SHORT-TERM FINANCIAL MGT: PROBLEMS & DETAILED SOLUTIONS
(copyright © 2014 Joseph W. Trefzger)
Comprehensive Problem Set
1. Aspen Industries has a complicated production process, in which it takes 81 days for raw materials to be turned
into finished goods inventory and sold. Then it takes an additional 33 days, on average, to collect payment in cash
(i.e., to receive a check) from the buyer. When Aspen takes delivery of a shipment of raw materials, the supplier
expects to be paid by day 40. What are Aspen’s operating cycle and cash (or cash conversion) cycle?
Type: Computing operating and cash cycles. Here we want to combine the inventory (sometimes called
inventory conversion) period, receivable (sometimes called receivable collection) period, and payables
(sometimes called payables deferral) period into the operating cycle and the cash conversion cycle.
The inventory conversion period is the 81 days it takes Aspen to convert raw materials into salable
finished goods and complete the sale. The receivable period is the 33 additional days that the
company must then wait to collect cash from its customer. Therefore the operating cycle, which
is the inventory period plus the receivable period, is 81 + 33 = 114 days.
But the payables deferral period is 40 days. So the cash (or cash conversion) cycle, which is the
operating cycle minus the payables deferral period, is 114 – 40 = 74 days.
Here is what happens. The company receives a shipment of raw materials on day 0. If it had to pay
cash for the materials on that day, then it would need to have short-term financing for 114 days
(the 81 days it would take to turn the raw materials into salable inventory and sell it, plus the 33
days it would take after the goods were sold to collect cash from the customer). However, the
company does not have to pay cash for the raw materials until day 40. So it needs short-term
financing only for the shorter 74-day period running from day 40 to day 114 (when Aspen must make
its own payment of cash).
2. The treasurer of Birch Corporation wants to obtain a 1-year bank loan. The Cottonwood National Bank offers a
simple interest loan with a 9.45% stated annual interest rate. Dogwood National Bank offers a discounted interest
loan with an 8.75% stated annual interest rate. Which bank’s loan would carry the higher effective annual cost?
Type: Short-term loans, full year period. Though this example deals with an “effective” periodic (here,
annual) cost, the “nominal vs. effective” comparison here is not the APR vs. EAR computation that
applies to partial-year periods. (Recall the APR vs. EAR issue: we like to talk about rates in annual
terms, but for a partial-year period our working rate is the applicable partial-year periodic rate
that sums to an APR or compounds to an EAR.) Here “effective” relates what the borrower pays
to what the borrower actually gets to use. A simple interest loan’s effective periodic cost is simply
the stated periodic rate, here 9.45%. In a simple interest loan there are no unusual features; the
borrower pays the stated periodic rate on the full indicated loan amount, after having had the use
of that full loan amount for the full period. What matters is the proportions, but if you like to
think in dollar terms think of $100 borrowed. It is as though the lender places $100 on the table,
and then raises no objection as the borrower leaves the bank with the entire $100. At the end of a
full period the borrower returns with the $100, and pays $9.45 in interest after having had the use
of the full $100 borrowed. In more general percentage terms, the borrower in this example pays
9.45% of the stated loan amount in return for the use of 100% of that amount, such that
Effective periodic cost =
Trefzger/FIL 240 & 404
What  Borrower  Pays
What  Borrower  Gets  to  Use

9.45%
= 9.45%.
100%
Topic 14 Problems & Solutions: Short-Term/Working Capital
1
A simple interest loan’s effective periodic cost always equals the stated periodic interest rate.
Because the period here is a full year, our 9.45% effective periodic cost is also the APR (and EAR)
for the simple interest loan from Cottonwood.
In a discounted loan, on the other hand, the interest is taken “off the top,” from the loan proceeds,
so the borrower pays the stated periodic interest rate on the full indicated loan amount, but gets
the use, for the period, of only 100% minus the periodic interest percentage. For a $100 loan, it
is as though Dogwood places $100 on the table but then, before Birch can take it, removes 8.75%
of the $100, or $8.75, from the pile. The lender states that the borrower is paying “interest” up
front, and thus must pay only the $100 principal, with no interest, a year later. But the borrower is
therefore leaving the bank with only $100 – $8.75 = $91.25, and at the end of the loan period (here,
a full year) must come back with an added $8.75 to repay the bank the $91.25 taken + $8.75 extra
= $100 owed. Because Birch pays $8.75 but gets the use of only $100 – $8.75 = $91.25, or in more
general percentage terms pays 8.75% for the use of only 91.25% of the loan amount stated by
Dogwood, the effective periodic cost would be
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

8.75%
8.75%
= 9.589%.

100%  8.75% 91.25%
A discounted interest loan’s effective periodic cost (here, 9.589%) is always greater than the
stated periodic interest rate (here, 8.75%). Again, because the period here is a full year, our
9.589% effective periodic cost is also the APR (and the EAR) for the loan from Dogwood.
(Another problem with a discounted loan is that the borrower must actually borrow more than the
amount of money needed, because the lender keeps some of the loan proceeds. To leave the bank
with $100, Birch would have to borrow (and pay interest on) $100 ÷ .9125 = $109.59. Then when
Dogwood takes 8.75% of the $109.59, Birch is left with the remaining 91.25% x $109.59 = $100.
This process of having to borrow more than the amount of money needed is known as “grossing up”
the loan amount.)
The point to note is that in this example the loan with the lower stated periodic rate is actually the
more expensive, because that lower rate is connected with a discounted loan. A discounted interest
loan’s effective periodic cost will always be greater than its stated periodic interest rate, because
the borrower pays for money that he/she does not actually get to use. But a discounted interest
loan is not always more expensive than a simple interest alternative would be; it just depends on the
specific rate figures. For example, if the periodic (here, annual) rate quoted on the discounted loan
were only 8.25%, its effective cost would be lower than that of the 9.45% simple interest loan:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

8.25%
8.25%
= 8.992%.

