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F1 Financial Reporting and Taxation

Module: 22

Inventories and Cash Management

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1. Managing inventories

Introduction

In 1976, rock giants Led Zeppelin released their seventh studio album entitled 'Presence'. The album came off the back of a long line of chart- topping albums and an enormous global tour which saw them regularly sell- out 20,000-seat shows. Unfortunately, the popularity and the 2-year long tour took its toll, and the songs on Presence did not quite meet the standards set by their previous records.

However, Zeppelin's record company obviously hadn't heard the album and proceeded to produce copies of the record in high volumes, expecting the kind of demand that the world's biggest rock band would create. Record stores also pre-ordered the album in large quantities, expecting to sell out very quickly.

The result now is that Presence is one of the most 'uncollectible' records in the world. It's so easy to get and so unpopular among fans that there remain to this day store cupboards full of plastic sealed copies of Presence, likely never to be heard!

So, why did this happen? Well, it's a classic example of too much stock with too little demand, which is a key component of managing inventory. In this case, it is likely to have led to a significant loss for the record company, who will have spent a lot of money paying the band, for the studio, for the production of the records, but only managed to sell a fraction of the expected amount. The same goes for the record stores: these 'uncollectible' records have to be stored, which isn't free, and possibly discounted to get people to buy them.

So, that's one way in which inventory management, when done poorly, can lead to lower profits and perhaps even losses. But there is much, much more to inventory management, and we will be taking a closer look at that in the following sections.

The need for inventory management

Let’s imagine that we own a toy car manufacturing company and we have a warehouse to store our entire toy car inventory. Orders can sometimes be erratic, so we generally have a decent stockpile on hand to cover peaks in demand. We also have several units of spare parts on hand for returns and repairs, and a decent materials stockpile, so production can commence as soon as new orders are received.

Having high amounts of inventory on hand allows us to dispatch orders immediately, avoiding the problem of having production delays interfere with deliveries. It also gives us a head start on any custom orders we receive, allowing us to fill these in a matter of days rather than weeks.

With all our materials on hand, we can:

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work on repairs as soon as they are received and returned goods can be replaced and dispatched instantly with products from our warehouse shelves. The ability to store high levels of inventory also gives us the ability to purchase materials in bulk and take advantage of bulk discounts, while also hedging against the possibility of material price increases.

However, there are also many costs involved. Renting, cleaning and staffing the warehouse all incur a significant level of expenditure. During the course of business, inventory in the warehouse gets lost, damaged or possibly stolen. In the case of stockpiled products, many of them need to be sold at discounts to avoid them becoming obsolete once new products are launched. And to avoid complete disaster, the entire warehouse and its contents needs to be insured.

As you can see, there are many costs and benefits that relate to inventory. The choices available to firms range between operating at maximum capacity and storing as many products as possible, to operating a 'just-in- time' system and storing no inventory at all.

Finding the balance between these factors is what good inventory management is all about.

Inventory costs

So, one key consideration in inventory management is inventory cost, and it includes more costs than you may immediately expect. However, to make things easy, the costs of holding inventory can be divided into four categories:

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Obviously, the goal of any management team would be to keep inventory costs at the lowest level possible without compromising service to customers.

Thinking back to our Led Zeppelin example, we know that one of the biggest costs ended up being holding costs, since the record company and shops struggled to sell the product. All of those records have to be stored somewhere! In order to reduce the holding cost, record stores might have sold the album at a discount, perhaps even cheaper than the purchase cost. This could of course lead to a loss, but it may actually work out cheaper than storage costs.

One thing we can say for sure though; there was no worry about the cost of running out of stock!

Lead times

The period of time between placing an order and receiving the goods is known as the lead time. So, if you order a book on Amazon.com at 5pm on a Monday and you receive the book at 2pm on Wednesday, the lead time is approximately 2 days. The lead time when you order a coffee at a café is, depending on how busy it is, between 1 and 5 minutes.

Lead times are a very real issue in the business world, as buyers obviously do not receive goods the instant their order is placed. Time is required for order processing, packaging, handover and delivery. Therefore, it is important that businesses account for this time lapse when managing inventory levels and setting re-order times and quantities.

