Relevant costs

The change in cash flow can be:

• additional amounts that must be paid
• a decrease in amounts that must be paid
• additional revenue that will be earned
• a decrease in revenue that will be earned.

A change in the cash flow can be identified by asking if the amounts that would appear on the company’s bank statement are affected by the decision, whether increased or decreased. Banks record cash so this test is reliable.

1. Sunk costs (past costs) or committed costs are not relevant

Sunk, or past, costs are monies already spent or money that is already contracted to be spent. A decision on whether or not a new endeavour is started will have no effect on this cash flow, so sunk costs cannot be relevant.

For example, money that has been spent on market research for a new product or planning a new factory is already spent and isn’t coming back to the company, irrespective of whether the product is approved for manufacture or the factory is built.

Committed costs are costs that would be incurred in the future but they cannot be avoided because the company has already committed to them through another decision which has been made.

For example, if a company has two year lease for piece of machinery, that cost will not be relevant to a decision on whether to use that machinery on a new project which will last for the next month.

2. Re-apportionment of existing fixed costs are not relevant

Irrespective of what treatment is used in the company’s management accounts to split up costs, if the total costs remain the same, there is no cash flow effect caused by the decision.

Note that additional fixed costs caused by a decision are relevant. So, if you were evaluating the viability of a new production facility, then the rent of a building specially leased for the new facility is relevant.

3. Depreciation and book values (notional costs) are not relevant

Depreciation is not a cash flow and is dependent on past purchases and somewhat arbitrary depreciation rates. By the same argument, book values are not relevant as these are simply the result of historical costs (or historical revaluation) and depreciation.

4. Increases or decreases in cash flows caused by a project are relevant

So, if an old product is discontinued three years early to make room for a new product, the revenue and cost decreases relating to the old product are relevant, as are the revenue and cost increases on the new. The cost effects relate to both changes in variable costs and changes in total fixed costs.

5. Revenues forgone (given up) because of a decision are relevant

If a company decides to keep an asset for use in the manufacture of a new product rather than selling it, then its cash flow is affected by the decision to keep the asset, as it will now not benefit from the sale of the asset. This effect is known as an opportunity cost, which is the value of a benefit foregone when one course of action is chosen in preference to another. In this case, the company has given up its opportunity to have a cash inflow from the asset sale.

Types of decision
We will now look at some typical examples where you have to decide which costs are relevant to decision-making. We suggest that you try each example yourself before you look at each solution. In all examples we ignore the time value of money.

Always think: what future cash flows are changed by the decision? Changes in future cash flows reliably indicate which amounts are relevant to the decision.

Example 1: Relevant cost of materials
A company is considering making a new product which requires several types of raw material:

What is the relevant cost of the materials required for manufacture of the new product?

Solution:
Taking each material in turn:

Material A – As there is no inventory, all 40 units required will have to be bought in at $7 per unit. This is a clear cash outflow caused by the decision to make the new product. Therefore, the relevant cost of Material A for the new product is (40 units x $7) = $280.

Material B – The 100 units of the material already in inventory has no other use in the company, so if it is not used on the new product, then the assumption is that it would be sold for $12/unit. If the new product is made, this sale won’t happen and the cash flow is affected. The original purchase price of $10 is a sunk cost and so is not relevant. In addition, another 50 units are needed for the new product and these will need to be bought in at a price of $14/unit.

The total relevant cost for Material B is:

Material C – This material is regularly used in the company, so if the 50 units in inventory are diverted to the new product then this will mean that inventory will need to be replenished. In order to do this, Material C purchases for existing products will be accelerated by 50 units. The current purchase price of $22 will be used to determine the relevant cost of Material C as this will be the value of each unit purchased. The original purchase price of $20 is a sunk cost and so is not relevant. Therefore the relevant cost of Material C for the new product is (120 units x $22) = $2,640.

Example 2: Relevant cost of labour
A company has a new project which requires the following three types of labour:

What is the relevant cost of the labour hours required for the new project?

Solution:
Taking each type of labour in turn:

Unskilled – 12,000 hours are required for the project and the company is prepared to hire more staff to meet this need. The incremental cash outflow of this decision is (12,000 hours x $8) = $96,000.

Semi-skilled – Of the 2,000 hours needed, 800 are already available and already being paid. There is no incremental cost of using these spare hours on the new project. However, the remaining 1,200 hours are still required and will need to be fulfilled by hiring temporary workers. Therefore, there is an extra wage cost of (1,200 hours x $14) = $16,800.

Skilled: Determining the relevant cost of labour if it is diverted from existing activities is tricky and is often done incorrectly. If this is the case, then the relevant cost is the variable cost of the labour plus the contribution foregone from not being able to use the labour for its existing purpose.

The temptation is to see that the same number of skilled employees are paid before and after being moved to the new project and therefore the opportunity cost of contribution foregone from diverting hours away from the existing production of Product X is the only relevant cost ($24/4 hours = $6 per hour). This is incorrect.

Say, for example, that 4 hours of labour were simply removed by ‘sacking’ an employee for four hours, one less unit of Product X could be made. Using the contribution foregone figure of $24 is the net effect of losing the revenue from that unit and also saving the material, labour and the variable costs. In this situation however, the labour is simply being redeployed so $24 understates the effect of this, as the labour costs are not saved.

