (1 + 0.020408)^{18} - 1 = 43.86\%$

Managerial Rule: A buyer should almost always take the cash discount. If the firm lacks cash, it should draw on a bank line of credit as long as the borrowing rate is less than the nominal cost of giving up the discount (e.g., borrowing at $12\%$ to save an annualized $36.73\%$ generates substantial net savings).

Evaluating a Change in Credit Policy

Relaxing credit standards or lengthening credit terms is worthwhile only if the incremental contribution margin exceeds the incremental carrying cost of receivables, bad debts, and collection costs.

Example. Credit sales are PHP 12,000,000 with a 30-day collection period. A looser policy is expected to raise sales to PHP 14,400,000, but the collection period stretches to 45 days and bad debts on the incremental sales will be 2%. The variable cost ratio is 70%, and the required return on funds tied up in receivables is 15%.

The policy should be adopted. Some problems measure the investment in receivables at the full sales value rather than at variable cost; follow the basis stated in the question.

Receivables Monitoring Frameworks

• Aging of Accounts Receivable: Stratifies outstanding invoices by age bands (e.g., 0-30 days, 31-60 days, 61-90 days, >90 days). A rising percentage of older receivables signals deterioration in customer solvency or lax collection follow-ups.
• Days Sales Outstanding ($DSO$) Trend: Tracks whether collections are diverging from stated credit terms over consecutive quarters.

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2. Inventory Management: EOQ and Reorder Point

Inventory balances must balance total inventory costs, comprising carrying costs, ordering costs, and stockout costs.

Cost Classifications

1. Carrying (Holding) Costs ($H$): Storage warehouse lease, refrigeration, insurance, personal property taxes, physical spoilage, shrinkage, obsolescence, and the opportunity cost of capital tied up in stock. Expressed as a fixed peso amount per unit or a percentage of unit purchase cost ($H = C \times h\%$).
2. Ordering / Setup Costs ($S$): Clerical processing, purchase requisition approvals, shipping dock inspection, setup labor, invoice matching, and electronic order placement. These costs are fixed per order regardless of order size.
3. Stockout Costs: Lost contribution margin on immediate lost sales, production downtime, expedited freight penalties, and impaired customer goodwill.

The Economic Order Quantity (EOQ) Formula

The EOQ model identifies the order quantity ($Q$) that minimizes the total annual cost of ordering and carrying inventory:

$EOQ = \sqrt{\frac{2DS}{H}}$

Where:

• $D$: Annual demand in units.
• $S$: Fixed cost incurred per purchase order placed.
• $H$: Annual carrying cost per unit of inventory.

$\text{Number of Orders per Year} = \frac{D}{EOQ}$ $\text{Total Annual Ordering Cost} = \frac{D}{EOQ} \times S$ $\text{Total Annual Carrying Cost} = \frac{EOQ}{2} \times H$ $\text{Total Inventory Cost (TIC)} = \left(\frac{D}{EOQ} \times S\right) + \left(\frac{EOQ}{2} \times H\right)$

Critical Mathematical Identity: At the exact EOQ point, Total Annual Ordering Cost strictly equals Total Annual Carrying Cost: $\frac{D}{EOQ} \times S = \frac{EOQ}{2} \times H$

Reorder Point ($ROP$) and Safety Stock

                               Reorder Point Mechanics

     Inventory (Units)
          ▲
          │  Order Received (Q = EOQ)
        Q ┼──────┐
          │      │\ 
          │      │ \ 
      ROP ┼──────┼──●─────────  Reorder Point Triggered
          │      │   \        (Place new order now)
          │      │    \ 
       SS ┼──────┼─────●──────  Safety Stock Level
          │      │      \ 
        0 └──────┴───────┴────► Time
                 ◄─ LT ──►

• Under Certainty (Zero Lead Time Variance): $ROP = \text{Lead Time Demand} = d \times LT$ Where $d$ is average daily demand in units ($d = D / 360$) and $LT$ is lead time in operating days.
• Under Uncertainty (Variable Demand or Lead Time): $ROP = (d \times LT) + \text{Safety Stock}$ $\text{Safety Stock (Max Method)} = (\text{Maximum Daily Usage} \times \text{Maximum Lead Time}) - (\text{Normal Daily Usage} \times \text{Normal Lead Time})$
• Average Inventory with Safety Stock: $\text{Average Inventory} = \frac{EOQ}{2} + \text{Safety Stock}$

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3. Short-Term Financing Sources and Their Effective Cost

Effective interest rate on bank loans. The effective rate equals the interest paid divided by the funds the borrower can actually use.