For instance, firms will rarely wait until their stockpiles are reduced to zero before re-ordering as this can result in long lead times and lost customers. Sufficient levels of inventory are generally kept on hand at all times to ensure that any anticipated demand can be met. Such stocks are known as buffer stocks, which are generally over and above what is needed to meet demand, however they can serve as a lifeline if lead times are longer than expected.

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2. The Economic Order Quantity (EOQ) model Now we move on to some more technical approaches to inventory management. As we have seen, good inventory management requires getting the balance right between how much demand there is for a product and how much of that product you keep in stock. But we also need to consider the associated costs, such as holding costs and the order cost, to get an idea of how much certain levels of stock will cost the business.

A really simple way to do this is to use the Economic Order Quantity (EOQ) Model. The EOQ model as the name suggests, is a formula used to calculate the order quantity that will minimise inventory costs.

The formula to find the EOQ is:

Key

D

Demand

Number of units expected to be sold – e.g. 1,000 newspapers a day, 300,000 books per year, etc. We just need be make sure that the units are used consistently.

Co

Order cost of 1 order

How much it costs to order a particular number of units. What is important here is that we consider the order costs not the cost per item. The order cost might, for instance, include a standard delivery charge irrespective of how many items are ordered.

Ch

Holding cost of 1 unit This is how much it would cost to store the

ordered item before it can be sold.

Example – EOQ model

Instead of the toy car manufacturer, let's instead imagine we sell toy cars in a retail store (so we would be purchasing stock from the toy car manufacturer). We have steady demand for the product which amounts to 1,000 units per year.

Each car we purchase costs us $25, the cost of placing each order is $75 and the cost of holding a unit is 20% of the purchase cost.

We want to determine the order quantity that will minimise our inventory costs and estimate what the total annual inventory cost will be.

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Step 1: Define the parameters

From the above information we can derive that: D

= 1,000

Co = $75

Ch = $25 x 20% = $5

Step 2: Calculate EOQ

Now we need to plug our parameters into the EOQ formula, which should look something like this:

EOQ = 173.21

This tells us that our economic order quantity is 173.21 units per order. That means that our best option is to buy 173.21 cars per order. Obviously, we can't but 0.21 of a car, so we would round that down to 173 units.

Let's see if we can understand this figure a little better. If we were to buy fewer than 173 units, let's say just 5. The $75 order costs would be spread over just 20 cars making the cost per car quite high (at $15 per car) and eat into our profit margin. If on the other hand, we were to buy 1,000 the $5 per year holding costs per car would become high. 173 units is the amount which balances the two and minimises the total cost.

So, now we need to work out how many orders we need to place in order to meet the demand of 1,000 toy cars per year:

1,000 173

= 5.78 orders per year

So. in order to fulfil demand of 1,000 units, we would need to place 5.78 orders. Obviously, this would be impractical in real life, so again we would round it up to 6 orders and adjust the order quantity slightly:

1,000 6

= 167 units per order

Step 3: Calculate annual inventory cost

We now need to total up our purchase costs, order costs and holding costs to calculate our total annual inventory cost:

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Annual order costs (6 orders at $75 each) $450 Annual holding costs (167 units at $5 each) x 0.5* $418 Purchase costs (1,000 units at $25 each) $25,000 Total inventory costs $25,868

*Note that we have multiplied our annual holding costs by 0.5. This is because, assuming we sell it evenly day by day, while we may start with 167 cards in stock, it gradually reduces to zero. On average 0.5 x 167 = 83.5 cards are held over the period.

Quantity discounts using EOQ

It is a common sales technique for suppliers to offer bulk purchase discounts. That way they are able to move larger amounts of stock faster and secure higher order quantities in return for a small discount in price.

In these situations, the purchaser needs to decide whether or not the discount is worthwhile from their standpoint. Order costs decrease due to fewer orders needing to be placed, and purchase costs decrease due to the discounted price. However, holding costs obviously increase due to the higher levels of inventory that will be acquired and need to be stored.