100%  8.25% 91.75%
3. Bonsai International sells raw materials on terms of 2/10, net 40. What is the annual cost, in percentage terms, to
Bonsai’s customers who do not take the discount (they pay the full invoice price on day 40, thus allowing Bonsai to
provide their financing from days 11 through 40)? What annual rate of return does Bonsai earn by selling on credit?
Type: Cost of trade credit. Let’s first describe what is going on here. Bonsai expects the customer to
pay no later than 40 days after the sale is completed. If Bonsai receives the customer’s check any
time from day 11 through day 40, then payment should be for the full invoice amount. But if the
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
2
check is received by day 10, the customer can tender a payment that is 2% less than the invoice
specifies. We assume that payment will be received either ON day 10 (discounted amount) or ON
day 40 (full invoice amount), since there is no added benefit to paying earlier. The account will be
overdue if it is not paid in full by day 40. [Terms of 2/10, net 40 are not commonly seen in real
transactions, but we like to use cases other than the common 2/10, net 30 to illustrate how the cost
of not taking a trade discount is computed.]
To compute the percentage cost that customers incur when they pass up the discount (and thus
borrow from Bonsai during days 11 – 40, providing Bonsai with a financial return by paying a higher
price at the later date), let’s assume that the invoice was for $100. What matters to us in
computing a percentage cost is the proportions, not the dollar figures (if we were computing the
dollar cost of financing we would certainly have to look at the dollar amounts), but illustrating with
a nice round figure like $100 lets us paint a clearer mental picture of what is going on. A customer
planning to pay on day 10 would expect to pay $98 instead of $100. But if it then reconsidered and
decided to pay the full invoice price on day 40, it would end up paying an extra $2 for the privilege
of keeping that $98 for another 40 – 10 = 30 days. Thus the effective periodic cost would be
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2%
2%
= 2.0408%.

100%  2% 98%
But then remember that we like to present rates of return or cost on an annual basis. So we need to
recognize that in a 365-day year there are 365  (40 – 10) = 365  30 = 12.1667 thirty-day periods.
We compute the annualized rate as either an APR (effective periodic cost x number of periods in a
year) or a more correct EAR [(1 + effective periodic cost)number of periods in a year – 1]:
APR = .020408% x 12.1667 = 24.8300%.
EAR = 1.02040812.1667 – 1 = 27.8644%.
So if customers engage in ongoing transactions in which they pay Bonsai the higher price at the later
date, then their annual cost for this short-term financing is 27.8644%. Is that the annual rate of
return that Bonsai earns for providing this financing? Answer: only if all customers pay in full on
day 40. The reality is that many of its customers who do not take the discount are likely to end
up paying late, because they have financial problems that prevent them from borrowing in more
traditional venues. Who would borrow at a 28% annual cost if they had better alternatives (e.g.,
borrowing from a bank at a low interest rate, and then paying Bonsai’s discounted price on day 10)?
Firms like Bonsai may have to extend credit to make it possible for some customers to buy; they will
have good results with some of these buyers, but will lose money lending to others. It is unlikely,
in a competitive market place, that a firm could make huge percentage profits providing a service
as widely available as financing.
(Note that this type of analysis does not take into account the price the supplier charges. A firm
that sells on credit will try to make money through a combination of credit charges and product
prices. A supplier that sells to customers with shaky credit histories may levy a high financing
charge, and also charge a higher price than some of its competitors do. These questionable-credit
customers may have little choice but to buy from such a supplier, because others will refuse to sell
to them on credit. And then many will pay late, and some will not pay at all, thereby harming the
seller’s bottom line – a vicious circle.)
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
3
4. Hemlock Manufacturing sells goods on stated credit terms of 1.5/10, net 45. But its customers do not always
observe those stated terms.
a. Pine Distributors, a large Hemlock customer, routinely pays the full invoice price on day 70. Because Hemlock
does not want to lose Pine’s business, it grudgingly accepts these late payments (for the time being, anyway). What
is Pine’s cost of trade credit (percentage cost of not taking the discount, and thus letting Hemlock provide short-term
financing)?
Type: Cost of trade credit: cheating. Here it is as though Pine has redefined Hemlock’s credit terms as
1.5/10, net 70. So we have
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

1.5%
1.5%
= 1.5228%.

100%  1.5% 98.5%
On a $100 invoice, the buyer could pay $98.50 on day 10, or could pay an extra $1.50 for the right
to keep the $98.50 for the period in question. But what is that period? Here the buyer cheats by
keeping the money for an extra 70 – 10 = 60 days (not the extra 45 – 10 = 35 days specified in the
seller’s terms). There are 365 ÷ 60 = 6.08333 sixty-day periods in a year. As always, we compute
the annualized rate as either an APR or a more correct EAR:
APR = .015228% x 6.08333 = 9.2640%.
EAR = 1.0152286.08333 – 1 = 9.6300%.
If it followed the stated terms, Pine’s cost of trade credit (365 ÷ 35 = 10.428571 periods in a year)
would be EAR = 1.01522810.428571 – 1 = 17.0714%. The cost of not taking the discount is lower if
a buyer cheats in this manner, because under the “redefined” credit terms the discount is less
attractive (by passing it up, the customer gets to keep its money for a longer period). If the
discount is less attractive, then passing it up is less costly. If Hemlock permits Pine to continue
cheating in this manner, then Pine’s percentage cost of credit from Hemlock is an EAR of only 9.63%
per year – cheaper than a bank loan might be. So Pine should pay the full invoice price on day 70.
b. Another major customer, Spruce Industries, routinely cheats in a different way, paying the discounted price on
day 25. Because Hemlock also does not want to lose Spruce’s business, it grudgingly accepts this situation, as well
(at least for now). What would be Spruce’s cost of trade credit (cost of not taking the discount, and thus letting
Hemlock provide short-term financing)?
Type: Cost of trade credit: cheating. Spruce has, in effect, redefined Hemlock’s credit terms as 1.5/25,
net 45. The effective periodic cost is unchanged from the above example: 1.5%/98.5% = 1.5228%;
on a $100 invoice, the buyer could pay $98.50 on day 10, or an extra $1.50 for the right to keep the
$98.50 for the period in question. But this buyer cheats by taking the discount 15 days later than
officially allowed, so if the alternative were to pay the full invoice price on day 45 it would keep its
$98.50 for only 45 – 25 = 20 extra days. There are 365 ÷ 20 = 18.25 twenty-day periods in a year,
so the annualized rate is:
APR = .015228% x 18.25 = 27.7919%.
EAR = 1.01522818.25 – 1 = 31.7616%.
Recall that if it followed the stated terms, Spruce’s cost of trade credit would be a lower 17.0714%
EAR. So in this case, cheating causes the cost of financing from Hemlock to be more expensive than
the stated terms suggest. How can cheating result in a higher cost? Because if a buyer cheats by
taking the discount after the specified date, then taking the discount becomes more attractive,
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
4
so the cost of not taking the discount becomes higher (passing up a better discount is more costly).
If Hemlock permits Spruce to continue cheating in this manner, then Spruce’s percentage cost of
credit from Hemlock is an EAR of almost 32% per year – much more expensive than a bank loan
might be. So Spruce would be wise to borrow from a bank (presumably at an EAR much less than
31.7616%), and pay Hemlock the discounted price on day 25.
[A possible flaw in our analysis is the implicit assumption that, if it decided not to take the discount
on day 25, Spruce would pay the full invoice price on day 45. After all, a buyer that would stretch
the discount date might also be willing to stretch the final payment date. If Spruce would pay
either the discounted price on day 25 or the full invoice price on day 80, then it would have
“redefined” the terms as 1.5/25, net 80. The effective periodic cost would be unchanged at
1.5228%, but the number of 80 – 25 = 55-day periods in a year would be 365 ÷ 55 = 6.636364, for
APR = .015228% x 6.636364 = 10.1061%.
EAR = 1.0152286.636364 – 1 = 10.5502%.]
Our purpose in studying these two “cheating” examples is not to encourage buyers to cheat on their
credit purchases. Indeed, a cheating buyer may find that the seller eventually refuses to make
additional credit sales – and the buyer, with its poor credit history, will then find it very difficult
to locate a new supplier that will sell to it on credit. We consider cheating examples just so we can
better understand what would motivate a buyer to violate the credit terms.
5. Buckeye Company must regularly purchase raw materials for use in a production process, and is considering
various short-term financing alternatives that it might use in paying for the inventory. Compute the percentage cost,
in annual percentage rate (APR) and effective annual rate (EAR) terms, for each of the four short-term financing
alternatives shown. Which alternative is the least expensive?




