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# The Arithmetic of Collective Bargaining

**Adapted from Research Department, USWAPaul K. RainsbergerDirector**

## Costing of wage and fringe benefits

The costing of wage and fringe benefits is a straightforward and simple procedure. It requires only a few easy arithmetical calculations. The costing methods presented in this document are the standard methods used in the costing of frequently negotiated benefits. There are alternate methods, but the costs arrived at by each method will be the same.

The costing of wage and fringe benefits does require good information to be used in the calculations. The NLRB and the courts have held that a company must make available to the Union all of the information needed for intelligent collective bargaining. Among the data you will need are a distribution of employees by wage rates, the average hourly rate, a total employment cost breakdown, annual hours worked per employee and a seniority list. A first step in negotiations is to obtain the data from the company.

In the following examples, all wage and fringe benefit figures are of imaginary companies. Wage rates are arranged on a job class system, but it is not the present system in steel or any other industry, so far as we know.

#### Problem 1

**Average Hourly Rate — What is the procedure for calculating the average hourly rate (AHR)?**

**Data needed**

A distribution of employees by wage rates (job classes or specific occupational rates) for a representative period near the expiration of the current agreement is needed to calculate the average hourly rate (AHR).

**Solution**

**Step 1**

Multiply each wage rate by number of employees receiving that rate.**Step 2**

Total column of number of employees. The total is 260.**Step 3**

Total column on wage rate times employees. Total is $3696.60. This represents the total hourly wages for all employees.**Step 4**

Divide total hourly wages by the total number of employees, resulting in the AHR.**Answer**

$3696.60 (total hourly wages)/260 employees = $14.22 AHR.

**Note**

The average hourly rate and the distribution of employees by wage rates are key costing data and are used in many cost calculations. In the following problems, the wage distribution and average rate as calculated in this problem will be used.

Job class | Current wage rates | Number of employees at wage rate | Wage rate times number of employees |
---|---|---|---|

1 | $12.50 | 2 | $25.00 |

2 | $12.80 | 11 | $140.80 |

3 | $13.20 | 24 | $316.80 |

4 | $13.60 | 47 | $639.20 |

5 | $14.00 | 58 | $812.00 |

6 | $14.45 | 54 | $780.30 |

7 | $15.00 | 35 | $525.00 |

8 | $15.50 | 17 | $263.50 |

9 | $16.00 | 8 | $128.00 |

10 | $16.50 | 4 | $66.00 |

Totals | 260 | $3696.60 |

**AHR = $3,696.60/260 = $14.22**

#### Problem 2

**Wage Increase — What is the average cents-per-hour cost of a first-year wage increase when the increases range from 40¢ to 58¢ for different jobs? What is the percent increase?**

**Data needed**

Same as for Problem 1.

**Solution**

**Step 1**

Obtain wage increase for each specific job class by subtracting the current wage rates from the first-year rates.**Step 2**

Multiply wage increase for each job class by number of employees in the job class.**Step 3**

Total column on number of employees and column on wage increases times employees, which gives the total hourly cost of the wage increases. Totals are 260 employees and $126.62 hourly cost.**Step 4**

Divide total hourly cost of the wage increase by total number of employees, which gives the average hourly increase for all employees.**Answer**

$126.62 (total hourly cost)/260 employees = 48.7¢, which is the average hourly cost of the increase.**Step 5**

To state the average increase as a percentage of average hourly rate, divide the average hourly increase by the old average hourly wage.**Answer**

$0.487/14.22 = 0.034, or 3.4 percent.

