Chapter 13: Differential Analysis Notes

Chapter 13: Differential Analysis: The Key to Decision Making

Learning Objectives

• Identify relevant and irrelevant costs and benefits in a decision.
• Keep or drop decision.
• Make or buy decision.
• Special order decision.
• Constrained resource.
• Sell or process further decision.

Relevant vs. Irrelevant Costs and Benefits

• Relevant costs (benefits): Future costs and benefits that differ between the alternatives.
• Irrelevant costs (benefits): Future costs and benefits that do not differ between alternatives.
• Opportunity costs: The potential benefit that is given up when one alternative is selected over another.
• Sunk costs: A cost that has already been incurred and cannot be changed regardless of the decisions.

Every decision involves choosing from among at least two alternatives. Relevant costs (benefits) should be considered when making decisions, while irrelevant costs (benefits) should be ignored.

Example: Cathy's Trip

Cathy is considering visiting her friend in New York. She can drive or take the train.

• Train ticket: 40

• Tuitions for the next semester: 8,000

• Dinner cost on Friday: 30

• A part-time job opportunity in NYC for earning 50.

• Annual straight-line depreciation on car: 2,800

• Cost of gasoline: 0.10 per mile

• Annual cost of auto insurance and license: 1,380

• Maintenance and repairs: 0.07 per mile

• Parking fees at school: 360

• Reduction in resale value of car per mile of wear: 0.03

• Round-trip train fare: 104

• Cost of putting dog in a hotel while gone: 40

• Per day cost of parking car in New York: 25

Based on the information provided:

• Irrelevant: The depreciation of the car, the annual cost of insurance, the school parking fee and the dog hotel cost
• Relevant: The cost of gasoline, The cost of maintenance and repairs, The decline in resale value, The round-trip train fare and the cost of parking.

From a financial standpoint, Cathy would be better off taking the train to visit her friend.

• Gasoline (460 @ 0.10 per mile): 46.00

• Maintenance (460 @ 0.07 per mile): 32.20

• Reduction in resale (460 @ 0.03 per mile): 13.80

• Parking in New York (2 days @ 25 per day): 50.00

• Total relevant cost: 142.00

• Round-trip ticket: 104.00

• Total relevant cost: 104.00

Total Cost Approach vs. Differential Cost Approach

• The management of a company is considering a new labor-saving machine that rents for 3,000 per year. The machine could save labor cost by 15,000.

• Total Cost Approach: Compare the total costs and revenues with and without the new machine.

• It is noted that sales (5,000 units @ 40 per unit) are 200,000 in both scenarios.

• With the current situation the net operating income is 18,000, but after the new machine is introduced it's 30,000.

• Differential Cost Approach: Focus on the costs and revenues that differ between the alternatives.

• Incremental contribution margin: 15,000.

• Incremental expenses (rent on new machine): 3,000.

• Financial advantage of renting the new machine: 12,000.

Using the differential approach is desirable for two reasons:

1. Only rarely will enough information be available to prepare detailed income statements for both alternatives.
2. Mingling irrelevant costs with relevant costs may cause confusion and distract attention away from the information that is really critical.

Keep or Drop Decisions

One of the most important decisions managers make is whether to add or drop a business segment. Ultimately, a decision to drop an old segment or add a new one is going to hinge primarily on its financial impact.

Example: Lovell Company's Digital Watch Line

Lovell Company’s digital watch line has not reported a profit for several years. Lovell is considering whether to keep this product line or drop it.

An investigation has revealed that:

1. The fixed general factory overhead and fixed general administrative expenses will not be affected by dropping the digital watch line.
2. The equipment used to manufacture digital watches has no resale value or alternative use.

• Sales: 500,000
• Less: variable expenses: 200,000
• Contribution margin: 300,000
• Less: fixed expenses: 400,000
• Net operating loss: (100,000)

Based on the information provided:

• Incremental contribution margin if digital watches are kept: 300,000
• Less: Incremental costs: 260,000 (Salary of the line manager + Advertising - direct + Rent - factory space)
• Financial advantage of keeping the digital watches product line: 40,000

Make or Buy Decisions

A decision to carry out one of the activities internally or to buy externally from a supplier is called a “make or buy” decision.