Example – Quantity discounts

Following on from our above example, let’s assume that the supplier offers a 5% discount for orders of over 500 units. All other information remains the same, that is:

D = 1,000

Co = $75

Ch = $25 x 20% = $5

Unit cost = $25

Let’s work through the implications of taking the discount by seeing if we would make a saving by buying 500 units in one go and taking the discount.

Step 1: Calculate order costs at the discount quantity

First, we’ll calculate the order costs for order quantities of 500 units.

Demand (units) 1,000 Order quantity (units) 500 Number of orders required 2 Cost per order $75 Total annual order cost $150

If demand is 1,000 and we are going to order 500 units per order, then we only require 2 orders per year (1,000 divided by 500). We know the cost per order is $75, and so the annual order cost will be $75 x 2 = $150.

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Step 2: Calculate holding costs at the discount quantity

Since the holding cost is based on the purchase cost, we need to first apply the discount to the purchase cost and then calculate the holding cost:

Price per unit $25.00 5% discount ($1.25) Discounted price per unit $23.75

Annual holding cost (20% of $23.75 price per unit) $4.75 x 500 units $2,375.00 Annual holding cost (midpoint) x 0.5 $1,187.50

As in our previous example, we take the midpoint of our holding costs by multiplying by 0.5.

Step 3: Calculate total annual inventory costs at the discount quantity

We now need to add our variable costs to our purchase cost. In our previous step we calculated the discounted purchase price to be $23.75 per unit (5% discount on $25).

Therefore, to meet demand of 1,000 units, our total purchase costs will be $23,750 ($23.75 per unit x 1,000 units).

Therefore, our total annual inventory costs will be:

Annual holding cost $1,187.50 Annual order cost $150 Annual purchase cost $23,750 Total annual costs $25,087.50

Let’s compare this to the inventory costs in our previous example, where we calculated annual inventory costs at an EOQ of 167 units:

Annual order costs (6 orders at $75 each) $450 Annual holding costs (167 units at $5 each) x 0.5 $418 Purchase costs (1,000 units at $25 each) $25,000 Total inventory costs $25,868

This reveals that ordering in bulk is $780.50 cheaper than ordering at our EOQ, making it a financially worthwhile option. Our results show that holding costs are significantly higher when we order in large quantities, but order costs decrease as a result of fewer orders and purchase costs decrease as a result of discounted prices, ultimately leading to a lower cost overall.

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Limitations of the EOQ model

The EOQ model is used under the following assumptions:

• Demand is constant, meaning inventory is reduced at a constant rate – This can sometimes be a fair assumption, but as we saw in the Led Zeppelin example, demand can be hard to predict!

• Price is constant, meaning that discounts and price fluctuations are non-existent – Obviously, the market is in constant flux with prices changing all the time. Often, prince changes can be predictable, but occasionally prices will move unexpectedly, and this can have a big impact on the calculation.

• Inventory is replenished at regular intervals – This is sometimes the case, but not always. For instance, an ice-cream vendor would need to re-order more ice-cream in the summer than in the winter.

• Zero or negligible lead time – You may have notice that the formula doesn't really account for the costs of a long lead time. Businesses who have an unavoidably large lead time will need to consider this in their calculations.

In practice then, many of these assumptions will not be accurate. Zero lead time is impossible in many cases and perfectly constant demand is very rare. Therefore, it is important that EOQ calculations are taken as a general guideline rather than a pinpoint accurate solution.

3. Inventory control systems Re-order level (ROL) system

In this system new orders are made any time the level of stock falls below a set amount. So, for instance, a supermarket store may have a threshold of 50 loaves of bread. Once the stock falls to 50 loaves, a new order is made that will replenish the stock.

Obviously, it will take some time for the new loaves to arrive, so the replenishment level needs to account for this time. At 50 loaves, there should be plenty of time!

This system works well when inventory levels and sales are fairly predictable so that the entity isn't left understocked.

Periodic review system

In this system inventory levels are reviewed at a fixed interval such as once a fortnight or once a quarter. Each review date the stock levels are replenished when necessary.

It is possible to use a system that is a mixture of the two, depending on the inventory levels and sales.

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Calculating ROL

There are two main scenarios under which the ROL system operates:

• Demand and lead time are known with certainty.

