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Incremental Analysis Practice Quiz

Here are some sample incremental analysis practice problems. See if you can work the problem before looking at the solution.

Incremental Analysis can be used for more than just complex business decisions. Here'?s a good example of a personal decision that can be evaluated using a differential accounting approach.

Dorothy's Car

Dorothy is an elderly woman living in an urban area with adequate public transportation to meet her needs. She has a car, and also some concerns. She is trying to decide whether to keep the car, or sell the car and use public transportation. If she keeps the car she will have the following annual expenses:

gasoline
$ 500
insurance
$ 480
maintenance
$ 360

She also takes a trip out of town every year to visit her sister. Her travel costs are:

gasoline
$ 125
lodging
$ 200

Dorothy is worried that she might have an accident with her car. Her insurance costs have been going up as her age increases. Also, the cost of maintenance will increase as the car gets older.

She estimates she would spend $1000 per year on public transportation for her regular activities. Airfare to visit her sister would cost $350.

REQUIRED:

Using Incremental Analysis, compare Dorothy?'s two options. Based on this analysis alone, which would be the better option? What other considerations might effect Dorothy'?s decision?

Dorothy's Car Solution

In this example we have 2 alternatives:

  1. maintain the status quo and keep the car, or
  2. sell the car and use public transportation
Costs
Keep car
Sell car
Gasoline
$ 625 
 
Insurance
480
 
Maintenance
360
 
Parking
240
 
Lodging
200
 
Public Transportation
 
1000
Airfare
 
    350 
Totals
$ 1665
$ 1350
     
Costs if she keeps the car
$ 1665
 
Costs if she sells the car
1350
 
Annual Savings from selling car
$   315
 
     
One time revenue from selling car
$ 2000
 

Dorothy will save $ 315 per year if she sells her car. If money is the only consideration, her best option will be to sell the car. She might also consider what she can do with the revenue from selling the car. She will have to give up the convenience of having a car available at any time. She may have to adjust her schedule to accommodate using public transportation. As the car gets older it will need more maintenance, and may also need to be replaced. Will she be able to afford those costs? Parking is an expensive proposition in many cities. Increased traffic can be a problem from many elderly drivers. If Dorothy takes taxicabs she won't have to worry about driving in traffic, parking, fuel, maintenance, etc.

A Stitch in Time

Here's another example of Incremental Analysis, based on some common business choices.

Easton Company is a custom stitchery specializing in the manufacture of men'?s and women?'s underwear. They manufacture for a variety of customers under several brand labels.

The stitchers are paid $4.80 per dozen of finished garments. At the end of the day each stitcher?s total production is calculated and valued. Full Dozens are calculated using a weighting method. The garments are inspected and graded as follows: Pass, Seconds, Scrap. Stitchers are paid full price for Pass, half price for Seconds and nothing for Scrap. In other words, two dozen Seconds will be paid equivalent to one dozen Pass.

The company has a waiting list of candidates for work. They want to establish some criteria for performance and be able to maximize their profits. They also want to reward excellent workers with a bonus, and replace poor workers who are not able to meet a minimum quota, or who consistently have too many Seconds and Scrap.

The company charges customers $6.35 per dozen for stitching, in addition to other charges for materials, cutting, inspection packaging, etc. The stitchery section has overhead of $12,000 per month and there are 30 workstations. They work 22 days per month, on average.

They are considering the following bonus incentive plan:

dozen per day bonus per dozen
20 10 cents
24 20 cents 

For output below these amounts there would be no bonus, just regular pay.

They also want to determine the lowest amount of production that should be acceptable. In management'?s opinion an average or above average worker is better than a poor worker, and the company would benefit by eliminating those who are not meeting some minimum level of output.

Workers produce between 8 dozen and 24 dozen per 8 hour shift. Average workers produce 14 to 18 dozen per shift. Most of the workers are Average, a few are Excellent and a few are Poor (low production and/or too many Seconds and Scrap).

REQUIRED

Evaluate management's options. Evaluate the company's cost structure in the stitching department. Hint: determine the total cost per dozen at different production levels.

Evaluate the bonus suggestion. Although a bonus will cost the company more, will they receive a sufficient benefit to offset the additional cost? Will a bonus encourage Average workers to produce at higher levels? Will this be good for the company?

What minimum production level is acceptable? We will assume that a worker not able to meet his level will be replaced. Is this a valid management concern and is replacing workers the correct solution?

Quantify your answers.

A Stitch in Time Solution

This one's a bit more difficult, but we can make it easy to understand using Incremental Analysis.

First we'll determine the daily overhead costs per work station.

Overhead per station per month

$12,000 monthly overhead / 30 stations = $400 per station per month

Overhead per station per day

$400 per station / 22 work days per month = $18.18 per station per day

The $18.18 per day in overhead costs applies to all workers. At a minimum each worker must produce enough product to cover their wages plus their station's overhead.