Passing up the discount from Magnolia Materials, which sells raw materials to Buckeye on terms of 2/10, net 55
Getting a 3-month, discounted interest loan with a 10.72% stated annual interest rate from Catalpa State Bank
Factoring its accounts receivable at a 1.65% discount (assume Buckeye’s average collection period is 42 days)
Issuing 182-day commercial paper, sold at a 4.8% discount from the $100,000 per-unit face value
Type: Computing financing costs under discounted terms. While these four alternatives may seem very
different, they are structurally almost identical. Each involves discounting, a process often used
with short-term financing, in which a money provider buys a financial claim for less than face value.
The claim later matures at the higher face value, thereby giving the money provider a financial
return. (A zero-coupon bond is a discount instrument used in long-term financing; the money
provider gets a financial return when the low-priced bond matures at its higher face value.)
In each of the four cases here, we compute an effective periodic cost – what the borrower gives
up in return for what the borrower gets to use – and then convert this effective periodic cost to
an annual value (APR or EAR) by incorporating the number of periods in a year. Effective costs are
proportional figures, unrelated to the dollar amount of a particular transaction. But we can often
create a useful mental picture by choosing a nice, round illustrative dollar figure, like $100.
First consider the effective periodic cost for the case of 2/10, net 55 terms of sale. Assume that
Buckeye buys $100 worth of raw materials on day 0. On day 10 the company has to make a choice:
either pay $98, or else come back on day 55 and pay $2 more (the $100 total invoice amount).
If the choice is to pay later, then Buckeye keeps its $98 for the time period in question. It is,
in effect, selling a financial claim against itself (an obligation to pay the supplier $100) at a price
discounted 2% from the claim’s $100 maturity value. Then on day 55, it pays an extra $2 (or 2% of
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
5
whatever the stated invoice is) for the privilege of having had use of the $98 (or 98% of whatever
the stated invoice is) for the period. So we can compute the effective periodic cost as:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2%
2%
= 2.0408%.

100%  2% 98%
Thus the periodic cost is 2/98 = .020408. (It’s not just .02, or 2%.) That 2.0408% working
periodic figure might not seem like a high percentage to pay, but paying the extra $2 allows Buckeye
to keep/use its $98 only from day 10 until day 55, or 55 – 10 = 45 extra days. Because there are
365 ÷ 45 = 8.1111 forty-five day periods in a year, the interest rate measure we like to talk about –
an annualized figure – must combine the effective periodic cost with the number of periods in a
year:
APR = .020408 x 8.1111 = 16.5533%.
EAR = 1.0204088.1111 – 1 = 17.8057%.
Now consider the bank loan. Here the relevant period is a fourth of a year, so it might seem that
the quarterly periodic rate we work with is .1072 ÷ 4 = .0268. But because the interest is paid on
a discounted basis, 2.68% of the amount borrowed is taken “off the top.” It is as though Buckeye
sells a financial claim against itself for 2.68% less than (which is 97.32% of) face value. We again
compute the effective periodic cost as:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2.68%
2.68%
= 2.7538%.

100%  2.68% 97.32%
Think of a $100 loan. Just as in the trade credit example above Buckeye paid $2 to get to use the
$98 net of the trade discount, here it pays $2.68 to get to use the $97.32 net of the discounted
interest. (Buckeye sells the bank a claim against itself for $97.32, and the bank’s financial return
comes when Buckeye buys the claim back at maturity for $100.) The effective periodic cost is
.027538, and with four quarterly periods in a year the annualized figure we like to talk about must
combine this periodic rate with the number of yearly periods:
APR = .027538 x 4 = 11.0152%.
EAR = 1.0275384 – 1 = 11.4786%.
[Buckeye would do better to borrow money from the bank so it could pay the discounted price for
inventory on day 10, rather than passing up the discount and letting the supplier provide financing.]
Next, consider the factoring option. Factoring is the sale of the right to collect a company’s
accounts receivable. The buyer is a financial company or other investor, which pays a discounted
amount (something less than the amount it expects to collect) and, if all goes well, is compensated by
ultimately collecting the receivables’ full face value. It is as though Buckeye sells a financial claim
against itself at a discounted price (1.65% less than, which is 98.35% of, face value). We again
compute the effective periodic cost as:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

1.65%
1.65%
= 1.6777%.