• Demand and/or lead time are variable.

Each scenario will require slightly different calculations.

Demand/lead time are known

Contraband Ltd is a retailer of fireworks. It sells 50 units of its most popular firework daily. Their supplier takes a two week to deliver the order to their warehouse.

In this case, the inventory manager should place an order before the inventory drops below 700 units. Let's think about why this is the case.

If it takes two weeks for new stock to come in, then Contraband Ltd can sell 50 x 14 = 700 units in that time. Therefore, once inventory levels reach 700 for this item then Contraband will have to make a new order to prevent running out of stock.

Therefore, the calculation is:

ROL = Demand (per unit) x Lead time (per unit)

Demand/lead time are variable

When the demand and lead time is unknown or variable, the ROL is based on the maximum demand and the maximum lead time. This is done as a safety net, so stock definitely doesn't run out. However, this approach will lead to 'buffer stock' i.e surplus stock that may not be sold before the next delivery.

So, if we take Contraband again, but this time we don't know their lead time or demand (because they are variable). Instead, we know that the maximum lead time is 1 month (28 days) and the maximum demand is 75 units per day. Using the same formula, we get a maximum ROL of 75 x 28 = 2,100.

If we also say that the average demand is 60 units per day and average lead time is 15 days, then the average ROL is 60 x 20 = 1,200.

Therefore, the buffer will be 900 units (Maximum ROL – Average ROL).

4. Cash flow forecasting Introduction

It's was a Friday morning and Anika's business’s bank account was empty. In a matter of hours, she’d have to make a £100,000 payroll payment to her loyal staff. As the CEO of a profitable and growing company, she had no clue how this had happened or what she would do; she couldn’t ask the bank for money, and no one else would give her that kind of cash on such short

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notice. As soon as those cheques were cashed by her staff, the company would have a massive overdraft and could, potentially, have to close its doors.

Having had no sleep the night before, Anika was certain that the end was near we she arrived at the office. But by some incredible stroke of luck, when the mail came that afternoon, just a couple of hours before payroll was to be issued, she received a number of outstanding cheques from clients that totalled more than £150,000.

She ran as fast as she could to the bank, made the deposit and vowed to never again be in a position where she didn't have enough cash on hand to cover current costs.

As you hopefully saw in the above story, good cash management is essential to the health of a business. Even profitable businesses can find themselves struggling to survive if sufficient funds are not available when needed. A lack of cash can lead to high financing costs, damaged customer/supplier relationships and lost investment opportunities from not having cash at the right time.

Cash flow forecasts

To facilitate good cash management, organisations use cash flow forecasts. Imagine you have a large payment due in a month and minimal cash in the bank. A cash flow forecast will help determine whether sufficient cash will be received in the interim, or if a source of finance will need to be arranged. Without a reliable forecast, emergency finance will need to be sourced which can damage the banking relationship, or a late payment will be made which will damage the supplier relationship. If Anika had better forecast her cash flow she could perhaps have arranged short term funding safe in the knowledge that cheques would be coming in soon, and this could have saved her the concerns of not being able to pay her loyal staff.

Similarly, if you have a large cash balance and have only forecast minimal outflows for the coming 6 months, you can commit your funds to an interest earning account for that period of time, confident that your funds will be able to stay there for the entire term. This ability to plan ahead means the organisation can make the most of its cash resources, while also avoiding the cash flow problems that can affect even the most profitable businesses.

When to hold cash

There are a number of reasons why an entity may me motivated to hold or spend cash. Let's have a look at some of the reasons why a company needs to make sure they have some cash available:

• Transactions motive - Cash is needed in a company most importantly to cover the cost of day-to-day expenses, to make sure the business can maintain its current operations.

• Precautionary motive - Once cash is used up to maintain operations, there will usually then be a resource of cash put aside for

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unexpected expenses. These are essentially saving for when things go wrong or not to plan.

• Investment/speculative motive - Once the previous two are covered, then cash can be put aside for more opportunistic ventures, such as taking advantage of market investment opportunities.

