# FORMULA FOR THE TABLE OF AMOUNTS CONTAINED IN THE FEDERAL CHILD SUPPORT GUIDELINES: A TECHNICAL REPORT

## 1.0 INTRODUCTION

Under the new Federal Child Support Guidelines, there are two main elements which determine the amount of child support awards:

• the amounts set out in the applicable table; and
• the amount, if any, determined under section 7 (special or extraordinary expenses).

The objective of this technical report is to explain the mathematical formula that generates the table amounts, the first of these elements.

## 2.0 UNDERLYING PRINCIPLES AND ASSUMPTIONS

In intact families, spending on children is directly related to family income, that is, the means of both parents. The concept of cost of raising children is an illusory theoretical construct. Spending on children is not fixed; it changes as the income of either parent changes. Families with higher incomes spend more on their children than do families of lower income. In the post separation arrangement, the Federal Child Support Guidelines aim to approximate, as closely as possible, the spending on the children that occurred in the pre-separation family. For a full description of the research and analysis conducted to arrive at the model for the formula used in the guidelines, please consult the following Department of Justice Canada publications:

• R. Finnie, C. Giliberti, and D. Stripinis, The Construction and Implementation of Child Support Guidelines (Ottawa: Department of Justice Canada, 1993).
• R. Finnie, C. Giliberti, and D. Stripinis, An Overview of the Research Program to Develop a Canadian Child Support Formula (Ottawa: Department of Justice Canada, 1995).

The objective of the formula that generates the child support tables is simply to find a means of calculating an amount to be transferred from the paying parent to the receiving parent. This transferred sum should maximise the amount available to be spent on the children while still allowing an adequate reserve for the self support of the paying parent. Several assumptions have been incorporated into the model. First, it is assumed that within the principal residence of the children, the parent and the children will share the same standard of living. A second assumption presumes that if the incomes of the parents are equal, it is fair and equitable that each should contribute equally to the financial support of the children, regardless of the extent of their contribution to the nurturing of the children.

## 3.0 THE MODEL

The following model, and the mathematical equation derived from it, makes the technical assumption that the household of the paying parent has one member: the paying parent. The receiving parent is also assumed to be single; the household of the receiving parent is made up of one parent and all the children of the marriage. Both parents earn income and pay taxes. These technical assumptions have the narrow purpose of producing the mathematical model. They do not restrict the application of the tables to real life situations which may involve more complex family arrangements.

Figure 1 - Finances of the Post Separation Households

Simply stated, the model equalises the financial circumstances of the two households. Expressed mathematically, the model of equality becomes: [1]

$\frac{{\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}-\mathrm{table amount}}{\mathrm{Expenditures of single adult}}=\frac{{\mathrm{income}}_{\mathrm{RP}}-{\mathrm{taxes}}_{\mathrm{RP}}+\mathrm{table amount}}{\mathrm{Expenditures of single adult AND children}}$
[ Description A ]

The denominators in this equation are solved in accordance with the Statistics Canada 40/30 Equivalence Scale which allows expenditure variables to be expressed as a set of ratios.[2] Like most equivalence scales, the Statistics Canada 40/30 values are expressed in adultequivalence units (or AEUs); a single person household has an AEU value of 1. Largerhouseholds have values greater than 1, dependingon the family's size and composition (i.e., whether there is one parent or two). The values in the equivalence scale are the multipliers required to determine the level of income a larger household needs in order to be as well-off as the household of a single adult.

Table 1 presents the numeric values of the 40/30 equivalence scale. Since the model postulates that each parent lives in a single adult household, the second column shows the values that are used in the formula. The fourth and fifth columns present an example of how the ratios of these adult equivalence units would translate into actual dollar amounts necessary to attain equivalency. The ratios reflect the fact that household expenditures are not a simple multiple of the number of family members. Economies of scale are realised through shared habitation.

 Adult Equivalence Units Income required for equivalent standards of living single adult household two adult household 1.0 1.4 10,000 14,000 1.4 1.7 14,000 17,000 1.7 2.0 17,000 20,000 2.0 2.3 20,000 23,000 2.3 2.6 23,000 26,000 2.6 2.9 26,000 29,000 2.9 3.2 29,000 32,000
• Note: The AEU for a single parent with one child (1.4) is identical to the AEU for two adults (1.4). This means the second person in a household generates the same cost, regardless of age.
• Note: \$10,000 is used as the base for a single person for illustrative purposes only.

Using the equivalence scale concept for the denominators in the basic equation (page 2), where AEU is the abbreviation for adult equivalence unit, the expression becomes:

$\frac{{\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}-\mathrm{table amount}}{\mathrm{AEU for the paying parent}}=\frac{{\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}+\mathrm{table amount}}{\mathrm{AEU for the receiving parent AND children}}$
[ Description B ]

Substituting the known value of the equivalence unit (AEUPP) for the paying parent single adult, the expression becomes:

$\frac{{\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}-\mathrm{table amount}}{1.0}=\frac{{\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}+\mathrm{table amount}}{\mathrm{AEU for the receiving parent AND children}}$
[ Description C ]

As stated earlier, the objective is to determine the amount that must be transferred from the one household to the other in order to make them equally well off, that is, the child support table amount. Using the term AEURP for the denominator on the right hand side of the above equation and solving for the variable table amount, the expression becomes:

$\mathrm{TABLE AMOUNT}=\frac{\left[\left({\mathrm{AEU}}_{\mathrm{RP}}\right)\left({\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}\right)\right]-\left({\mathrm{income}}_{\mathrm{RP}}-{\mathrm{taxes}}_{\mathrm{RP}}\right)}{1.0+{\mathrm{AEU}}_{\mathrm{RP}}}$
[ Description D ]

If there are two children with the receiving parent, using the equivalence table on page 3, the value of AEURP is 1.7 and the expression becomes:

$\mathrm{TABLE AMOUNT}=\frac{1.7\left({\mathrm{income}}_{\mathrm{PP}}-{\mathrm{taxes}}_{\mathrm{PP}}\right)-\left({\mathrm{income}}_{\mathrm{RP}}-{\mathrm{taxes}}_{\mathrm{RP}}\right)}{2.7}$
[ Description E ]

In generating the table amounts, income level by income level, the formula actually makes the incomePP and the incomeRP equal, in keeping with the technical assumption of the model. Based on the equation, the formula produces a set of tables for each province/territory, by income level and by number of children up to a total of six children. As explained, the number of children variable is accommodated through the equivalence scale. The province/territory variable is required because each province/territory has its own taxing formula.

## 4.0 INCOME

In the Federal Child Support Guidelines, income is defined under Sections 15 to 20. For the majority of cases, income will be similar to Total Income from line 150 of the Revenue Canada T1 General form. However, that amount may have to be adjusted by the requirements of Schedule III of the guidelines that take into account certain deductions and inclusions deemed to be fair when applied to child support circumstances. In the formula used to generate the tables, the values are based on the guidelines' definition of income.

## 5.0 TAX VARIABLES

Generally speaking, the formula uses those tax calculations, deductions and credits that apply to all employees. Included are Employment Insurance (EI) premiums, Canada Pension Plan/Québec Pension Plan (CPP/QPP) contributions and the Goods and Services Tax (GST) credits for both parents. Not included are discretionary actions on the part of tax-payers, such as charitable donations, RRSP savings and political contributions. Also omitted are factors which are not discretionary, but are specific to a situation, such as deductions for union dues, or allowances for disabilities, dependent relatives, and other special circumstances.

Not included in the calculation of the receiving parent's taxes are the federal Child Tax Benefit and the GST rebate for children. These are deemed to be the government's contribution to children and not available as income to the receiving parent. The only difference in tax calculations between the two parents is the inclusion, in the calculations for the receiving parent, of the federal equivalent-to-spouse deduction and certain provincial tax reductions and credits. For details on federal and provincial/territorial tax parameters used in the formula, see Appendix 1.

## 6.0 MODIFICATION TO THE FORMULA FOR BASIC NEEDS

It is recognised that all persons have basic needs that must be met. If the formula does not take this into account, persons could begin paying child support on the first dollar earned. Therefore, the first modification to the formula incorporates an amount required to allow for the self-support of the paying parent. This basic need amount, termed self-support reserve, is an amount deemed to be required for a minimal standard of living for a single adult. It is used as the starting point for child support responsibility.

