# Marginal Tax Rate

Marginal tax rate is the income tax rate that applies to each additional dollar of taxable income. In a progressive tax structure, it is the income tax rate applicable to the highest tax bracket in which the last dollar of taxable income falls.

Marginal tax rate is an important number in tax planning and investment analysis. It helps determine the after-tax return on an investment and the weighted average cost of capital.

Marginal tax rate is different from the effective tax rate and average tax rate. Effective tax rate is the ratio of total income tax payable to the taxable income and the average tax rate is the ratio of total income tax payable to taxable income.

## Formula

Marginal income tax rate can also be defined as the ratio of increase in income tax liability to a $1 dollar increase in taxable income. This can be expressed mathematically as follows:

$$ \text{Marginal tax rate}=\frac{\Delta \text{Tax}}{\Delta \text{Taxable Income}} $$

The numerator is the change in tax payable and the denominator is the change in taxable income.

## Example

Let’s consider example of Mark whom we helped in calculation of effective income tax rate. His annual income is $120,000; available tax exemptions and deductions are $25,000. He is single and the following tax brackets are relevant to him:

Tax rate | Single |
---|---|

10% | Up to $9,325 |

15% | $9,326 to $37,950 |

25% | $37,951 to $91,900 |

28% | $91,901 to $191,650 |

33% | $191,651 to $416,700 |

35% | $416,701 to $418,400 |

39.60% | $418,401 or more |

Mark’s taxable income is $95,000 which falls into four brackets as shows below:

Bracket | Tax rate | Lower Limit | Upper Limit | Mark's Income | Tax Payable |
---|---|---|---|---|---|

1 | 10% | - | 9,325 | 9,325 | 933 |

2 | 15% | 9,326 | 37,950 | 28,625 | 4,294 |

3 | 25% | 37,951 | 91,900 | 53,950 | 13,488 |

4 | 28% | 91,901 | 191,650 | 3,100 | 868 |

Total | 95,000 | 19,582 |

Because the tax structure is progressive, the marginal tax rate is 28%, the statutory tax rate applicable to the highest tax bracket. Now, let’s work out the marginal income tax rate using the formula approach. Assume Mark’s income increased by $100, his new income tax liability rises to $19,610.

In response to a $100 increase in taxable income, Mark’s income tax liability increased by $28 ($19,610 - $19,582). This shows that the marginal tax rate is 28%:

$$ \text{Marginal tax rate}=\frac{\text{\$19,610}\ -\ \text{\$19,582}}{\text{\$100}}=\text{28%} $$

The effective income tax rate and the average income tax rate are 16.32% (=$19,582/$150,000) and 20.61% (=$19,582/$95,000) respectively.

by Obaidullah Jan, ACA, CFA and last modified on