The cost of running out of cash

If a firm runs out of cash, bad things are likely to happen. Following is a list of the most likely and most serious problems caused by running out of cash:

• Settlement discounts for early payment are unavailable. This means the full price must be paid every time in the future.

• Trade suppliers will almost certainly refuse further credit and are quite likely to charge higher prices and downgrade the priority with which orders are processed.

• If wages are not paid on time... well, I think you can imagine how that would play out!

5. Cash budgets In order to keep an eye on cash flow we can use something called a cash budget. A cash budget is a detailed forecast of cash receipts and payments, used to determine the expected cash balance of a business over a certain period.

To illustrate the value of this let’s work through an example of preparing a cash budget:

Example

Imagine we have a toy car company that has been expanding rapidly. With several new machinery purchases coming up, we’ve decided to prepare a cash budget for June to August to help manage the company’s cashflow. Below is the budgeted data for the 6-month period to August:

March April May June July Aug

£ 000 £ 000 £ 000 £ 000 £ 000 £ 000 Credit sales 500 500 500 540 540 560 Cash sales 70 81 88 92 93 97 Wages 200 200 200 220 220 220 Credit purchases 140 145 155 160 170 170 Operating costs 120 122 125 128 131 136 (excl. depreciation)

Note that this is what would appear in the accounts and is not necessarily cash. Credit customers pay later, so of the £500,000 sold in March the cash

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is not received until subsequent months. Credit purchases are not necessarily paid for in the month of purchase either.

We'll use the following additional information to help us work out how much is received and paid in each month:

• Credit customers are expected to pay as follows: 75% in the month following sale, 15% in the second month, 6% in the third month, and 4% written off as bad debts.

• 60% of wages are paid in the month they are incurred, with the remaining 40% paid the following month.

• 80% of credit purchases are paid for in the month after purchase, with the remaining 20% paid two months after purchase.

• Operating costs are paid in full each month.

• The company recently sold an old piece of machinery for £85,000, for which full payment is expected in June.

• The company has just purchased 3 new machines, each for £140,000. The first machine must be paid for in full by June, while the other 2 must be paid for by July.

• The opening cash balance on March 1 is £81,000

In order to prepare our cash budget, we will go through the following process:

Step 1: Calculate cash receipts

Cash sales

From the budgeted data above, we know that our cash sales will be as follows:

June £92,000 July £93,000 August £97,000

Credit sales

We need to calculate our receipts from our credit sales based on the following model:

1 month after sale 75

% 2 months after sale 15

% 3 months after sale 6% Bad debts 4%

We can summarise these receipts as follows:

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Receipts

Credit sales (from table) June July Aug £ 000 £ 000 £ 000 £ 000 March 500 (6%) 30

April 500 (15%) 75 (6%) 30

May 500 (75%) 375 (15%) 75 (6%) 30 June 540 (75%) 405 (15%) 81 July. 540 (75%) 405

480 510 516

The above chart shows that in June, we will collect 6% of March’s sales (£30,000), 15% of April’s sales (£75,000) and 75% of May’s sales (£375,000) for a total of £480,000 in cash receipts. The same collection pattern is applied to both July and August.

Other receipts

We forecast that we will receive £85,000 in payment for our machinery in June.

Summarise cash receipts

We’re now able to summarise all cash receipts for June-August:

June July Aug £ (000) £ (000) £ (000)

Cash sales (from table) 92 93 97 Receipts from credit sales 480 510 516 Receipts from machinery sal. 85

Total receipts 657 603 613

Step 2: Calculate cash payments

Credit purchases

We know that 80% of credit purchases are paid in the month following purchase, with the remaining 20% paid two months following purchase. Therefore, we can summarise payments for purchases as follows:

Credit sales (from table) Payments

June July

Aug

£ 000 £ 000 £ 000 £ 000 April 145 (20%) 29

May 155 (80%) 124 (20%) 31

June 160 (80%) 128 (20%) 32 July. 170 (80%) 136

153 159 168

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The above chart shows that in June, we will pay for 80% of May’s purchases (£124,000) and 20% of April’s purchases (£29,000) for a total of £153,000. The same pattern is applied to July and August.

