To determine the sales needed to achieve a target income of $170,000, we can use the following formula based on the contribution margin:

1. Calculate the Contribution Margin Ratio (CMR): $\text{CMR} = \frac{\text{Contribution Margin}}{\text{Sales}} = \frac{728,000}{2,912,000} \approx 0.25$

2. Calculate the required sales for the target income: The required sales (R) can be calculated using the formula: $R = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{CMR}}$ Plugging in the numbers: $R = \frac{567,000 + 170,000}{0.25} = \frac{737,000}{0.25} = 2,948,000$

So, Hudson needs sales of $2,948,000 to achieve a target income of $170,000.

3. Calculate the Margin of Safety: The margin of safety (MOS) in dollars can be calculated as follows: $\text{MOS} = \text{Actual Sales} - \text{Required Sales}$ $\text{MOS} = 2,912,000 - 2,948,000 = -36,000 \text{ (indicating a loss)}$

   However, if Hudson achieves its target income of $170,000, we need to calculate the new actual sales: $\text{New Actual Sales} = 2,948,000$

   The original actual sales are $2,912,000, so if we consider this, the margin of safety in dollars when achieving the target would be: $\text{MOS} = 2,948,000 - 2,912,000 = 36,000$

   To find the percentage: $\text{MOS Percentage} = \frac{\text{MOS}}{\text{Actual Sales}} \times 100 = \frac{36,000}{2,948,000} \times 100 \approx 1.22\%$

Summary:

• Sales needed for target income: $2,948,000
• Margin of Safety (in percent): approximately 1.22%

Would you like any further details or clarifications? Here are some questions you might consider:

1. How does the contribution margin impact overall profitability?
2. What strategies could Hudson implement to increase sales?
3. How would changes in variable costs affect the required sales?
4. What are the implications of a low margin of safety?
5. How can Hudson better forecast future income and expenses?

Tip: Regularly review fixed and variable costs to maintain profitability.