100%  1.65% 98.35%
Here the relevant period is the 42 days that the lender (the “factor,” which purchases the right
to collect the receivables) must wait to collect, and there are 365 ÷ 42 = 8.690476 forty-two
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
6
day periods in a year. Think of $100 in receivables. Buckeye gives up $1.65 to get money 42 days
faster than it otherwise would. But it does not get the full $100; it gets only the $98.35 net of the
factor’s discount. The effective periodic cost is .016777, and with 8.690476 periods in a year the
annualized figure we like to talk about must combine this periodic rate with the number of yearly
periods:
APR = .016777 x 8.690476 = 14.5799%.
EAR = 1.0167778.690476 – 1 = 15.5565%.
Finally, consider the commercial paper possibility. Commercial paper (large denomination, shortterm corporate bonds) sometimes carries a stated interest rate, and is sold at face (maturity) value.
But our example involves commercial paper sold at a discount, such that Buckeye sells a financial
claim against itself for a 4.8% discount from, which is 95.2% of, face value. Then later, at maturity,
Buckeye pays back 100% of face value, thereby giving the lender a financial return. (So discount
commercial paper might be thought of as a short-term, zero-coupon corporate bond.) The buyer
pays $100,000 minus 4.8% of $100,000, so Buckeye gets the use of only $100,000 – $4,800 =
$95,200 (in more general percentage terms, it pays 4.8% for the use of 95.2%). So its effective
periodic cost is:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

4.8%
4.8%
= 5.0420%.

100%  4.8% 95.2%
Then the loan matures in 182 days at $100,000. Because there are 365 ÷ 182 = 2.005495 of these
periods in a year, we compute an annualized cost measure as:
APR = .050420 x 2.005495 = 10.1117%.
EAR = 1.0504202.005495 – 1 = 10.3681%.
[Firms that issue commercial paper sometimes arrange for standby lines of credit from large banks,
just in case they have trouble carrying out their planned borrowing in the commercial paper market.
Let’s assume that Buckeye borrows by issuing commercial paper, but also pays a commitment fee of
½ of 1% per year to its bank for access to an emergency line of credit. This fee is 182/365 x .005 =
.002493, so every 182-day period it incurs an effective periodic cost of:
Effective periodic cost =
What  Borrower  Pays
4.8%  .2493% 5.0493%


= 5.3039%.
What  Borrower  Gets  to  Use
100%  4.8%
95.2%
APR = .053039 x 2.005495 = 10.6369%.
EAR = 1.0530392.005495 – 1 = 10.9206%.]
Notice the magnitudes. The highest EAR accompanies the trade discount financing, which we might
expect because firms that sell on credit know they will often be lending to (because that is the only
way to sell goods to) risky buyers that can not obtain better borrowing terms from banks or other
traditional lenders. Next highest is the factoring possibility, which could carry a high cost if the
factor were uncertain of the credit-worthiness of customers that Buckeye has sold goods to (those
customers are who the factor must collect from). Next highest is the bank loan, which might be
fairly low in cost because banks can choose to lend only to borrowers with strong credit. Finally,
commercial paper might be expected to be the cheapest, since only financially strong companies can
typically raise money in the big, impersonal commercial paper market.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
7
6. Cedar Refrigeration Industries uses 150,000 thermostats in its manufacturing process each year. It costs Cedar
$1,250 to place an order (including the supplier’s charge for setting up its equipment to Cedar’s specifications), and
Cedar’s cost of carrying a thermostat in inventory for a year (borrowed money, storage, insurance) is $5.00. Cedar
currently orders 2,000 thermostats 75 times each year (about once every 5 days). The company’s managers fear that
the ordering costs are excessive, and plan to remedy the situation by instead ordering 15,000 units 10 times each
year. Based on economic ordering quantity (EOQ) analysis, would the proposed change be a better way for Cedar
to manage its inventory? What would the average inventory be if Cedar maintained a safety stock of 1,000 units?
Type: Economic Ordering Quantity. EOQ analysis is based on these inputs: total usage T over the
course of a year, the largely-fixed cost F of placing an order for new inventory units, and the cost
cc of carrying a unit in inventory for a year. By ordering the EOQ quantity
EOQ =
2TF
cc
every time it places an order, a firm minimizes its annual inventory management costs. Consider
Cedar’s total costs of managing its inventory. Under the current system, 150,000  2,000 = 75
orders are placed each year. And if the supply falls steadily from the 2,000 ordered down to a 0
remainder (at which time a new shipment should be scheduled to arrive), the average inventory is
2,000  2 = 1,000. So the total annual cost of managing the inventory currently is:
Ordering cost: 75 orders x $1,250 per order =
Carrying cost: 1,000 avg. units x $5 per unit =
Total
$93,750
$ 5,000
$98,750
We can see how management might be concerned by the huge total ordering cost. But what would
happen under the proposed change? First, 150,000  15,000 = 10 orders would be placed each year
(once about every 36 days). And if the supply were to fall steadily from the 15,000 ordered down
to a 0 remainder, the average inventory would be 15,000  2 = 7,500. So Cedar’s total annual cost
of managing its thermostat inventory would be:
Ordering cost: 10 orders x $1,250 per order =
Carrying cost: 7,500 avg. units x $5 per unit =
Total
$12,500
$37,500
$50,000
So the proposed change would certainly bring down the total cost of managing the inventory of
thermostats. But could Cedar do even better? Note that the economic ordering quantity is
EOQ =
2TF
2  150,000  $1,250