Wages

We know that wages are paid 60% in the month they relate to and 40% the following month:

Wages Payments

June July

August

£ (000) £ (000) £ (000) £ (000) May 200 (40%) 80

June 220 (60%) 132 (40%) 88

July 220 (60%) 132 (40%) 88 August. 220 (60%) 132

212 220 220

Operating costs

Operating costs are paid in full each month. For June to August this amounts to:

June £128,000 July £131,000 August £136,000

Capital expenditure

Lastly, we need to account for our new machinery payments. One machine is being paid for in June, which amounts to £140,000. In July, two more machines are paid for, which cost £280,000 in total.

Summarise cash payments

We can now summarise our cash payments for June to August as follows:

June £ 000

July £ 000

Aug £ 000

Payment for purchases (153) (159) (168) Wages (212) (220) (220) Operating costs (128) (131) (136) Payments for new machinery (140) (280) Total payments (633) (790) (524)

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Step 3: Prepare cash budget

Putting our cash receipts and cash payments forecasts together, our cash budget will appear something like this:

June July Aug

£ 000. £ 000 £ 000

Receipts from cash sales 92 93 97 Receipts from credit sales 480 510 516 Receipts from machinery sale 85 Total receipts 657 603 613

Payment for purchases (153) (159) (168) Wages (212) (220) (220) Operating costs (128) (131) (136) Payments for new machinery (140) (280) Total payments (633) (790) (524)

Opening cash balance 81 105 (82) Net cash movement 24 (187) 89 Closing cash balance 105 (82) 7

Notice that the cash balance at the start of June is added to the net cash movement of receipts and payments to make the end of month balance. This then becomes the new opening balance in the following month.

Step 4: Cash management

In the above example, we see that although a positive cash position is expected by the end of August, there will be a negative cash balance during the month of July. This is largely due to the payments for the new machinery that are due that month. In this situation, the issue becomes how to manage this cash deficit and look for ways to minimise it or avoid it completely.

Some options available would be:

Factoring or invoice discounting

At our current collection rates, it takes us 3 months to fully cash up each of our debtors. That’s a long time to have cash tied up in receivables. With a factoring or invoice discounting arrangement in place we could typically cash in 80% of our debtors instantly, significantly improving our cash position.

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Delaying large items of capital expenditure

During July we’re expecting a cash outflow of £280,000 for new machinery. That’s a big cash commitment for a single month. If we could negotiate just a one-month delay on at least a portion of this payment it would go a long way towards improving our cash position. If we could go one step further and negotiate payment by instalments that would be even better.

Delaying payments to creditors

Good cash management is often about speeding up receipts while delaying payments as much as possible. In this situation, we pay around £160,000 to creditors each month, so delaying a portion of this could go a long way towards keeping us out of overdraft during July. However, care must be taken to not damage supplier relationships in the process.

Overdraft

Short term overdrafts are common, and many businesses will already have these in place with their banks. However, in this example we are looking at a negative £82,000 cash balance in July, which, depending on the business in question can be a rather high limit to secure.

Long term finance

Cash requirements that fall beyond the remedy of an overdraft can be met by obtaining long term finance. Common examples of this are a long-term bank loan or issuing new capital.

6. Cash management models Baumol model

William Baumol is an American economist who noted similarities between cash balances and inventory levels. His model for managing cash is therefore precisely based around Economic Order Quantity assumptions:

Q (cash investment) = √ 2CoD

Ch

Where:

D Demand

Co Order Cost of One Order

Ch Holding Cost of One Order

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Example

This should be a cake walk because we've already looked at EOQ management of inventories!

Bloop Heating have a really strong year in 20X7 and generate £100,000 per month in excess cash that they want to invest it in securities. The interest rate on such investments is 3% pa. The transaction costs associated with each separate investment of funds is constant at $30.

Calculate the following on Bloop's behalf:

• What is the optimum cash to investment to be made in securities?

• How many transactions should Bloop make per year?

• How much interest will Bloop make on their investments every year?

• What's the cost of making Bloop's investments?