Example: Essex Company

Essex Company manufactures part 4A that is used in one of its products. The unit product cost of this part is:

• Direct materials: 9
• Direct labor: 5
• Variable overhead: 1
• Depreciation of special equipment: 3
• Supervisor's salary: 2
• General factory overhead: 10
• Unit product cost: 30

An outside supplier has offered to provide the 20,000 parts at a cost of 25 per part. The special equipment used to manufacture part 4A has no resale value. The total amount of general factory overhead would be unaffected by this decision.

Should the company stop making part 4A and buy it from an outside supplier?

• Outside purchase price: 25 per part which results in 500,000
• Total relevant cost: 340,000 (Direct materials + Direct labor + Variable overhead + Supervisor's salary).

Given that the total relevant costs are less than the cost of buying the part, Essex should continue to make the part. Financial advantage of making part 4A is: 160,000

• If the space to make Part 4A had an alternative use, the opportunity cost would have been equal to 200,000 revenue that could have been derived from the alternative use of the space, making the total relevant cost 540,000.

Special Order Decisions

A special order is a one-time order that is not considered part of the company’s normal ongoing business. When analyzing a special order, only the incremental benefits and costs are relevant. Since the existing fixed manufacturing overhead costs would not be affected by the order, they are irrelevant.

Example: Jet Inc.

A foreign distributor offers to purchase 3,000 units for 10 per unit. This is a one-time order that would not affect the company’s regular business and fixed expenses. Annual capacity is 10,000 units, but Jet Inc. is currently producing and selling only 5,000 units.

Should Jet accept the offer?

• Incremental Revenue: 10 per unit, 3,000 units which results in 30,000
• Variable costs: 8 per unit, 3,000 units which results in 24,000
• Incremental contribution margin: 2 per unit which results in 6,000

If Jet accepts the special order, the incremental revenue will exceed the incremental costs. In other words, net operating income will increase by 6,000. This suggests that Jet should accept the order.

Constrained Resource

A manufacturing company may have limited number of machine-hours, labor-hours or limited amount of other resource.

Companies are forced to make volume trade-off decisions when they do not have enough capacity to produce all of the products and sales volumes demanded by their customers.

Products that provide the highest contribution margin per unit of the constrained resource.

Example: Ensign Company

Ensign Company produces two products and selected data are shown below:

Machine-hour on Machine A1 is the constrained resource and is being used at 100% of its capacity. Machine A1 has a capacity of 500 MH per month. There is 400 units demand on Product 1, which needs 1 machine-hour on machine A1. There is 600 units demand on Product 2, which needs 0.5 machine-hour on machine A1

Should Ensign focus its efforts on Product 1 or Product 2?

Ensign should emphasize Product 2 because it generates a contribution margin of 30 per MH of the constrained resource relative to 24 per MH for Product 1.

• Contribution margin per unit of Product 1: 24/ 1.00 MH equals 24
• Contribution margin per unit of Product 2: 15/ 0.50 MH equals 30

Focus on Product 2:

• 600 units demand for Product 2 * 0.50 MH result in 300MH, which will allow enough time for 200 units of product 1.
• 200 units * 24 result in 4,800, while all 600 units of product 2 * 15 result in 9,000

Sell or Process Further Decision

In some industries, two or more products, known as joint products are produced from a single raw material input.

The point in the manufacturing process where joint products can be recognized as a separate product is called the split-off point.

A decision as to whether a joint product should be sold at the split-off point or processed further is known as a sell or process further decision.

Example: Sawmill, Inc.

Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the joint products. Unfinished lumber is sold “as is” or processed further into finished lumber. Sawdust can also be sold “as is” to wholesalers or processed further into “fine-logs.”

The lumber should be processed further and the sawdust should be sold at the split-off point.