cc
$5.00
$375,000,000
 75,000,000 = 8,660.25 .
$5.00
According to EOQ analysis, Cedar should obtain about 8,660 units each time it places an order.
Getting 150,000 in lots of about 8,660 each, the company should place about 150,000  8,660 = 17
orders per year (EOQ numbers typically don’t work out perfectly, because partial units typically
can not be ordered). Over a 365-day year, that would mean ordering about every 365  17 = 21
days. Therefore, instead of ordering 2,000 units every five days or 15,000 units every 36 days,
Cedar should order about 8,660 units every 21 days, or once every three weeks.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
8
That approach would cause ordering costs to be lower than under current practice, but higher than
under the proposed plan. But carrying costs would also be between the two, higher than currently
realized but lower than under the proposed change. Specifically, if Cedar were to order based on
the EOQ (and assuming it could order exactly 8,660.25 units, which it actually could not because a
fraction of a thermostat can not be bought), then it would place 150,000  8,660.25 = 17.320516
orders per year. And if the supply fell steadily from the 8,660.25 ordered down to a 0 remainder,
the average inventory would be 8,660.25  2 = 4,330.125. So the total annual cost would be:
Ordering cost: 17.320516 orders x $1,250 per order = $21,650.65
Carrying cost: 4,330.125 avg. units x $5 per unit =
$21,650.63
Total
$43,301.27
Even if Cedar had to choose whole numbers close to what the EOQ suggests (17 annual orders of
8,824 units each), its costs would be close to what the EOQ indicates:
Ordering cost: 17 orders x $1,250 per order =
Carrying cost: 4,412 avg. units x $5 per unit =
Total
$21,250.00
$22,060.00
$43,310.00
So while the proposed change would be an improvement, it would not be optimal; Cedar could save
an additional $50,000 – $43,310 = about $6,700 per year with the in-between plan indicated by
the EOQ. Note that at the true EOQ, where the total inventory management cost is minimized,
the ordering and carrying costs are equal. (It is always that way; this example is not a fluke – the
chapter outline shows, mathematically, why ordering cost always equals carrying cost at the EOQ.)
Finally, consider what happens to inventory if there is a safety stock. While EOQ analysis is based
on the assumption that inventory falls steadily from the amount ordered down to zero, a safety
stock is thought of as remaining intact (it does not steadily decline to zero). Think of a safety
stock as a sealed barrel sitting in a locked room; the company does not access the safety stock
unless there is an emergency. So the average inventory would be
1,000 + 1,000 safety stock = 2,000 under the current ordering plan
7,500 + 1,000 safety stock = 8,500 if it changed to the proposed ordering plan
4,330.125 + 1,000 safety stock = 5,330.125 if the EOQ were ordered
7. Wyoming-based Ginkgo Great Steaks By Mail sells $9,125,000 worth of goods each year to individuals in the
northeastern United States. It faces “negative float” problems on these sales because of mail and check-clearing
delays. (If Ginkgo sold primarily to businesses, it would collect most payments electronically, and float would not
be much of an issue.) Rhode Island Bankcorp (RIB) could clear checks locally and frequently wire collected money
to Ginkgo’s Laramie bank account. In providing this “lockbox” service, RIB could reduce Ginkgo’s negative float
by two days. If Ginkgo pays a 9.5% effective annual interest rate on money it borrows short-term, and if RIB would
charge $7,000 per year to manage a lockbox system, should Ginkgo negotiate a contract with RIB?
Type: cost of lockbox system. A company needs cash so it can complete transactions. One way to obtain
cash is to speed up the collection of cash that customers have committed to pay. Here Ginkgo’s
total annual northeastern sales are $9.125 million, which comes out to $9,125,000 ÷ 365 = $25,000
daily. So if it can reduce float by 2 days, Ginkgo frees up 2 x $25,000 = $50,000 in cash on an
ongoing basis. (It will always be two days ahead on its collections, relative to where it would be
without the lockbox plan.) Having ongoing access to $50,000 in this manner costs $7,000 per year.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
9
Another way to obtain cash is to borrow it; here Ginkgo pays a 9.5% effective annual rate. So the
cost of having ongoing access to $50,000 by borrowing would be .095 x $50,000 = $4,750 per year.
Because borrowing the money costs only $4,750 per year while the lockbox system would cost
$7,000 per year, Ginkgo should not hire RIB as its collection agent.
In other words, Ginkgo will have to face one of two problems. It can either live with the current
situation (delayed cash collections from selling to customers in distant locations), or else pay
the price to solve this delay problem (hiring RIB as its collection agent in the distant local area).
Because having the delay problem (and thus having to borrow money) costs only $4,750 per year
while solving the problem would cost $7,000 per year, Ginkgo should just live with the delay and
borrow money to help meet its cash needs.
Additional Examples
8. Calculate the annual cost of nonfree trade credit (also called “cost of not taking the discount”) incurred by Elm
Enterprises, which obtains much of its short-term financing from the suppliers of goods and services it purchases.
Compute both the annual percentage rate (APR) and the effective annual rate (EAR), based on these terms:








1/15, net 30
2/15, net 30
2/15, net 90
2.5/10, net 45
3.5/15, net 60
2/10, net 30
5/10, net 30
5/30, net 90
Type: Cost of trade credit. In a problem of this type, the buyer is expected to pay no later than the
day that follows the word “net;” otherwise the buyer’s account will be overdue. If the seller of
the products or services receives the buyer’s check any time from the end of the discount period
through the final payment date, then payment should be for the full invoice amount. But if the
check is received by the end of the discount period, the buyer can submit a payment that is less
than the specified invoice amount by the indicated discount percentage. (We assume that payment
will be received either ON the last day of the discount period or else ON the final payment date,
since there is no added benefit to paying the discounted price or the full invoice price earlier.)
Most of the terms shown in this example are not commonly seen in real transactions (2/10, net 30
seems to be the most common), but we can use all of them to illustrate how the cost of not taking a
trade discount is computed.
To compute the percentage cost that customers incur when they pass up the discount (and thus
receive supplier financing from day after the discount period ends through the final payment date),
let’s assume that every invoice is for $100. What matters to us in computing a percentage cost is
the proportions, not the dollar figures (computing the dollar cost of financing would require us to
look at the dollar amounts), but a nice round figure like $100 helps create a useful mental picture.
Consider our first case, 1/15, net 30. A customer planning to pay on day 15 would expect to pay $98
instead of $100. But if it then reconsidered and decided to pay the full invoice price on day 30, it
would end up paying an extra $2 for having had the use of that $98 for another 30 – 15 = 15 days.
Thus the effective periodic cost would be
Effective periodic cost =
Trefzger/FIL 240 & 404
What  Borrower  Pays
What  Borrower  Gets  to  Use

1%
1%
= 1.0101%.

