## Step-by-Step Solution ### **Given Data** - **Government Direct Costs:** $4,000,000 - **Private Direct Costs:** $1,000,000 - **Government Number of Contracts:** 20 - **Private Number of Contracts:** 30 - **Negotiations Costs:** $750,000 - **General Administrative Costs:** $850,000 - **Total Overhead Costs:** $1,600,000 --- ## 1. **Plantwide Rate Based on Direct Costs** ### **Step 1: Calculate Total Direct Costs** \[ \text{Total Direct Costs} = \$4,000,000 + \$1,000,000 = \$5,000,000 \] ### **Step 2: Calculate Plantwide Overhead Rate** \[ \text{Plantwide Overhead Rate} = \frac{\text{Total Overhead Costs}}{\text{Total Direct Costs}} = \frac{\$1,600,000}{\$5,000,000} = .32 \text{ or } 32\% \] ### **Step 3: Allocate Overhead** - **Government Allocation:** \[ \$4,000,000 \times .32 = \$1,280,000 \] - **Private Allocation:** \[ \$1,000,000 \times .32 = \$320,000 \] --- ## 2. **Departmental Rates** - **Negotiations Costs** allocated by **number of contracts** - **General Admin Costs** allocated by **direct costs** ### **Step 1: Negotiations Cost Allocation** - **Total Contracts:** \(20 + 30 = 50\) - **Rate per contract:** \(\frac{\$750,000}{50} = \$15,000\) per contract - **Government:** \(20 \times \$15,000 = \$300,000\) - **Private:** \(30 \times \$15,000 = \$450,000\) ### **Step 2: General Admin Allocation** - **Total Direct Costs:** \$5,000,000 - **Rate per direct cost:** \(\frac{\$850,000}{\$5,000,000} = .17 \text{ or } 17\%\) - **Government:** \( \$4,000,000 \times .17 = \$680,000 \) - **Private:** \( \$1,000,000 \times .17 = \$170,000 \) ### **Step 3: Add Allocations per Group** | Group | Negotiations | General Admin | **Total** | |-------------|--------------|---------------|----------------| | Government | \$300,000 | \$680,000 | **\$980,000** | | Private | \$450,000 | \$170,000 | **\$620,000** | --- ## **Summary Table** | Method | Government | Private | Total | |----------------|------------|---------|-----------| | Plantwide | \$1,280,000| \$320,000| \$1,600,000| | Dept. Rates | \$980,000 | \$620,000| \$1,600,000| --- ## **Advantages and Disadvantages** ### **Plantwide Rate** - **Advantages:** - Simple to compute and apply. - Requires less information. - **Disadvantages:** - May be less accurate; ignores differences in overhead consumption between groups. - Can distort cost allocation if groups use resources differently. ### **Departmental Rates** - **Advantages:** - More accurate; reflects actual resource usage. - Provides better cost information for pricing and management decisions. - **Disadvantages:** - More complex to compute and track. - Requires more detailed data. --- ## **Final Answers** ### **Overhead Costs Allocated** - **Plantwide Rate:** - Government: **\$1,280,000** - Private: **\$320,000** - **Departmental Rates:** - Government: **\$980,000** - Private: **\$620,000** ### **Summary of Methods** - **Plantwide rate** is simple but less accurate. - **Departmental rates** are more accurate but require more effort to implement.