Question

A business has a gross income of $1.32 million. It has promised to pay the CEO a bonus of 20% of net income, which is income after taxes. But the bonus is not subject to taxes because the bonus is an operating expense. The total tax owed is 20% of gross income less the bonus. Our goal is to find the company profit after the bonus and taxes are paid. Let B be the amount on which the bonus is based, and let T be the amount on which taxes are calculated, both in millions of dollars.

(a) Express the taxes paid in terms of the variable T.

(b) The gross income of $1.32 million equals the amount B on which the bonus is based plus the taxes paid. Express this as an equation involving T and B. (Part (a) may be helpful.)

(c) Express the bonus paid in terms of the variable B.

(d) The gross income also equals the amount T on which taxes are based plus the bonus paid. Express this as an equation involving T and B. (Part (c) may be helpful.)

  

(e) Solve the system of two equations in two unknowns from parts (b) and (d) for the variables T and B.

(f) How much is the bonus?
$  million

How much is paid in taxes?
$  million

How much profit is left over?
$  million

Answer 1

Answers to Questions

Given

B is the amount on which bonus is based

T is the amount on which taxes are calculated

So,

a) Tax paid is 20% of "T" so Tax paid = 0.20*T

b) Gross income (i.e 1.32 million) = B+ .0.20* T ------ Equation (1)

c) Bonus is 20 % of "B", so bonus paid = 0.20* B

d) Gross income (i.e 1.32 million) = 0.20B+ T --------- Equation (2)

e) On solving both equation 1& 2

1.32 = B + 0.20T

1.32 = 0.20B +T (Multiply by 0.20 to Subtract from Equation 1)

So ,we get

1.32 = B +0.20T (Equation 1)

0.264 = 0.04B + 0.20T (Equation 2)

Substracting equation 2 from equation 1

1.056 = 0.96B

B = 1.056/0.96

B = 1.1 million

Put B value in any one of the equation to get T, So we are putting Value in Equation 1

1.32 = B +0.20T

1.32 = 1.1 + 0.20T

0.20T = 1.32 - 1.1

T = 0.22/0.20

T = 1.1

f) Bonus = 0.20 *B

So, 0.20 * 1.1

Bonus = 0.22 million

Taxes paid = 0.20 *T

0.20* 1.1

0.22 Million

Profit left over is

Gross income = 1.32 million

Less: Bonus paid = 0.22 million

Income before tax = 1.1 million

Less : Taxes paid = 0.22 million

Net income or profit =  0.88 million