Therefore, the relevant cost of skilled labour is:

Example 3: Relevant cost of machinery
Some years ago, a company bought a piece of machinery for $300,000. The net book value of the machine is currently $50,000. The company could spend $100,000 on updating the machine and the products subsequently made on it could generate a contribution of $150,000. The machine would be depreciated at $25,000 per annum. Alternatively, if the machine is not updated, the company could sell it now for $75,000.

On a relevant cost basis, should the company update and use the machine or sell it now?

Solution:
Immediately we can say that the $300,000 purchase cost is a sunk cost and the $50,000 book value and $25,000 depreciation charge are not cash flows and so are not relevant.

If the investment in the machinery is made, then the following cash flow changes are triggered:

• Machine update cost: $100,000
• Contribution from products: $150,000
• Opportunity cost: $75,000

Therefore, the relevant cost is:

As the relevant cost is a net cash outflow, the machine should be sold rather than retained, updated and used.

Example 4: Relevant cost of machinery
A business rents a factory for $60,000 per annum. Only half of the floor space is currently used and the company is considering installing a new machine in the unused part. The machine would cost $2.1m, be depreciated over 10 years at $200,000 per annum and then be sold for $100,000. The company would insure the new machine against damage for $5,000 per annum.

What are the relevant costs of the new machine purchase?

Solution:
Rent – this is not a relevant cost. Irrespective of how the company might use the floor space in the factory to generate a return, there is no change in cash flow relating to the rent as a result of the new machine.

Cost of machine – this is a relevant cost as $2.1m has to be paid out.

Depreciation – this is not a relevant cost as it is not a cash flow.

Sale proceeds – this is a relevant cost as it is a cash inflow which will occur in 10 years as a result of the decision to invest.

Annual insurance cost – this is a relevant cost as this is an additional fixed cost caused by the decision to invest.

These costs will have to be compared to the contribution that can be earned by the new machine to determine if the overall investment in the asset is financially viable.

The effects shown in Examples 1 – 4, above, are often found in questions where you are to determine whether or not a company should go ahead with a new project/investment/product, or if you are asked to calculate the minimum price a company should charge a customer for a piece of work.

Example 5: Further processing decision
A company buys a chemical for $12,000, which it breaks down into two components:

Component A can be converted into Product A if $6,000 is spent on further processing. Product A would sell for $12,000.

Component B can be converted into Product B if $8,000 is spent on further processing. Product B would sell for $15,000.

What processing decision should the company make in order to maximise profits?

Solution:
As the initial chemical is split into both components, it is not possible to make one component without the other, therefore if the company were to make only the components, the costs and revenues of both components will need to be recognised:

This is not worthwhile as incremental costs exceed incremental revenues.

Next we should consider whether the components should be further processed into the products.

Further processing Component A to Product A incurs incremental costs of $6,000 and incremental revenues of $5,000 ($12,000 – $7,000). It is not worthwhile to do this, as the extra costs are greater than the extra revenue.

Further processing Component B to Product B incurs incremental costs of $8,000 and incremental revenues of $11,000 ($15,000 – $4,000). It is worthwhile to do this, as the extra revenue is greater than the extra costs.

The production plan is therefore:

Example 6: Shut down decision
A company has two production lines and its management accounts show the following:

The total fixed costs of $24m have been apportioned to each production line on the basis of the floor space occupied by each line in the factory.

The company is concerned about the loss that is reported by Production Line B and is considering closing down that line. Closing down either production line would save 25% of the total fixed costs.

Should the company close down Production Line B?

Solution:
The incremental cash flows of closing down Production Line B are:

Therefore, the closure of Production Line B is not a good idea as the revenue lost is greater than the value of the costs saved.

What about closing down Production Line A?

The incremental cash flows of this decision would be:

The closure of Production Line A would also result in the revenue lost being greater than the value of the costs saved, so this isn’t a good idea either.

Really, the heart of the matter is the misleading effect of the relatively arbitrary apportionment of the fixed costs. A more useful presentation of the figures for decision-making would be:

Note that the $2m total profit is the same as the profit of $6m from Production Line A and the loss of $4m from Production Line B as shown in the table at the start of this example.

If either production line were closed down, fixed costs saved are 25% x $24m = $6m, however the contribution lost from the products (and contribution looks at cash flows caused by production) would be either $16m or $10m, which exceed the cash saved on the fixed costs.

Example 7: Make or buy decision
A company makes a product which requires two sequential operations (Operation 1 and Operation 2) on the same machine. The machine is fully utilised. Material costs $12 per unit.

Instead of carrying out Operation 1, the company could buy in components, for $15 per unit. This would allow production to be increased because the machine has to deal with only Operation 2.

Operation 1 takes 0.25 hours of machine time and Operation 2 takes 0.5 hours of machine time. Labour and variable overheads are incurred at a rate of $16/machine hour and the finished products sell for $30 per unit.

Should the company make the entire product internally or buy in the components and complete them in Operation 2?

Solution:
Some care is needed here to ensure all incremental cash flows caused by the decision are taken into account.

Machine running costs – the machine is already fully utilised on Operations 1 and 2 and will remain fully utilised, but only on Operation 2. Therefore, the machine running costs will not change, so are not relevant to the decision.

Material – if the buy-in option is accepted, the material cost increases from $12 to $15 per unit.

Production volume – this can increase by 50% because currently each item takes 0.5 hours in Operation 2, but 0.25 hours per unit will be released by Operation 1 which now will not be needed.

Assuming output is 1,000 units, the following would occur (ignoring labour and variable overheads which we know to be constant):

Therefore, it is worth buying in as incremental revenue exceeds incremental costs.