Let's break down the expenses step by step, ensuring all the costs are included:
1. First Year Fee:
- Since the salary is [tex]\( \$160,000 \)[/tex] and the first year fee is [tex]\( 10\% \)[/tex], we calculate:
[tex]\[
\text{First Year Fee} = 0.10 \times 160,000 = \$16,000
\][/tex]
2. Real Estate Fee:
- The real estate fee is [tex]\( 6\% \)[/tex] of the house sale price (\[tex]$340,000):
\[
\text{Real Estate Fee} = 0.06 \times 340,000 = \$[/tex]20,400
\]
3. Family Travel Cost:
- The family travel cost is [tex]\( \$400 \)[/tex] per person for a family of 5:
[tex]\[
\text{Family Travel Cost} = 400 \times 5 = \$2,000
\][/tex]
4. Interview Costs:
- The interview costs per person are [tex]\( \$2,000 \)[/tex]. Assuming only one candidate was interviewed, the cost remains:
[tex]\[
\text{Interview Costs} = \$2,000
\][/tex]
5. Job Posting Fee:
- The job posting fee is simply:
[tex]\[
\text{Job Posting Fee} = \$1,000
\][/tex]
6. Shipping Fee:
- The shipping fee for moving is:
[tex]\[
\text{Shipping Fee} = \$4,000
\][/tex]
Now, let's add all these expenses to find the total recruitment expense for the company:
[tex]\[
\text{Total Recruitment Expense} = \text{Salary} + \text{Interview Costs} + \text{Job Posting Fee} + \text{First Year Fee} + \text{Real Estate Fee} + \text{Shipping Fee} + \text{Family Travel Cost}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Total Recruitment Expense} = 160,000 + 2,000 + 1,000 + 16,000 + 20,400 + 4,000 + 2,000 = \$205,400
\][/tex]
So, the total recruiting expense for hiring the new employee is [tex]\( \boxed{\$205,400} \)[/tex].
