Answer :
To determine Alex's equity income in Steinbart to be reported in 2024, let's break down the problem into a series of steps.
### Step 1: Calculate the Purchase Percent and Value
Alex purchased 30% of Steinbart for \[tex]$599,000. ### Step 2: Determine the Excess Cost Over Book Value Steinbart’s net assets on January 1, 2023, were \$[/tex]165,000,000.
[tex]\[ \text{30% of Steinbart’s net assets} = 0.30 \times 165,000,000 = 49,500,000 \][/tex]
The excess cost over book value is:
[tex]\[ \text{Excess Cost} = \text{Purchase Price} - ( \text{Purchase Percent} \times \text{Net Assets} ) \][/tex]
[tex]\[ \text{Excess Cost} = 599,000 - 49,500,000 \][/tex]
### Step 3: Attribute Excess Cost to Trade Name and Amortize It
The excess cost is attributable to a trade name with a remaining life of 20 years.
[tex]\[ \text{Annual Amortization} = \frac{\text{Excess Cost}}{20} \][/tex]
### Step 4: Calculate Deferred Gross Profit (DGP) for 2023
Steinbart is transferring inventory to Alex:
- 2023: Cost to Steinbart is \[tex]$171,760, transfer price is \$[/tex]226,000, and the amount held by Alex at year-end is \[tex]$56,500. Deferred gross profit for 2023 is calculated as: \[ \text{Deferred GP}_{2023} = (\text{Transfer Price}_{2023} - \text{Cost to Steinbart}_{2023}) \times \left( \frac{\text{Inventory Held}_{2023}}{\text{Transfer Price}_{2023}} \right) \] ### Step 5: Recognize Deferred Gross Profit From 2023 in 2024 Recognize the deferred gross profit attributing from 2023 sale in 2024: \[ \text{Recognized GP}_{2023} = \text{Deferred GP}_{2023} \] ### Step 6: Defer Gross Profit for 2024 Steinbart is transferring inventory to Alex: - 2024: Cost to Steinbart is \$[/tex]118,320, transfer price is \[tex]$174,000, and the amount held by Alex at year-end is \$[/tex]53,000.
Deferred gross profit for 2024 is:
[tex]\[ \text{Deferred GP}_{2024} = (\text{Transfer Price}_{2024} - \text{Cost to Steinbart}_{2024}) \times \left( \frac{\text{Inventory Held}_{2024}}{\text{Transfer Price}_{2024}} \right) \][/tex]
### Step 7: Calculate Alex's Share of Steinbart's Net Income for 2024
Steinbart’s net income in 2024 is \[tex]$139,300. Alex owns 30%, so: \[ \text{Share of Net Income}_{2024} = 0.30 \times 139,300 = 41,790 \] ### Step 8: Adjust the Equity Income in Steinbart Finally, compute the equity income Alex is to report by adjusting for the recognized and deferred gross profits and the annual amortization of excess cost: \[ \text{Equity Income}_{2024} = \text{Share of Net Income}_{2024} - \text{Trade Name Amortization} \] \[ \text{Equity Income}_{2024} -= \text{Recognized GP}_{2023} \] \[ \text{Equity Income}_{2024} += \text{Deferred GP}_{2024} \] Summarizing, the final equity income in Steinbart to be reported by Alex in 2024 is: \[ \boxed{2500410.0} \] Thus, none of the provided multiple-choice answers (\$[/tex]35,570; \[tex]$3,570; \$[/tex]51,470; \$44,570) match the final equity income.
### Step 1: Calculate the Purchase Percent and Value
Alex purchased 30% of Steinbart for \[tex]$599,000. ### Step 2: Determine the Excess Cost Over Book Value Steinbart’s net assets on January 1, 2023, were \$[/tex]165,000,000.
[tex]\[ \text{30% of Steinbart’s net assets} = 0.30 \times 165,000,000 = 49,500,000 \][/tex]
The excess cost over book value is:
[tex]\[ \text{Excess Cost} = \text{Purchase Price} - ( \text{Purchase Percent} \times \text{Net Assets} ) \][/tex]
[tex]\[ \text{Excess Cost} = 599,000 - 49,500,000 \][/tex]
### Step 3: Attribute Excess Cost to Trade Name and Amortize It
The excess cost is attributable to a trade name with a remaining life of 20 years.
[tex]\[ \text{Annual Amortization} = \frac{\text{Excess Cost}}{20} \][/tex]
### Step 4: Calculate Deferred Gross Profit (DGP) for 2023
Steinbart is transferring inventory to Alex:
- 2023: Cost to Steinbart is \[tex]$171,760, transfer price is \$[/tex]226,000, and the amount held by Alex at year-end is \[tex]$56,500. Deferred gross profit for 2023 is calculated as: \[ \text{Deferred GP}_{2023} = (\text{Transfer Price}_{2023} - \text{Cost to Steinbart}_{2023}) \times \left( \frac{\text{Inventory Held}_{2023}}{\text{Transfer Price}_{2023}} \right) \] ### Step 5: Recognize Deferred Gross Profit From 2023 in 2024 Recognize the deferred gross profit attributing from 2023 sale in 2024: \[ \text{Recognized GP}_{2023} = \text{Deferred GP}_{2023} \] ### Step 6: Defer Gross Profit for 2024 Steinbart is transferring inventory to Alex: - 2024: Cost to Steinbart is \$[/tex]118,320, transfer price is \[tex]$174,000, and the amount held by Alex at year-end is \$[/tex]53,000.
Deferred gross profit for 2024 is:
[tex]\[ \text{Deferred GP}_{2024} = (\text{Transfer Price}_{2024} - \text{Cost to Steinbart}_{2024}) \times \left( \frac{\text{Inventory Held}_{2024}}{\text{Transfer Price}_{2024}} \right) \][/tex]
### Step 7: Calculate Alex's Share of Steinbart's Net Income for 2024
Steinbart’s net income in 2024 is \[tex]$139,300. Alex owns 30%, so: \[ \text{Share of Net Income}_{2024} = 0.30 \times 139,300 = 41,790 \] ### Step 8: Adjust the Equity Income in Steinbart Finally, compute the equity income Alex is to report by adjusting for the recognized and deferred gross profits and the annual amortization of excess cost: \[ \text{Equity Income}_{2024} = \text{Share of Net Income}_{2024} - \text{Trade Name Amortization} \] \[ \text{Equity Income}_{2024} -= \text{Recognized GP}_{2023} \] \[ \text{Equity Income}_{2024} += \text{Deferred GP}_{2024} \] Summarizing, the final equity income in Steinbart to be reported by Alex in 2024 is: \[ \boxed{2500410.0} \] Thus, none of the provided multiple-choice answers (\$[/tex]35,570; \[tex]$3,570; \$[/tex]51,470; \$44,570) match the final equity income.
