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A special type of accrued liability arises when a firm agrees to pay a bonus to management contingent upon operating results. There are no substantive conceptual problems as to the classification or disclosures to be provided for liabilities created by these plans. The only difficulty lies in the calculation of the amount of the bonus under different definitions of the base income to which the bonus rate is applied. Three situations can be identified where the “bonus” is computed differently.

## sample bonus accrual

**Accrual bonus paid later**

## Bonus accrual equations

The general solution technique is to create a set of simultaneous equations which can be solved to determine the size of the bonus. These symbols will be used:

b = bonus rate

B = amount of the bonus

t = income tax rate

T = amount of income tax

Y = income before tax and bonus

## Calculation of bonus accrual

**Situation 1.** The bonus is based strictly on pre-bonus income. The equations are:

**B = bY**

**T = t(Y – B)**

**Situation 2.** The bonus is based on pre-bonus income less the taxes. The equations are:

**B = b(Y – T)**

**T = t(T – B)
**

**Situation 3. **The bonus is based on income after taxes and after the bonus. The equations are:

**B = b(Y – T – B)**

**T = t(Y – B)**

Solutions to these three situations are presented below, assuming that:

b = 10%

t = 45%

Y = $1,000,000

**Solution 1:**

B = (.10)(1,000,000) = 100,000

T = (.45)(1,000,000 – 100,000) = $405,000

**Solution 2:**

B = (.10)(1,000,000 – T)

B = 100,000 – .1T)

T = .(45)(1,000,000 – B)

T= 450,000 – .45B

T = 450,000 – .45(100,000 – .1T)

T = 450,000 – 45,000 + .045T

.955T = 405,000

T = $424,084

B = 100,000 – (.10)(424,084)

B = 100,000 – 42,408

B = $57,592

**Solution 3:**

B = (.10)(1,000,000 – B – T)

10B = 1,000,000 – B – T

T = 1,000,000 – 11B

T = .45(1,000,000 – B)

1,000,000 – 11B = 450,000 – .45B

10.55B = 550,000

B = $52,133

T = .45(1,000,000 – 52,133)

T = $426,540

The following table summarizes the results: