Answer :
To determine the "composite life" of the machinery assets owned by Rain Bird Manufacturing Company, we will go through the detailed steps required in the calculation:
1. Determine the depreciable cost for each machine:
Depreciable Cost = Total Cost - Salvage Value
For Machine A:
[tex]\[ \text{Depreciable Cost}_A = \$450,000 - \$30,000 = \$420,000 \][/tex]
For Machine B:
[tex]\[ \text{Depreciable Cost}_B = \$170,000 - \$10,000 = \$160,000 \][/tex]
For Machine C:
[tex]\[ \text{Depreciable Cost}_C = \$40,000 - \$0 = \$40,000 \][/tex]
2. Calculate the total depreciable cost:
[tex]\[ \text{Total Depreciable Cost} = \text{Depreciable Cost}_A + \text{Depreciable Cost}_B + \text{Depreciable Cost}_C \][/tex]
[tex]\[ \text{Total Depreciable Cost} = \$420,000 + \$160,000 + \$40,000 = \$620,000 \][/tex]
3. Calculate the sum of the life ratios for each machine:
For Machine A:
[tex]\[ \text{Life Ratio}_A = \text{Depreciable Cost}_A \times \text{Life in Years}_A = \$420,000 \times 6 = 2,520,000 \][/tex]
For Machine B:
[tex]\[ \text{Life Ratio}_B = \text{Depreciable Cost}_B \times \text{Life in Years}_B = \$160,000 \times 8 = 1,280,000 \][/tex]
For Machine C:
[tex]\[ \text{Life Ratio}_C = \text{Depreciable Cost}_C \times \text{Life in Years}_C = \$40,000 \times 4 = 160,000 \][/tex]
4. Calculate the total of the life ratios:
[tex]\[ \text{Total Life Ratio} = \text{Life Ratio}_A + \text{Life Ratio}_B + \text{Life Ratio}_C \][/tex]
[tex]\[ \text{Total Life Ratio} = 2,520,000 + 1,280,000 + 160,000 = 3,960,000 \][/tex]
5. Calculate the composite life of the assets:
[tex]\[ \text{Composite Life} = \frac{\text{Total Life Ratio}}{\text{Total Depreciable Cost}} \][/tex]
[tex]\[ \text{Composite Life} = \frac{3,960,000}{620,000} \approx 6.3871 \][/tex]
The composite life of the assets is approximately 6.39 years, which rounds to around 6.4 years. This value is closest to answer option (B) 6.6, but since our exact calculation is roughly 6.39, let's take it literally as:
Hence, the correct choice is none of the provided options exactly.
1. Determine the depreciable cost for each machine:
Depreciable Cost = Total Cost - Salvage Value
For Machine A:
[tex]\[ \text{Depreciable Cost}_A = \$450,000 - \$30,000 = \$420,000 \][/tex]
For Machine B:
[tex]\[ \text{Depreciable Cost}_B = \$170,000 - \$10,000 = \$160,000 \][/tex]
For Machine C:
[tex]\[ \text{Depreciable Cost}_C = \$40,000 - \$0 = \$40,000 \][/tex]
2. Calculate the total depreciable cost:
[tex]\[ \text{Total Depreciable Cost} = \text{Depreciable Cost}_A + \text{Depreciable Cost}_B + \text{Depreciable Cost}_C \][/tex]
[tex]\[ \text{Total Depreciable Cost} = \$420,000 + \$160,000 + \$40,000 = \$620,000 \][/tex]
3. Calculate the sum of the life ratios for each machine:
For Machine A:
[tex]\[ \text{Life Ratio}_A = \text{Depreciable Cost}_A \times \text{Life in Years}_A = \$420,000 \times 6 = 2,520,000 \][/tex]
For Machine B:
[tex]\[ \text{Life Ratio}_B = \text{Depreciable Cost}_B \times \text{Life in Years}_B = \$160,000 \times 8 = 1,280,000 \][/tex]
For Machine C:
[tex]\[ \text{Life Ratio}_C = \text{Depreciable Cost}_C \times \text{Life in Years}_C = \$40,000 \times 4 = 160,000 \][/tex]
4. Calculate the total of the life ratios:
[tex]\[ \text{Total Life Ratio} = \text{Life Ratio}_A + \text{Life Ratio}_B + \text{Life Ratio}_C \][/tex]
[tex]\[ \text{Total Life Ratio} = 2,520,000 + 1,280,000 + 160,000 = 3,960,000 \][/tex]
5. Calculate the composite life of the assets:
[tex]\[ \text{Composite Life} = \frac{\text{Total Life Ratio}}{\text{Total Depreciable Cost}} \][/tex]
[tex]\[ \text{Composite Life} = \frac{3,960,000}{620,000} \approx 6.3871 \][/tex]
The composite life of the assets is approximately 6.39 years, which rounds to around 6.4 years. This value is closest to answer option (B) 6.6, but since our exact calculation is roughly 6.39, let's take it literally as:
Hence, the correct choice is none of the provided options exactly.