If the firm already keeps a cash balance at the bank that satisfies part of the compensating balance, only the additional balance reduces usable funds. For an installment (add-on) loan, the average usable balance is roughly half of the principal, so the effective rate is about double the stated rate.

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4. Comprehensive Worked Computational Example

Scenario: Pampanga Trading Corporation presents the following annual operational and financial data for 2026:

• Annual sales (all on credit): $\text{PHP }72{,}000{,}000$
• Cost of Goods Sold ($75\%$ of sales): $\text{PHP }54{,}000{,}000$
• Accounts Receivable (average balance): $\text{PHP }9{,}000{,}000$
• Merchandise Inventory (average balance): $\text{PHP }6{,}750{,}000$
• Accounts Payable (average balance): $\text{PHP }4{,}500{,}000$
• Raw material component annual demand ($D$): $36{,}000\text{ units}$
• Ordering cost per order ($S$): $\text{PHP }500$
• Carrying cost per unit per year ($H$): $\text{PHP }10$
• Supplier credit terms available on purchases: $3/15, n/45$
• Short-term bank loan borrowing rate: $14\%$ per annum
• Assume a 360-day operational year.

Required Calculations

1. Compute the Operating Cycle ($OC$) and Cash Conversion Cycle ($CCC$).
2. Compute the Economic Order Quantity ($EOQ$) and total annual inventory costs at $EOQ$.
3. Determine the nominal annual cost of giving up the cash discount and evaluate whether the firm should take the discount using bank credit.

Step-by-Step Solution

1. Operating Cycle and Cash Conversion Cycle

• Days Inventory Outstanding ($DIO$): $DIO = \frac{\text{PHP }6{,}750{,}000}{\text{PHP }54{,}000{,}000} \times 360 = 0.125 \times 360 = 45\text{ days}$
• Days Sales Outstanding ($DSO$): $DSO = \frac{\text{PHP }9{,}000{,}000}{\text{PHP }72{,}000{,}000} \times 360 = 0.125 \times 360 = 45\text{ days}$
• Operating Cycle ($OC$): $OC = DIO + DSO = 45 + 45 = 90\text{ days}$
• Days Payables Outstanding ($DPO$): $DPO = \frac{\text{PHP }4{,}500{,}000}{\text{PHP }54{,}000{,}000} \times 360 = 0.08333 \times 360 = 30\text{ days}$
• Cash Conversion Cycle ($CCC$): $CCC = DIO + DSO - DPO = 45 + 45 - 30 = 60\text{ days}$ Interpretation: Pampanga Trading must finance its operating assets for 60 net days before cash is recouped from sales.

2. Economic Order Quantity and Inventory Costs

• $EOQ$ Computation: $EOQ = \sqrt{\frac{2 \times 36{,}000 \times 500}{10}} = \sqrt{\frac{36{,}000{,}000}{10}} = \sqrt{3{,}600{,}000} = 1{,}800\text{ units}$
• Number of Orders per Year: $36{,}000 / 1{,}800 = 20\text{ orders}$
• Total Annual Ordering Cost: $20 \times \text{PHP }500 = \text{PHP }10{,}000$
• Total Annual Carrying Cost: $(1{,}800 / 2) \times \text{PHP }10 = 900 \times 10 = \text{PHP }10{,}000$
• Total Inventory Cost: $\text{PHP }10{,}000 + \text{PHP }10{,}000 = \text{PHP }20{,}000$ Notice: Total ordering cost perfectly matches total carrying cost at the $EOQ$ point.

3. Cash Discount Evaluation

• Nominal Annual Cost of Forgoing Discount ($3/15, n/45$): $\text{Nominal Cost} = \frac{3}{100 - 3} \times \frac{360}{45 - 15} = \frac{3}{97} \times \frac{360}{30} = 3.0928\% \times 12 = 37.11\%$
• Effective Annual Rate ($EAR$): $EAR = (1 + 0.030928)^{12} - 1 = (1.030928)^{12} - 1 = 44.02\%$
• Managerial Recommendation: The nominal cost of foregoing the trade discount is $37.11\%$, while bank credit costs only $14.00\%$. Pampanga Trading should borrow funds from its commercial credit line at $14\%$ to pay within 15 days, securing an annual net arbitrage savings of $23.11\%$ ($37.11\% - 14.00\%$).