100%  1% 99%
Topic 14 Problems & Solutions: Short-Term/Working Capital
10
But we like to present rates of return or cost on an annual basis. In a 365-day year there are
365  (30 – 15) = 30 ÷15 = 24.333333 fifteen-day periods. We compute the annualized rate
as either an APR (effective periodic cost x number of periods in a year) or more correct EAR
[(1 + effective periodic cost)number of periods in a year – 1]:
APR = .010101% x 24.333333 = 24.5791%.
EAR = 1.01010124.333333 – 1 = 27.7057%.
So if customers engage in ongoing transactions in which they pay the higher price at the later date,
then their annual cost for this short-term financing is 27.7057%. (The supplier also earns that EAR
for providing the financing, but only if all buyers pay in full on the final payment date – an unlikely
outcome, since supplier financing generally is so costly that only the worst credit risks, without
better financing alternatives like bank loans, would select it.) This cost does not seem overly high;
after all, a 1% discount is not all that great, so passing it up is not all that costly.
Now we can quickly find the cost of passing up the discount under the other terms given. For 2/15,
net 30, the number of periods in a year is again 365 ÷ (30 – 15) = 24.3333. So we can compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2%
2%
= 2.0408%; and

100%  2% 98%
APR = .020408% x 24.3333 = 49.6599%.
EAR = 1.02040824.3333 – 1 = 63.4929%.
Here the annual financing cost is higher, because a buyer that skips taking the discount has to pay
a higher price; if the discount is more generous, then the cost of passing it up is greater. But for
2/15, net 90 terms, the number of periods in a year is a much smaller 365 ÷ (90 – 15) = 4.8667.
So we compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2%
2%
= 2.0408%; and

100%  2% 98%
APR = .020408% x 4.8667 = 9.9320%.
EAR = 1.0204084.8667 – 1 = 10.3316%.
Here the annual financing cost is quite low, perhaps competitive with bank financing, because a buyer
that skips taking even the generous 2% discount gets to retain the use of its money for a fairly long
90 – 15 = 75 extra days before paying the higher price.
For 2.5/10, net 45, the number of periods in a year is 365 ÷ (45 – 10) = 10.428571. So we compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2.5%
2.5%
= 2.5641%; and

100%  2.5% 97.5%
APR = .025641% x 10.428571 = 26.7399%.
EAR = 1.02564110.428571 – 1 = 30.2165%.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
11
For 3.5/15, net 60, the number of periods in a year is 365 ÷ (60 – 15) = 8.1111. So we compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

3.5%
3.5%
= 3.6269%; and

100%  3.5% 96.5%
APR = .036269% x 8.1111 = 29.4185%.
EAR = 1.0362698.1111 – 1 = 33.5060%.
For the standard 2/10, net 30, there are 365 ÷ (30 – 10) = 18.25 periods in a year, and we compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2%
2%
= 2.0408%; so

100%  2% 98%
APR = .020408% x 18.25 = 37.2449%.
EAR = 1.02040818.25 – 1 = 44.5853%.
For 5/10, net 30, there are still 365 ÷ (30 – 10) = 18.25 periods in a year, but here we find
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

5%
5%
= 5.2632%; so

100%  5% 95%
APR = .052632% x 18.25 = 96.0526%.
EAR = 1.05263218.25 – 1 = 155.0024%.
Passing up a typical 2% discount imposes about a 45% cost per year, but passing up a much more
generous 5% discount equates to a financing cost of about 155% per year! Finally, for 5/30, net 90,
there are only 365 ÷ (90 – 30) = 6.083333 periods in a year, so we compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

5%
5%
= 5.2632%; and

100%  5% 95%
APR = .052632% x 6.083333 = 32.0175%.
EAR = 1.0526326.083333 – 1 = 36.6201%.
Because a 5% discount is quite generous, passing it up is likely to be costly. However, if the buyer
gets to keep its money for a substantial period (e.g., 60 days) before ultimately paying, then the
cost of passing up the discount, while high, is not staggeringly so.
9. Maple Manufacturing Corporation sells on stated credit terms of 2/20, net 65, but its customers do not always
observe those stated terms. Because Maple is trying to build its sales and does not want to discourage customers
from placing orders, it tolerates this cheating, at least for the time being.
a. What is the annual cost of trade credit (cost of not taking the discount, and thus letting Maple provide short-term
financing) to Oak Distributors, which routinely pays the discounted price on day 41?
Type: Cost of trade credit: cheating. Oak has, in effect, redefined Maple’s credit terms as 2/41, net 65.
The effective periodic cost is
What  Borrower  Pays
2%
2%
Effective periodic cost =
= 2.0408%.


What  Borrower  Gets  to  Use 100%  2% 98%
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
12
On a $100 invoice, Oak could pay $98 on day 20, or an extra $2 for the right to keep the $98 for
the period in question. But this buyer cheats by taking the discount 21 days later than officially
allowed, so if the alternative were to pay the full invoice price on day 65 it would keep its $98 for
only 65 – 41 = 24 extra days. There are 365 ÷ (65 – 41) = 365 ÷ 24 = 15.208333 twenty-four day
periods in a year, so the annualized percentage cost is:
APR = .020408% x 15.208333 = 31.0374%.
EAR = 1.02040815.208333 – 1 = 35.9680%.
If it followed the stated terms, Oak’s cost would be a lower 1.020408 8.111111 – 1 = 17.8057% EAR.
Cheating in this manner results in a higher financing cost than the stated terms suggest, because
taking the discount after the specified date makes the discount more attractive, so the cost of not
taking the discount becomes higher (foregoing a better discount is more costly). If it continues to
cheat this way, Oak’s percentage cost (EAR) of credit from Maple is almost 36% per year – much
higher than a bank loan might be. So Oak would be wise to borrow from a bank (presumably at an
EAR much less than 35.9680%), and pay Maple the discounted price on day 41. (A possible error
in our logic is the implicit assumption that, if it did not take the discount on day 41, Oak would pay
the full invoice price on day 55. A party that would pay the discounted price after the sanctioned
discount date might also be inclined to pay the full invoice price after the final payment due date.)
b. What is the annual cost of trade credit for Willow Stores, which routinely pays the full invoice price on day 100?
Type: Cost of trade credit: cheating. Here it is as though Willow has redefined Maple’s credit terms
as 2/20, net 100. So we still have an effective periodic cost of 2%/98% = 2.0408%. On a $100
invoice, the buyer could pay $98 on day 20, or could pay an extra $2 for the ability to keep the $98
for the period in question. This buyer cheats by keeping the money for an extra 100 – 20 = 80 days
(not the extra 65 – 20 = 45 days officially allowed). There are 365 ÷ (100 – 20) = 365 ÷ 80 = 4.5625
eighty-day periods in a year. As always, we compute the annualized rate as either an APR or a more
correct EAR:
APR = .020408% x 4.5625 = 9.3112%.
EAR = 1.0204084.5625 – 1 = 9.6557%.
As shown above, if it followed the stated terms Willow’s cost of trade credit would be a higher
17.8057% EAR. Cheating in this manner (paying the full invoice price at a late date) makes the
cost of not taking the discount lower, because the “redefined” credit terms make the discount less
attractive (after passing it up, the customer gets to keep its money for a longer period). If the
discount is less attractive, passing it up is less costly. If Willow continues cheating in this manner
(and Maple allows it to happen), Willow’s percentage cost of credit from Maple is cheaper than a
bank loan would likely be. So Willow realizes a financial benefit by paying the full price on day 100.
But a buyer that cheats on the credit terms may find that the seller eventually refuses to make
additional credit sales – and the buyer, with its poor credit history, will then find it very difficult
to locate a new supplier that will sell to it on credit. We consider cheating examples just so we can
better understand what would motivate a buyer to violate the credit terms.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
13
10. Compute the effective annual rate (EAR) of interest that Redwood Enterprises would pay on each of the
following loans from the Sequoia National Bank.