You can analyze this by looking at revenue and costs at different production levels. Look at the 24 and 20 dozen levels and divide the range as follows, and calculate pay per day, based on different levels of output.

Dozen of output per day 

Stitcher's Pay per day
24
20
16
12
8
TIMES pay rate per dozen @ $4.80
$115.20
$96.00
$76.80
$57.60
$38.40
PLUS overhead per day @ $18.18
   18.18
   18.18
   18.18
   18.18
   18.18
TOTAL cost per stitcher per day
$133.38
$114.18
$94.98
$75.78
$56.58
COST per dozen
$ 5.56
$ 5.71
$ 5.94
$ 6.32
 $7.07
Profit per dozen          
REVENUE per dozen
$ 6.35
$ 6.35
$ 6.35
$ 6.35
$ 6.35
COST per dozen
5.56
5.71
5.94
6.32
7.07
PROFIT before bonus
0.79
0.64
0.41
0.03
(0.72)
LESS Bonus per dozen
.20
.10
     
PROFIT (LOSS) per dozen
0.59
.054
0.41
0.03
(0.72)

This chart shows that the company is losing money on workers producing below 12 dozen per day. They only make 3 cents per dozen for workers at the 12 dozen level. Clearly management should expect workers to produce above the 12 dozen level per day. A time limit should be set to train new workers. Management should expect new workers to improve quickly to keep their jobs.

The company can improve it's overall profit by eliminating low output workers, and replacing them with better workers. The incentive plan may work, if it encourages workers to achieve the 20 and 24 dozen levels. Even if they pay the bonus, the company still makes more money with excellent workers, compared with average workers.

Also remember that dozen per day includes Seconds and Scrap. We can assume that better workers produce fewer Seconds and Scrap. The next step would be to analyze the cost of wasted materials from Seconds and Scrap, plus added inspection and handling costs from these sub-standard units of output. This would further tilt the scales in favor of better workers, and help management set clear, measurable expectations for workers.

Shave and a Haircut

Max owns a salon. He has 6 barber chairs and workstations. His total overhead is $7,000 per month, which includes mortgage interest, utilities, depreciation, supplies, etc. Max allocates his overhead to the 6 barber chairs.

Max has several barbers working for him full time. Barbers work 8 hours per day, 6 days per week; they work an average of 26 days per month. Max pays his barbers $12.50 per hour (including payroll taxes, etc.), and they average three haircuts per hour. (Yes, they also make tips.)

Max would like to improve his income. His business appears profitable, but he is paying off a mortgage on the building, and has other business expenses to think of as well. As far as he'?s concerned, an empty chair is lost revenue. He is considering several options, including hiring stylists and/or renting chairs by the day to other barbers and stylists who would work their own hours and bring in their own customers.

If he hires stylists his payroll costs would be $15.50 per hour. He estimates a stylist will serve 1 customer per hour, and the average income will be $30 per customer.

He is also considering leasing chairs by the day to barbers or stylists who would provide their own clients, and charge any amounts they want. Max will make only the lease amount, which will be paid by the stylist or barber directly to Max.

REQUIRED

Help Max analyze this decision.

What are his average costs and profit per chair per day for barbers?

What will his average costs and profit be per chair/per day if he hires stylists?

He is considering renting chairs for an amount roughly equal to the profit per day from barbers. Is this a good idea? Or should he hire stylists instead?

Max makes nothing for an empty chair, and must pay the average daily overhead on that chair. Considering this, what is the minimum amount Max could rent a chair for to just cover his overhead costs?

Do you have any other suggestions for Max?

Shave and a Haircut Solution

First let's calculate the daily overhead per chair. Under-utilized chairs cost Max money every day.

$7,000 monthly overhead / 6 chairs / 26 days = $44.87 per day per chair

 
Barbers
Stylists
 
Customers per hour
Revenue rate per customer
   $  10.00
$  30.00
Revenue per hour (Rate x Customers)
  30.00
   30.00
Barber/Stylist wage per hour
  12.50
   15.50
Gross Profit per hour
  $  17.50
   $  14.50
TIMES Hours per day
     8.00
   8.00
Gross Profit per day
  $ 140.00
   $ 116.00
LESS Chair cost per day 
     44.87
   44.87
PROFIT per day
  $  95.13
   $  71.13

From this analysis we see that hiring Barbers is more profitable than hiring Stylists. Max should hire as many Barbers as he can keep busy all day. Then he should hire Stylists to fill the remaining seats.

If he isn't able to hire enough Barbers and Stylises, he can also rent chairs by the day to Barbers and Stylists working as independent contractors - a practice common to this industry. The miminum rental per chair would be $44.87 per day, just enough to cover his overhead costs and break even (i.e., not lose money on an empty chair).

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