Example of Relaxing Credit Standards
Basket Wonders is not operating at full capacity and wants to determine if a relaxation
of their credit standards will improve profitability.
• The firm is currently producing a single product with variable costs of $20 and
selling price of $25.
• Relaxing credit standards is not expected to affect current customer payment
habits.
• Additional annual credit sales of $120,000 and an average collection period
for new accounts of 3 months is expected.
• The before-tax opportunity cost for each dollar of funds “tied-up” in additional
receivables is 18%.
Ignoring any additional bad-debt losses that may arise, should Basket Wonders
relax their credit standards?
Profitability of
($5 contribution) x (4,800 units) =
additional sales
$24,000
(120,000/25 = 4,800 units)
Additional
receivables
(120,000/(3/12) = 30,000)
($120,000 sales) / (4 Turns) =
$30,000
Investment in
add. receivables
($20/$25) x ($30,000) =
$24,000
Req. pre-tax return
(18% opp. cost) x $24,000 =
on add. investment
$4,320
(18% of additional investment)
Yes!
Profits > Required pre-tax return
Example of Relaxing the Credit Period
Basket Wonders is considering changing its credit period from “net 30” (which has
resulted in 12 A/R “Turns” per year) to “net 60” (which is expected to result in 6 A/R
“Turns” per year).
• The firm is currently producing a single product with variable costs of $20 and
a selling price of $25.
• Additional annual credit sales of $250,000 from new customers are forecasted,
in addition to the current $2 million in annual credit sales
• The before-tax opportunity cost for each dollar of funds “tied-up” in additional
receivables is 20%.
Ignoring any additional bad-debt losses that may arise, should Basket Wonders relax
its credit period?
Profitability of
additional sales
(250,000/25 = 10,000)
($5 contribution)x(10,000 units) =
$50,000
Additional
receivables
($250,000 sales) / (6 Turns) =
$41,667
Investment in add.
receivables (new sales)
($20/$25) x ($41,667) =
$33,334
Previous
receivable level
($2,000,000 sales) / (12 Turns) =
$166,667
New
receivable level
($2,000,000 sales) / (6 Turns) =
$333,333
Investment in
add. receivables
(original sales)
$333,333 - $166,667 =
$166,666
Total investment in
add. receivables
$33,334 + $166,666 =
$200,000
Req. pre-tax return
on add. investment
(20% opp. cost) x $200,000 =
$40,000
Yes!
Profits > Required pre-tax return
Changing credit standards
u Li Hong Company is currently selling a product for $10 per unit. Sales (all on
credit) for last year were 60,000 units. The variable cost per unit is $6. The
firm’s total fixed costs are $120,000.
u The firm is considering a relaxation of credit standards that is expected to
result in the following: a 5% increase in unit sales to 63,000 units; an increase
in the average collection period from 30 days (its current level) to 45 days; an
increase in bad-debt expenses from 1% of sales (the current level) to 2%. The
firm’s required return on equal-risk investments, which is the opportunity cost
of tying up funds in accounts receivable, is 15%.
u
u
u
u
u
Need to calculate the effect on the firm’s additional profit contribution from
sales, the cost of the marginal investment in accounts receivable and the cost
of marginal bad debts.
Additional profit contribution from sales
Fixed costs are ‘sunk’ and thereby unaffected by a change in the sales level.
Variable cost is the only cost relevant to a change in sales. Sales are expected
to increase by 5%, or 3,000 units. The profit contribution per unit equals the
difference between the sale price per unit ($10) and the variable cost per unit
($6) and so the profit contribution per unit will be $4.
Thus, the total additional profit contribution from sales will be $12,000 (3,000
units × $4 per unit).
Cost of the marginal investment in accounts receivable
u
u
u
u
u
To determine the cost of the marginal investment in accounts receivable, Li
Hong must find the difference between the cost of carrying receivables before
and after the introduction of the relaxed credit standards. We are only
concerned about the out-of-pocket costs so the relevant cost in this analysis is
the variable cost.
The average investment in accounts receivable can be calculated using the
following formula:
Average investment in accounts receivable = total variable cost of annual
sales/ turnover of accounts receivable
Where Turnover of accounts receivable = 365/average collection period
The total variable cost of annual sales, using the variable cost per unit of $6
are,
Total variable cost of annual sales:
u Under present plan: ($6 × 60,000 units)
= $360,000
u Under proposed plan: ($6 × 63,000 units) = $378,000
u The proposed plan increases total variable cost of sales by $18,000.
u The turnover of accounts receivable shows the number of times each year that
accounts receivable are turned into cash. It is found by dividing the average
collection period into 365.