The self-support reserve concept is used here solely to determine the level of income at which a parent would begin to pay child support. The chosen cut-off was a modification of the federal income tax basic personal non-refundable tax credit which represents the income threshold for payment of federal income tax. This threshold reflects what society deems to be the minimum income necessary for individuals to look after their own needs. It is national in scope, is close to the average social assistance available to single persons across Canada and is thus a credible choice as the minimum income needed to meet basic needs. In determining the child support table amounts, the self-support reserve is defined as the federal basic personal amount plus the necessary standard employment deductions of EI contributions and CPP/QPP premiums. For 1997, the self-support reserve is \$6,730. [3] An income above this amount will normally be subject to child support payments.

## 7.0 MODIFICATION TO THE FORMULA AT LOW INCOME LEVELS

A "marginal capping rate" is added at lower income levels to ensure that the amount of child support does not constitute a disincentive to working for a higher income which would simply increase tax and child support obligations, leaving little or no improvement in the payer's financial state. Paying parents with incomes below the self-support reserve do not have to pay child support. Unless the formula is modified to prevent it, those earning a single dollar above that threshold could be required to make child support payments of several hundreds of dollars. In order to avoid such discontinuities, a special adaptation was made to the formula so that the transition from \$0 payment to "full" payment would be gradual.

In this low income transition zone, the formula was adjusted so that the paying parent keeps a proportion of earnings above the self-support reserve amount.[4] The rates which determine the amount the parent keeps vary with the number of children. The numerical details of how the transition is accomplished are shown in table 2.

Table 2 Marginal Capping Rates in the Transition Zone

Number of children

% of each earned dollar above the self support reserve and under the ceiling of the transition zone that the paying parent retains (in the transition zone).

Marginal Capping Rate -- Maximum for Taxes and Child Support Combined

1 40% 60%
2 35% 65%
3 30% 70%
4,5,6 25% 75%

As shown in Table 2, a paying parent with one child and an income within the transition zone would keep the self-support reserve amount plus forty cents for each dollar earned above the self support reserve amount. The other sixty cents would be divided between taxes and child support.

Figure 2 illustrates the impact of the marginal capping mechanism. The horizontal axis is the paying parent's income in the low-income range up to \$20,000. The vertical axis represents the table amount for two children in Ontario. The two curves show the contrasting amounts for the capped version of the formula and for the non-capped version.

Figure 2: Effect of Capping Versus No-Capping on Child Support Table Amounts

As can be seen, the amounts without capping would increase dramatically once income exceeds the self-support reserve amount. In fact, at an income of about \$7,000, a paying parent could be paying close to \$2,000 a year. On the other hand, with capping, the amounts increase gradually. For the payer, this realistically takes into account basic needs, taxes to be paid on additional income and the obligation to pay child support.

## 8.0 MODIFICATION TO THE FORMULA TO SMOOTH THE CURVE

Because of the manner in which certain provincial/territorial tax functions come into play at different income levels, the curve of the table amounts was not always unidirectional as income increased. Within restricted ranges, some very slight discontinuities required smoothing in order to ensure that amounts never decreased with increasing income.

## 9.0 USE OF THE CHILD SUPPORT TABLES

An excerpt from the official Federal Child Support Tables and instructions for determining child support amounts can be found in Appendix 2. The formula generates the award amounts by province/territory, by income of the payer and by number of children, up to six children. The tables are specific to the jurisdiction because of differences in provincial/territorial tax parameters. Income intervals of \$1000, with an interpolation factor between intervals, are used in the official guidelines.[5] For each province/territory, there is a single page for each family size, based on the number of eligible children of the marriage for whom support is to be paid. The province/territory is determined by the residence of the paying parent.[6] The number of children variable is the number of children of the marriage living with the receiving parent.

In cases of split custody, where each parent has sole custody of one or more children, the mother will be the paying parent for each child in the father's custody and the father will be the paying parent for each child in the mother's custody. Table amounts are found separately for each payer, based on the payer's income and the number of children in the custody of the other parent. The difference between the two table values is the amount to be paid by one parent to the other parent.

## 10.0 UPDATING THE TABLES

The Federal Child Support Guidelines that include the table amounts were implemented on 1 May 1997. The Department of Justice Canada will be monitoring any changes in tax parameters or legislation that may materially change table amounts.

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