Job class | Current wage rate | First year wage rates |
First year wage increase |
Number of employees at rate | Wage increase times number of employees |
---|---|---|---|---|---|

1 | $12.50 | $12.90 | $.40 | 2 | $0.80 |

2 | $12.80 | $13.22 | $.42 | 11 | $4.62 |

3 | $13.20 | $13.64 | $.44 | 24 | $10.56 |

4 | $13.60 | $14.06 | $.46 | 47 | $21.62 |

5 | $14.00 | $14.48 | $.48 | 58 | $27.84 |

6 | $14.45 | $14.95 | $.50 | 54 | $27.00 |

7 | $15.00 | $15.52 | $.52 | 35 | $18.20 |

8 | $15.50 | $16.04 | $.54 | 17 | $9.18 |

9 | $16.00 | $16.56 | $.56 | 8 | $4.48 |

10 | $16.50 | $17.08 | $.58 | 4 | $2.32 |

Totals | 260 | $126.62 |

**Cents per hour increase = $126.62/ 260 = $0.487**

**Practice example**

What is the average cents-per-hour cost, using the job class distribution in the above problem, if the rates for job classes 1, 2 and 3 are increased by $.40 per hour; job classes 4, 5, 6 and 7 are increased by $.50 per hour; and job classes 8, 9, and 10 are increased by $.60 per hour? What is the percent increase?

#### Problem 3

**Percent Wage Increase — What is the average cents-per-hour cost of a 5 percent (.05) increase in all rates in the first, second and third year of a new agreement?**

**Data needed**

Average hourly rate, as computed in Problem 1.

**Solution**

First year increase.

**Step 1**

Multiply the current AHR by the .05 wage increase.**Answer**

$14.22 x .05 = .71. The first year average increase is $.71.

**Solution**

Second year increase.

**Step 2**

Determine the first year AHR by adding the average first year wage increase to the prior AHR. $14.22 + .71 = $14.93.**Step 3**

Multiply the first year AHR by the .05 wage increase for the second year, as in Step 1**Answer**

$14.93 x .05 = .75. The second year average increase is $.75.

**Solution**

Third year increase.

**Step 4**

Determine the second year AHR by adding the average second year wage increase to the prior AHR. $14.93 + .75 = $15.68.**Step 5**

Multiply the second year AHR by the .05 wage increase for the third year, as in Steps 1 and 3.**Answer**

$15.68 x .05 = .78. The second year average increase is $.78.

**Practice example**

What is the average cents-per-hour cost if wages are increased by 7 percent in the first year, 10 percent in the second year, and 8 percent in the third year? Assume an AHR of $14.22.

#### Problem 4

**Inequity increases — What is the average cents-per-hour cost of inequity increases for selected workers?**

**Data needed**

Number of workers to be upgraded. For this example, assume 3 helpers upgraded from Job Class 2 to Job Class 3 and 5operators from Job Class 3 to Job Class 4.

**Solution**

**Step 1**

Determine amount of wage increases needed for the upgraded employees. In this example, all upgraded employees are increased by $.40 per hour.**Step 2**

Multiply the number of employees upgraded (8) by the amount of wage increases, for a total hourly cost of the increase. 8 x $.40 = $3.20.**Step 3**

Divide the total hourly cost of the increase (Step 2) by the total number of workers employed (260).**Answer**

$3.20/260 = 1.2¢ per hour.

**Practice example**

What is the cost of inequity increases, assuming the following data

- 15 helpers upgraded from $12.00 to $12.80 per hour.
- 10 assemblers upgraded from $12.80 to $13.20 per hour.
- Three machinists upgraded from $15.50 to $16.00 per hour.
- Total workforce of 200 employees.

**Note**

To fully consider all costs, after other wage increases, it is necessary to change the number of workers at each rate for purposes of calculating other wage increases as in Problem 2, in accordance with these changes. That extra step is not performed in this example.

#### Problem 5

**Holidays — What is the average cents-per-hour cost of increasing the number of holidays from 11 to 12?**

**Data needed**

Average hourly rate and average hours worked per year per employee.

**Solution**

**Step 1**

Calculate the cost of one holiday by multiplying hours paid for the holiday (8 hours) by the AHR. 8 x $14.22 = $113.73. This represents the average cost of one additional holiday per worker.**Step 2**

Obtain the hours worked per year per employee from company or estimate by subtracting average hours off for holidays and vacations from 2080 hours, which is the number of hours in a full work year. For instance, in a plant with 11 paid holidays and an average vacation of three weeks (15 days), the total paid days off is 26 and total paid hours off is 208 (26 x 8). The number of hours worked during the year is 1,872 (2080-1872).**Step 3**

Divide the average cost of one holiday (Step 1) by the number of hours worked per year per employee (Step 2).**Answer**

$113.76/1872 = $.061 or 6.1¢per hour worked.