Turnover of accounts receivable (rounded):
u Under present plan: 365/30 = 12.2
u Under proposed plan: 365/45 = 8.1
u Substitute the cost and turnover data just calculated to get the following
average investments in accounts receivable:
Average investment in accounts receivable:
u Under present plan: $360,000/12.2 = $29,508
u Under proposed plan: $378,000/8.1 = $46,667
The marginal investment in accounts receivable, and its cost, are calculated as
follows:
Cost of marginal investment in accounts receivable (A/R):
u Average investment under proposed plan
$46,667
u – Average investment under present plan
29,508
u Marginal investment in accounts receivable
$17,159
u × Required return on investment
0.15
u Cost of marginal investment in A/R
$2,574
u The value of $2,574 is a cost because it represents the maximum amount that
could have been earned on the $17,159 had it been placed in the best equalrisk investment alternative available at the firm’s required return on
investment of 15%.
Cost of marginal bad debts
u The cost of marginal bad debts is the difference between the level of bad debts
before and the level of bad debts after the change in credit standards:
Cost of marginal bad debts:
u Under proposed plan: 0.02 × $10 × 63,000 units = 12,600
u Under present plan: 0.01 × $10 × 60,000 units = 6,000
u Cost of marginal bad debts
$6,600
u Bad debts costs are calculated by using the sale price per unit ($10) to identify
not just the true loss of variable (or out-of-pocket) cost ($6) that results when a
customer fails to pay its account, but also the profit contribution per unit—in
u
u
this case, $4 ($10 sales prices – $6 variable cost)—that is included in the
‘additional profit contribution from sales’. Thus, the resulting cost of marginal
bad debts is $6,600.
To decide whether the firm should relax its credit standards, the additional
profit contribution from sales must be compared with the sum of the cost of
the marginal investment in accounts receivable and the cost of marginal bad
debts. If the additional profit contribution is greater than marginal costs, credit
standards should be relaxed.
The effect of Li Hong’s credit relaxation policy:
Credit Terms
u Li Hong Company has an average collection period of 40 days (turnover =
365/40 = 9.1). The firm’s credit terms are net 30, so this period is divided into
32 days until the customers place their payments in the mail (not everyone
pays within 30 days) and 8 days to receive, process and collect payments once
they are mailed. Li Hong is considering changing its credit terms from net 30
to 2/10 net 30. This change is expected to reduce the amount of time until the
payments are placed in the mail, resulting in an average collection period of 25
days (turnover = 365/25 = 14.6).
u As shown in the EOQ example (slide 74), Li Hong has a raw material with
current annual usage of 1,100 units. Each finished product produced requires
one unit of this raw material at a variable cost of $1,500 per unit, incurs
another $800 of variable cost in the production process and sells for $3,000 on
terms of net 30. Li Hong estimates that 80% of its customers will take the 2%
discount and that offering the discount will increase sales of the finished
product by 50 units (from 1,100 to 1,150 units) per year but will not alter its
bad-debt percentage. Li Hong’s opportunity cost of funds invested in accounts
receivable is 14%. Should Li Hong offer the proposed cash discount?
u Analysis of initiating a cash discount for Li Hong Company
u
Li Hong’s opportunity cost of funds is 14%
Example of Introducing a Cash Discount
A competing firm of Basket Wonders is considering changing the credit period from
“net 60” (which has resulted in 6 A/R “Turns” per year) to “2/10, net 60.”
• Current annual credit sales of $5 million are expected to be maintained.
• The firm expects 30% of its credit customers (in dollar volume) to take
the cash discount and thus increase A/R “Turns” to 8.
• (30% x 10 days + 70% x 60 days = 3 + 42 days = 45 days
• 360 days per year / 45 days = 8 turns per year
• The before-tax opportunity cost for each dollar of funds “tied-up” in
additional receivables is 20%.
Ignoring any additional bad-debt losses that may arise, should the competing firm
introduce a cash discount?
Receivable level
($5,000,000 sales) / (6 Turns) =
(Original)
$833,333
Receivable level
(New)
($5,000,000 sales) / (8 Turns) =
$625,000
Reduction of
investment in A/R
$833,333 - $625,000 =
$208,333
Pre-tax cost of
the cash discount
0.02 x 0.3 x $5,000,000 =
$30,000.
Pre-tax opp. savings
(20% opp. cost) x $208,333 =
on reduction in A/R
$41,667.
Yes!
Savings > Costs
Textbook p.251
An Example of the Trade-off.
To assess the profitability of an extension of credit, we must know the profitability of
additional sales, the added demand for products arising from the relaxed credit standards, the
increased length of the average collection period, and the required return on investment.
Suppose that a firm's product sells for $10 a unit, of which $8 represents variable costs before
taxes. The firm is operating at less than full capacity, and an increase in sales can be
accommodated without any increase in fixed costs. Therefore the contribution margin per unit
for each additional unit sold is the selling price less variable costs involved in producing an
additional unit, or $10-$8=$2.
Currently, annual credit sales are $2.4 million. The firm may liberalise credit, which will
result in an average collection period of two months for new customers. Existing customers
are not expected to alter their payment habits. The relaxation in credit standards is expected to
produce a 25 percent increase in sales, to $3 million annually. The $600,000 increase
represents 60,000 additional units if the price per unit stays the same. Finally, assume that the
firm's opportunity cost of carrying the additional receivables is 20 percent before taxes.