Answer

First up we're going to calculate the optimum cash investment to be made using the Baumol Model:

Q (cash investment) = √ 2CoD

Ch

D Demand £1,200,000 (12 x £100,000)

Co Order Cost of One Order £30

Ch Holding Cost of One Order 3%

Q (cash investment) = √ 2 (30 x 1,200,000)

0.03

Q (cash investment) = √

72,000,000

0.03

Q (cash investment) = √£2.4 billion = £48,989.79

What is the optimum cash to investment to be made in securities?

We just worked it out! £48,989.79

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How many transactions should Bloop make per year?

This tricky calculation is not as bad as it looks! We know the optimum amount to invest in each calculation (see above), and we know how much Bloop have in surplus per year. We accordingly need to calculate how many optimum calculations they can make per year!

Yearly surplus cash Optimum number of transactions =

£48,989.79

12 x £100,000 Optimum number of transactions =

£48,989.79

£1.2 million Optimum number of transactions =

£48,989.79

Optimum number of transactions = 24.49

You can't make 24.49 transactions! We round this to 24 - the nearest whole number.

How much interest will Bloop make on their investments every year?

Well, we know Bloop are making twelve transactions of £100,000 each, and that 30% (0.3) is made on each in interest. Therefore:

Interest = £1.2 million x 0.03 = £36,000

What's the cost of making Bloop's investments?

We also know that they're going to be making 24 transactions per year, and we know it costs £30 per transaction... Therefore:

24 x £30 = £720

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Miller-Orr model

The Miller-Orr model was developed in an attempt to regulate the movement of a company's cash. It does this by setting upper and lower limits on the amount of cash a company is allowed to hold. Let's take a look at how it works for Bloop Heating:

We can see that the model sets an upper limit (H) and lower limit (L) for cash. In Bloops case, H = £50,000 and L = £10,000.

Okay so far, but what's Z? Z is the amount of cash Bloop want to have ideally, and this is called a target cash balance or return point. It's called a return point because this is the point to which cash returns from H. In Bloop's case Z = £20,000, and this means that this is what happens when cash reaches H:

The opposite happens when cash drops to L, when (Z-L) dollars are transferred from securities into cash:

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Usually, the company sets their own lower limit and the upper limit is calculated by the model.

Formulae

You will be given the Miller-Orr formulae in the exam, and they look like this:

1 Return point = lower limit + ( 3

X spread)

(3/4 x Transaction costs x variance of cash flows)1/3 Spread = 3 x

Interest rate

When using these formulae, variance and interest rates should be expressed in daily terms. Also, it's really worth remembering that Variance is Standard Deviation squared, as this is one way they'll try and catch you out!

The Miller-Orr model makes some unrealistic assumptions such as normally distributed cash flows but, Miller and Orr claim the model is strong and claimed that it saved companies significant cash.

Example

Bloop decide to increase their minimum cash balance to £20,000. Given that transferring money costs £50 and the interest rate is 0.05% per day, calculate the following:

• the spread between the upper and lower limits

• the upper limit

• the return points

The standard deviation is £4,000, meaning that the variance is £16 million.

Answer

Spread

This looks complicated, but don't panic. All we are doing is taking the original equation for calculating spread and then inputting the information from the question. So first up, let's remind ourselves how to calculate spread:

Spread = 3 x (3/4 x Transaction costs x variance of cash flows)1/3

Interest rate

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Even better, we are told that transaction costs are £50, interest is 0.05% (or 0.0005), and the variance of cash flows is £16 million:

( 3/4 x £50 x £16,000,000)1/3

Spread = 3 x 0.0005

( 3/4 x £600,000,000)1/3 Spread = 3 x

0.0005

Spread=3x 10,626.59 Spread

= £31,879.76

Upper limit

We've just calculated the spread between the upper and lower limits of Bloop's cash. This means that adding the spread to the lower limit gives us the upper limit.

£20,000 + £31,879.76 = £51,879.76

Return point

Here we are using the return point equation and just inserting our spread of £31,879.76 and lower limit of £20,000:

1 Return point = lower limit + ( x spread)

3 1

Return point = 20,000 + ( X £31,879.76) 3

Return point = 20,000 + 10,626.59 = £30,626.59