A 1-year simple interest loan with a 7.95% stated annual interest rate
A 1-year discounted interest loan, with a 7.55% stated annual interest rate
A discounted interest loan with a 7.75% stated annual interest rate, but maturing in just 6 months
Type: Short-term bank loans. The “stated” (or “nominal”) vs. “effective” cost for a 1-year loan is not
exactly the same as the APR vs. EAR cost for a partial-year period. But the term “effective” does
always relate what the borrower pays to what the borrower actually gets to use. A simple interest
loan has no unusual features, so the borrower pays the stated periodic rate on the full indicated
loan amount, after having had the use of that full loan amount for the full period. Effective cost is
a proportional figure, which is not affected by the dollar amounts involved, but it can be easier to
think about the situation by considering a simple dollar example – let’s say a nice, round $100. It is
as though Redwood takes $100 from the bank. At the end of a full period Redwood comes back with
the $100, and pays $7.95 in interest after having had the use of the full $100 borrowed. In more
general percentage terms, the borrower in this example pays 7.95% of the stated loan amount in
return for the use of 100% of that amount, such that
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

7.95%
= 7.95% .
100%
A simple interest loan’s effective periodic cost always equals the stated periodic interest rate.
Because the period here is a full year, the 7.95% effective periodic cost is also the EAR (and APR).
Interest for a discounted loan, however, is taken from the stated loan proceeds. The borrower pays
the stated periodic interest rate on 100% of the indicated loan amount, but gets to use only 100%
minus the periodic interest percentage. For a $100 loan, it is as though Sequoia (the lender in this
example) puts $100 on the table but then grabs $7.55 (7.55% of the $100) before Redwood can
take it. The lender’s view is that the borrower is paying “interest” up front, and thus must pay back
only the $100 principal, with no interest, a year later. But the borrower leaves the bank with only
$100 – $7.55 = $92.45, and at the end of the loan period (here, a full year) must come back with
an added $7.55 to repay the bank the $92.45 taken + $7.55 extra = $100 owed. Because Redwood
pays $7.55 but gets the use of only $100 – $7.55 = $92.45, or in percentage terms pays 7.55% for
the use of only 92.45% of the stated loan amount, its effective periodic cost would be
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

7.55%
7.55%
= 8.1667% .

100%  7.55% 92.45%
A discounted interest loan’s effective periodic cost (here, 8.1667%) will always be greater than its
stated periodic interest rate (here, 7.55%), because the borrower pays for money that it does not
actually get to use. Because the period in this example is a full year, our 8.1667% effective periodic
cost is also the EAR (and the APR). So based on the two examples above, the loan with the lower
stated periodic rate has the higher effective periodic cost, because the lower stated rate applies to
a discounted loan. (A discounted interest loan is not always more expensive than a competing simple
interest loan would be; it just depends on the specific rate figures.)
Finally, for the 6-month loan the relevant period is half of a year. But because the interest is paid
on a discounted basis, 7.75% ÷ 2 = 3.875% of the amount borrowed is taken “off the top.” The bank
figuratively places $100 on the table, but before the borrower can take it the bank grabs $3.875
(3.875% of the $100) from the pile, so the borrower leaves the bank with only $100 – $3.875 =
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
14
$96.125. The borrower returns at the end of the period (here, 6 months) with the $96.125, and
then has to pay another $3.875 for having had the use of the $96.125 (so at the end of the period
it pays $100 total). As always, we compute Redwood’s effective periodic cost as:
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

3.875%
3.875%
= 4.0312%.

100%  3.875% 96.125%
With two six-month periods in a year the annualized figure we like to talk about must combine this
periodic rate with the number of yearly periods:
APR = .040312 x 2 = 8.0624%.
EAR = 1.0403122 – 1 = 8.2249%.
The lowest cost loan, from among these three choices, happens to be the one with the highest
stated percentage intererst cost.
11. Based on the most recent year’s financial statements, Linden Company’s sales were $17,000,000 and its
inventory turnover ratio was 2.5. The chief financial officer hopes to reduce the company’s inventory holdings,
which are seen as excessive. If sales in the coming year remain at $17,000,000 but the inventory turnover is
increased to the industry average of 4, how much cash will be made available for Linden to use for other purposes?
Type: Cash position. Under the current situation, Sales/Inventory = $17,000,000/Inventory = 2.5,
so Inventory = $17,000,000/2.5 = $6,800,000. The goal is to reduce inventory to a point where
$17,000,000/Inventory = 4, such that inventory would be only $17,000,000/4 = $4,250,000. So if
Linden could reduce its inventory holdings (sell off inventory and not replace it) without reducing
sales, it could free up $6,800,000 – $4,250,000 = $2,550,000 in cash for other uses.
12. One way the United States Treasury raises money for the government’s use is to issue Treasury Bills (“T-Bills”),
which are short-term bonds sold on a discounted basis. What effective annual rate (EAR) of return does Ms. Locust
receive if she buys a 91-day T-Bill on its issue date for 97.65% of face value, and then collects 100% of face value
on the day it matures?
Type: cost of discounted financing. If a financial instrument is sold on a discounted basis, then instead
of quoting an interest rate, the borrower specifies the discount from face value at which the claim
is to be sold; the lender earns a financial return by buying at the discounted price and then
collecting the full face value when the instrument matures. Here the T-Bill buyer, Ms. Locust,
invests 97.65% of the par value. Then she earns the difference between the 100%-of-par maturity
value and the 97.65%-of-par purchase price, which is 100% – 97.65% = 2.35%. Thus we can compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

2.35%
2.35%
= 2.4066%.