**Practice example**

What is the average cost of increasing the number of holidays from 8 to 10, assuming an AHR of $7.25?

#### Problem 6

**Vacations — What is the average cents-per-hour cost of changing the vacation schedule from three weeks vacation for 10 years of service to three weeks of vacation for seven years of service?**

**Data needed**

The exact number of employees who will receive the additional vacation can be determined from a seniority list. The number of employees receiving the increased vacation is assumed to be 35 for the following example.

**Solution**

**Step 1**

Total additional weeks of vacation is 35 (35 workers x 1 additional week of vacation per worker).**Step 2**

Total cost per week of vacation is the average hourly rate ($14.22) times 40 hours, or $568.80.**Step 3**

Total annual cost is 35 (additional weeks) x $568.80 = $19,908.00.**Step 4**

Calculate total annual hours by multiplying total employees by hours worked per year per employee, as calculated in Problem 5. Total hours worked per year are 486,720 (260 employees x 1872 hours).**Step 5**

To determine hourly cost, divide the annual cost (Step 3) by total plant hours (Step 4).**Answer**

$19,908/486,720 = $.041 or 4.1¢ per hour.

**Practice example**

What is the average hourly cost of changing vacation schedule from four weeks vacation for 20 years of service to four weeks vacation for 15 years of service? Assume 300 employees, $14.22 AHR and 52 employees affected by the proposed change.

#### Problem 7

**Shift Differentials — What is the average hourly cost of increasing the shift differential on the second shift from 40¢ per hour to 50¢ per hour and on the third shift from 45¢ per hour to 55¢ per hour? **

**Data needed**

To calculate the cost of increased shift premiums, the number of employees on each shift is needed. In the following example, it is assumed that there are 60 employees on the second shift and 30 employees on the third shift.

**Solution**

**Step 1**

Calculate total hourly cost of improvement by multiplying the number of employees on the shift by the increase in the shift differential, as follows- 60 (second shift employees) x 10 ¢ (increased differential) = $6.00.
- 30 (third shift employees) x 10¢ (increased differential) = $3.00.
- Total hourly cost of increased differential = $9.00.

**Step 2**

Divide hourly cost of increase by the total number of employees.**Answer**

$9.00/260 = 3.5¢ per hour.

**Practice example**

What is the average hourly cost of increasing the second shift differential from 40¢ per hour to 50¢ per hour and the third shift differential from 45¢ per hour to 55 ¢ per hour? Assume 300 employees with 120 on the second shift and 40 on the third shift.

#### Problem 8

**Premium Pay — What is the average hourly cost to increase the overtime premium for work on both Saturday and Sunday from time and one-half to double time?**

**Data needed**

The number of hours worked on Saturday and Sunday during the last year is needed to calculate the cost of increased premiums. In the following example, it is assumed that 12,400 hours were worked on Saturday and Sunday.

**Note**

The same method is applicable to any premium pay including all overtime items, Saturday, Sunday and holiday premiums.

**Solution**

**Step 1**

The increase in the premium from 1-1/2 X to 2 X is a 1/2 X increase in the premium. Cents per hour increase is 1/2 of the average hourly rate, or $7.11 (1/2 x 14.22).**Step 2**

Calculate annual cost of increased premium by multiplying the number of overtime hours by the increase in the premium pay. 12,400 x $7.11 = $88,164.00.**Step 3**

Divide the annual cost by the total annual hours worked (as in Problem 6) to obtain an hourly cost.**Answer**

$88,164/486,720 = 18.1¢ per hour.

**Practice example**

What is the average hourly cost of changing daily overtime from 1-1/2 X to 2 X after 8 hours, and holiday premium pay from 2-1/2 X to 3 X? Assume an AHR of $14.22, 300 employees, 10,000 daily overtime hours and 2000 holiday overtime hours.

#### Problem 9

**Rest Periods — What is the cost of increasing the length of rest periods from 10 minutes to 15 minutes twice per shift?**

**Solution**

**Step 1**

Calculate the additional minutes of rest per day. 10 minutes.**Step 2**

Calculate additional minutes off as a percent of one hour. 10/60 = 16.7 percent.**Step 3**

Calculate daily cost of extra minutes by multiplying average wage rate by the additional time off as a percent of hours. .167 x $14.22 = $2.37.**Step 4**

Convert daily cost to hourly cost by dividing by 8 hours.**Answer**

$2.37/8 = 29.6¢ per hour.

#### Problem 10

**Impact Costs — What are impact (sometimes called creep or roll-up) costs? How can they be calculated?**

**What is impact**

When wages increase, the cost of fringe benefits that are directly tied to wages also increases. For instance, the average hourly wages for one holiday at the assumed company at the end of the prior agreement were $14.22. After a first-year wage increase of 5%, the average cost of the holiday will be $14.93. The cost of other benefits directly tied to the wage rates, such as vacations and overtime, will also increase when wages increase. The amount by which fringe benefits increase when wages increase is referred to as impact costs.

**Data needed**

In order to calculate impact costs, it is necessary to obtain from the company a complete total employment cost breakdown with cents-per-hour figures for each major fringe benefit. The following data are assumed.

Wage or benefit | Hourly rate | Does item vary with wage rates? |
---|---|---|

Average hourly rate | 14.22 | |

Shift differentials | .10 | No^{1} |

Overtime premium | .96 | Yes |

Holidays | .64 | Yes |

Vacations — regular | 1.12 | Yes |

Vacation bonus | .16 | No^{1} |

SUB | .22 | No^{1} |

Pensions | 1.52 | No^{1} |

Insurance | 1.02 | No |

Total employment costs | $19.96 |

^{1}These items may in some cases vary with wage rates, i.e., percentage shift differentials, percentage or hourly SUB payments and percentage pension plans.

**Solution**

**Step 1**

Total cost of fringe items that vary with wages. In this example, overtime premium, holiday and vacation costs vary with wages. The total is $2.72.**Step 2**

Obtain impact factor by dividing total cost of items that vary with wages by the AHR. The impact factor = $2.72/$14.22 = 19.1 percent.**Step 3**

Calculate the average wage increase (use procedures describe in Problems 2 and 3). In this example, the assumed average wage increase is 71 ¢ per hour.**Step 4**

Calculate cents-per-hour impact by multiplying impact factor (Step 2) times the average wage increase (Step 3). .191 x 71¢ = 13.6¢.**Answer**

The impact amount is 14¢ per hour. The wage increase plus the impact is $.85.

**Note**

The impact factor is applied only to the wage increase. It is not correct to apply the impact factor to non-wage employment costs.

#### Problem 11

**Total Package Cost — How do you calculate hourly cost, annual cost, and percent cost of a total package for the first year of the agreement and during all three years of an agreement?**

**Data needed**

Total employment costs (as in Problem 10) and cost of each specific improvement.

Item | First year cost | Cost over three years |
---|---|---|

Wage increase (9 percent/year) | $ .710 | $2.240 |

Inequity increase (Problem 4) | .012 | .020 |

Impact costs (Problem 10) | .136 | .430 |

One additional holiday (Problem 5) | .061 | .061 |

Vacation improvement (Problem 6) | .041 | .035 |

Shift improvement (Problem 7) | .035 | .039 |

Sunday premium (Problem 8) | .181 | .181 |

Pension improvement (assumed) | 0 | .150 |

Insurance improvement (assumed) | 0 | .150 |

Total improvements | $1.176 | $3.486 |

**Solution**

**Step 1**

Hourly cost — simply add the cents-per-hour improvements for the first-year and for all three years. Note that the wage impact figures are included. The first year cost is $1.176 and the three-year cost is $3.486.**Step 2**

Percent increase — Calculate the percent increase by dividing the cents-per-hour increase by the total employment cost per hour. Total employment costs are $19.96, from Problem 10.- The first-year percentage increase is 5.9 percent. 1.176/19.96 = .059.
- The three-year increase is 17.5 percent. 3.486/19.96 = .175.