Question

Income tax is 5% on the first $50,000.00 of income or less, and 8% on any income in excess of $50,000.00. Let T(x) be a function of the income x.

Answer 1

2Sales $1,120,000.00 $1,000,000.00

3 Cost of goods sold 971,250.00 875,000.00

4 Gross profit $148,750.00 $125,000.00

5 Selling expenses $71,250.00 $62,500.00

6 Administrative expenses 56,000.00 50,000.00

7 Total operating expenses $127,250.00 $112,500.00

8 Income before income tax $21,500.00 $12,500.00

9 Income tax expense 8,000.00 5,000.00

10 Net income $13,500.00 $7,500.00

Required: A. Prepare a comparative income statement with horizontal analysis for the two-year period, indicating the increase (decrease) for the current year when compared with the previous year. Use the minus sign to indicate an amount or percent decrease. If required, round percentages to one decimal place. B. What conclusions can be drawn from the horizontal analysis?

Explanation:

Answer 2

To calculate the income tax T(x) based on the provided tax brackets for income x, we can define the function T(x) as follows:

1. If the income x is $50,000.00 or less, then the tax is 5% of the income.
2. If the income x is more than $50,000.00, then the tax is 5% on the first $50,000.00 plus 8% on the amount in excess of $50,000.0.

We can express this with a piecewise function:

T(x) = 0.05 * x, for x ≤ $50,000.00
T(x) = 0.05 * $50,000.00 + 0.08 * (x - $50,000.00), for x > $50,000.00

Let's break it down with an example calculation:

Example 1: If the income x is $40,000.00
Since the income is less than or equal to $50,000.00, we use the first part of the function:

T(x) = 0.05 * $40,000.00
T(x) = $2,000.00

So the income tax would be $2,000.00.

Example 2: If the income x is $60,000.00
Since the income is greater than $50,000.00, we use the second part of the function:

T(x) = 0.05 * $50,000.00 + 0.08 * ($60,000.00 - $50,000.00)
T(x) = $2,500.00 + 0.08 * $10,000.00
T(x) = $2,500.00 + $800.00
T(x) = $3,300.00

So the income tax would be $3,300.00.

This is how you would manually calculate the income tax for any given income using the function T(x) with the specified tax brackets.