100%  2.35% 97.65%
There are 365 ÷ 91 = 4.010989 ninety-one day periods in a year, so we can compute an annualized
return as:
APR = .024066 x 4.010989 = 9.6527%.
EAR = 1.0240664.010989 – 1 = 10.0081%.
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
15
13. Walnut Warehouses plans to borrow money on a short-term basis by issuing 270-day commercial paper.
Compute the effective annual cost of borrowing (in EAR terms) if these instruments are sold at a price discounted
8.625% from their maturity value.
Type: cost of discounted financing. Commercial paper (short-term corporate bonds) is another type of
financial instrument that can be sold on a discounted basis (though some commercial paper is instead
sold at par, with an explicit stated interest rate). Here the commercial paper buyer invests 100% –
8.625% = 91.375% of the par value. Then he collects 8.625% more than he invested when Walnut
pays him 100% at maturity. Thus we can compute
Effective periodic cost =
What  Borrower  Pays
What  Borrower  Gets  to  Use

8.625%
8.625%
= 9.4391%.

100%  8.625% 91.375%
Commercial paper typically has maturities of about 3, 6, or 9 months (it always matures within 270
days of its issue date, because longer maturities require the issuing company to go through a more
rigorous registration process with the government). This particular issue matures in 270 days,
and there are 365 ÷ 270 = 1.351852 of these 270-day periods in a year, so we compute Walnut’s
annualized cost (and the buyer’s annualized return) as:
APR = .094391 x 1.351852 = 12.7603%.
EAR = 1.0943911.351852 – 1 = 12.9680%.
14. Palmetto Products uses 11,000 tons of high-carbon steel in its production process each year. The cost of placing
an order with its supplier, Cypress Steel Mills, is $40 (this cost primarily involves workers’ time spent phoning
Cypress and checking off the order when it is delivered). The annual cost of carrying a ton of steel in inventory
(borrowed money, storage, insurance) is approximately $115. Analyze this situation using the economic ordering
quantity (EOQ) model.
Type: Economic ordering quantity. The EOQ model is an approach to determining how many items a firm
should bring into inventory every time it places an order. (The “items” are specified in the context
of the problem; here, the units are tons of steel.) It yields meaningful results only if the inventory
is used fairly steadily, such that the inventory declines steadily – from the amount ordered down
to zero – before a new order is received. The idea is to trade ordering costs off against carrying
costs, toward the goal of minimizing the total of these two inventory management costs, with the
formula
EOQ =
2TF
cc
.
Here T is the total number of units used each year, F is the essentially-fixed cost of placing and
taking delivery of an order, cc is the annual cost of holding an item in inventory, and EOQ is the
most cost-effective quantity to order each time. For Palmetto, we therefore find
EOQ =
2  11,000  $40

$115
$880,000
 7,652.173913 = 87.476705.
$115
So each time it places an order, Palmetto should request delivery of about 87½ tons of steel. If
it does so, then it will place about 11,000 ÷ 87.476705 = 125.747763 orders per year, for an order
about once every 365 ÷ 125.75 = 3 days or so. Its average steel inventory would be 87.476705/2 =
43.738352 tons. Note that Palmetto’s carrying cost is quite high while its ordering cost is fairly
Trefzger/FIL 240 & 404
Topic 14 Problems & Solutions: Short-Term/Working Capital
16
low, so Palmetto is likely to find that it should place a lot of orders and not hold much of its annual
steel usage in inventory at a given time. If it did follow this plan (and could do so with the exact
EOQ values), then its total annual inventory management costs would be
Ordering cost: 125.747763 orders x $40 per order = $ 5,029.91
Carrying cost: 43.738352 avg. tons x $115 per ton = $ 5,029.91
Total
$10,059.82
(Note that at the EOQ, annual carrying costs and ordering costs are equal.) Of course, the numbers
generated by the EOQ formula sometimes can not be adhered to exactly; for example, ordering
partial units may or may not be plausible (a firm could perhaps order a fraction of a ton of steel,
but not a fraction of a pair of shoes, or of a computer). And a partial order seems strange, as well.
But EOQ might at least prevent a company from making huge mistakes in its inventory management.
If, for example, Palmetto has instead been following a plan of ordering 1,000 tons 11 times per year
(average inventory of 1,000 ÷ 2 = 500 tons), then its total inventory management costs would be
Ordering cost: 11 orders x $40 per order =
Carrying cost: 500 avg. tons x $115 per ton =
Total
$
440
$57,500
$57,940
The high carrying cost per ton on this high average number of tons held would result in extremely
high total management costs. But trading off in the other direction also would not be optimal;
if Palmetto had instead been ordering 44 tons 250 times per year (average inventory of 44 ÷ 2 =
22 tons), then ordering costs would be quite high and total inventory management costs would be
Ordering cost: 250 orders x $40 per order =
Carrying cost: 22 avg. tons x $115 per ton =
Total
$10,000
$ 2,530
$12,530
Thus even if it had to use approximate figures, Palmetto could bring its inventory management costs
down, relative to one of these two more extreme cases. For example, if the company approximated
the values suggested by the EOQ analysis, it might order 125 times per year, placing an order for
11,000 ÷ 125 = 88 tons each time. Average inventory would be 88 ÷ 2 = 44 tons, and we would see
Ordering cost: 125 orders x $40 per order =
Carrying cost: 44 avg. tons x $115 per ton =
Total
Trefzger/FIL 240 & 404
$ 5,000
$ 5,060
$10,060
Topic 14 Problems & Solutions: Short-Term/Working Capital
17