This information reduces our evaluation to a trade-off between the added expected
profitability on the additional sales and the opportunity cost of the increased investment in
receivables. The increased investment arises solely from new, slower-paying customers. We
have assumed that existing customers continue to pay in 1 month. With additional sales of
$600,000 and a receivable turnover of six times a year for new customers (12 months divided
by the average collection period of 2 months), the additional receivables are $600,000/6 =
$100,000. For these additional receivables, the firm invests the variable costs tied up in them.
For our example, $0.80 of every $l in sales represents variable costs. Therefore the added
investment in receivables is 0.80 x $100,000 = $80,000. With these inputs, we are able to
make the calculations shown in Table 10.1. Inasmuch as the profitability on additional sales,
$2 x 60,000 = $120,000, far exceeds the required return on the additional investment in
receivables, 0.20 x $80,000 = $16,000, the firm would be well advised to relax its credit
standards. An optimal policy would involve extending credit more liberally until the marginal
profitability on additional sales equals the required return on the additional investment in
receivables necessary to generate those sales. However, as we take on poorer credit risks, we
also increase the risk of the firm, as reflected in the variance of the firm's expected cash-flow
stream. This increase in risk also manifests itself in additional bad-debt losses, a subject we
deal with shortly.
Present
Policy
Demand
Incremental sales
Default losses
Original sales
Incremental Sales
Avg. Collection Pd.
Original sales
Incremental Sales
$2,400,000
Policy A
Policy B
$3,000,000
$ 600,000
$3,300,000
$ 300,000
2%
10%
18%
1 month
12 times
2 months
3 months
per year6 times
4 times
1.
2.
3.
4.
5.
6.
Additional sales
Profitability: (20% contribution) x (1)
Add. bad-debt losses: (1) x (bad-debt %)
Add. receivables: (1) / (New Rec. Turns)
Invest in add. receivables: (.80) x (4)
Required before-tax return on
additional investment: (5) x (20%)
7. Additional bad-debt losses +
additional required return: (3) + (6)
8. Incremental profitability: (2) - (7)
Policy A
$600,000
120,000
60,000
100,000
80,000
Policy B
$300,000
60,000
54,000
75,000
60,000
16,000
12,000
76,000
44,000
66,000
(6,000)
Adopt Policy A but not Policy B.
Example of the Economic Order Quantity
Basket Wonders is attempting to determine the economic order quantity for fabric used in the
production of baskets.
• 10,000 yards of fabric were used at a constant rate last period.
• Each order represents an ordering cost of $200.
• Carrying costs are $1 per yard over the 100-day planning period.
What is the economic order quantity?
We will solve for the economic order quantity given that ordering costs are $200 per order,
total usage over the period was 10,000 units, and carrying costs are $1 per yard (unit).
Q*
Q*
=
=
=
√[2(o)(s)]/c
√[2 x 200 x 10,000]/1
2,000 units
Example of When to Order
Julie Miller of Basket Wonders has determined that it takes only 2 days to receive the order of
fabric after the placement of the order.
When should Julie order more fabric?
Lead time
= 2 days
Daily usage
= 10,000 yards / 100 days
= 100 yards per day
Order Point
= 2 days x 100 yards per day
= 200 yards
Safety Stock – Inventory stock held in reserve as a cushion against uncertain demand (or
usage) and replenishment lead time.
Our previous example assumed certain demand and lead time. When demand and/or lead
time are uncertain, then the order point is:
Order Point = (Avg. lead time x Avg. daily usage) + Safety stock
EOQ and JIT example
u Li Hong Company has an A group inventory item that is vital to the production
process. This item costs $1,500, and Li Hong uses 1,100 units of the item per year. Li
Hong wants to determine its optimal order strategy for the item. To calculate the
EOQ, we need the following inputs:
u Order cost per order
= $150
u Carrying cost per unit per year = $200
u Substituting into EOQ Equation, we get
u EOQ =
√(2 × 1,100 × $150)/200
u
u
u
u
u
u
u
u
u
u
≈ 41 units
The reorder point depends on the number of days Li Hong operates per year.
Assuming that he operates 250 days per year and uses 1,100 units of this item, its
daily usage is 4.4 units (1,100 / 250).
If its lead time is two days and Li Hong wants to maintain a safety stock of four units,
the reorder point for this item is 12.8 units ((2 × 4.4) + 4). However, orders are made
only in whole units, so the order is placed when the inventory falls to 13 units.
Now assume the same information as before, but assume that the marginal cost of
placing an order is (i) $11 or (ii) $2.
1 Order cost of $11
EOQ = √(2 × 1,100 × $11)/200
= √121 = 11 units
2 Order cost of $2
EOQ = √(2 × 1,100 × $2)/200
= √22 = 5 units