Joint Costs: Sales Value - Cost Accounting

1. What is the sales price per unit for Beta at the split-off point?
   Answer: $20.00 This problem requires working backward from the allocated costs to find a missing input (sales price). 1. Determine the allocation ratio: The ratio of allocated costs is equal to the ratio of the sales values at split-off. * Allocated to Alpha: $120,000 * Allocated to Beta: $180,000 * The ratio is $120,000 : $180,000, which simplifies to 2 : 3. This means the total sales value of Alpha is 2/3 of the total sales value of Beta. 2. Calculate the total sales value of Alpha: * 10,000 units × $20/unit = $200,000 3. Use the ratio to find the total sales value of Beta: * Sales Value of Alpha / Sales Value of Beta = 2 / 3 * $200,000 / Sales Value of Beta = 2 / 3 * Sales Value of Beta = ($200,000 × 3) / 2 = $300,000 4. Calculate the sales price per unit for Beta: * $300,000 / 15,000 units = $20.00 per unit Distractor B ($13.33) results from incorrectly dividing Beta's allocated cost by Alpha's sales value ($180,000 / $200,000) and applying that to price, or a similar miscalculation. Distractor C ($18.00) might arise from using the total joint cost ($300,000) in the ratio instead of the individual allocated costs. Distractor D ($12.00) is the allocated cost per unit for Beta ($180,000 / 15,000 units), not its sales price.
2. The company uses the sales value at split-off method for product costing. What is the total joint cost allocated to the lotion?
   Answer: $84,000 This question requires the correct application of the sales value at split-off method, which means ignoring any information about costs and revenues after the split-off point. The data about processing lotion into premium cream is irrelevant for this specific allocation method. 1. Calculate the total sales value at the split-off point for each product: * Serum: 20,000 bottles × $9/bottle = $180,000 * Lotion: 30,000 bottles × $4/bottle = $120,000 2. Calculate the total sales value of all joint products: * $180,000 (Serum) + $120,000 (Lotion) = $300,000 3. Determine the allocation proportion for the lotion: * $120,000 (Lotion) / $300,000 (Total) = 40% 4. Allocate the joint cost to the lotion: * $210,000 (Total Joint Costs) × 40% = $84,000 Distractor A ($95,455) incorrectly uses the Net Realizable Value (NRV) for the lotion in the allocation base (NRV = 30,000 × ($7-$2) = $150k. Base = $180k+$150k=$330k. Allocation = ($150k/$330k)×$210k). Distractor B ($126,000) incorrectly uses the physical measure (bottles) for allocation (30,000 / 50,000 = 60%; 60% × $210,000). Distractor D ($113,077) incorrectly uses the final sales value of the cream instead of the split-off value for lotion in the allocation base.
3. A manager suggests that because Product Y has the lowest profit margin, its production should be decreased. An accountant correctly points out that the sales value at split-off allocation method is not designed for such decisions, but is appropriate for financial reporting. Which of the following statements best justifies the use of the sales value at split-off method for inventory costing?
   Answer: It allocates costs in proportion to a product's expected revenue-generating power, which aligns with the matching principle. This is a conceptual question about the justification for the sales value at split-off method. * Correct Answer B: The primary justification for market-based methods like sales value at split-off is that they allocate costs based on the product's ability to absorb those costs, as indicated by its revenue-generating power (sales value). This is consistent with the matching principle in accounting, which seeks to match expenses with the revenues they help to generate. * Distractor A is incorrect. While the method prevents any product from showing a loss at split-off if the total revenue exceeds total costs, it does not guarantee a positive gross margin for every product under all circumstances, especially if there are further processing costs. * Distractor C is incorrect. The physical measures method is often considered simpler to apply as it does not require market price data, which can sometimes be unavailable or volatile. * Distractor D is incorrect. The defining characteristic of joint costs is that they are indivisible and cannot be specifically traced to individual products before the split-off point. This statement describes the costing of separable costs, not joint costs.
4. ChemCo uses the sales value at split-off method to allocate joint costs. What is the value of the ending inventory for Alphanate at the end of May?
   Answer: $28,800 To find the value of ending inventory, you must first allocate joint costs, then determine the cost per unit, and finally multiply by the number of units in ending inventory. 1. Calculate total sales value at split-off (based on production): * Alphanate: 10,000 gallons × $20/gallon = $200,000 * Betanate: 20,000 gallons × $15/gallon = $300,000 * Total Sales Value: $200,000 + $300,000 = $500,000 2. Allocate joint costs to Alphanate: * Proportion for Alphanate: $200,000 / $500,000 = 40% * Allocated Cost: 40% × $360,000 = $144,000 3. Calculate cost per unit for Alphanate: * $144,000 / 10,000 gallons produced = $14.40 per gallon 4. Calculate ending inventory units and value: * Ending Inventory (units): 10,000 produced - 8,000 sold = 2,000 gallons * Ending Inventory Value: 2,000 gallons × $14.40/gallon = $28,800 Distractor B ($24,000) results from using the physical units method for allocation (10k/30k $360k = $120k allocated cost; $120k/10k = $12/unit; 2k units $12 = $24,000). Distractor C ($36,000) incorrectly calculates the cost per unit by dividing the allocated cost by units sold ($144,000 / 8,000 = $18/unit; 2k units * $18 = $36,000). Distractor D ($40,000) values ending inventory at its sales price (2,000 units × $20/gallon), not its cost.
5. Assuming the sales value at split-off method is used, how did the joint cost allocated per gallon of Skim Milk change from July to August?
   Answer: It decreased by approximately $0.09. This question tests the understanding that a change in one joint product's market value affects the cost allocation for all other joint products. We must calculate the cost per gallon for Skim Milk in both months. July Calculation: 1. Total Sales Value: (10,000 gal Cream × $5.00) + (40,000 gal Skim × $1.50) = $50,000 + $60,000 = $110,000 2. Skim Milk's proportion: $60,000 / $110,000 3. Allocated cost to Skim Milk: $80,000 × ($60,000 / $110,000) = $43,636.36 4. Cost per gallon of Skim Milk (July): $43,636.36 / 40,000 gallons = $1.0909 August Calculation: 1. Total Sales Value: (10,000 gal Cream × $6.00) + (40,000 gal Skim × $1.50) = $60,000 + $60,000 = $120,000 2. Skim Milk's proportion: $60,000 / $120,000 = 50% 3. Allocated cost to Skim Milk: $80,000 × 50% = $40,000 4. Cost per gallon of Skim Milk (August): $40,000 / 40,000 gallons = $1.00 Change in Cost: * $1.0909 (July) - $1.0000 (August) = $0.0909 decrease. Therefore, the cost per gallon decreased by approximately $0.09. Distractor B is incorrect as it has the wrong sign; an increase in the other product's value will decrease this product's allocated cost. Distractor C is a calculation error. Distractor D reflects a misunderstanding of how relative values work; a change in any product's value changes the proportions for all products.
6. If PetroCo implements the new process, what will be the approximate change in the joint cost allocated to one gallon of gasoline using the sales value at split-off method?
   Answer: An increase of $0.21 This question requires calculating the cost per unit under two different scenarios and then finding the difference. Original Process: 1. Sales Value: Gas = 20,000×$2.50=$50,000; Oil = 30,000×$2.00=$60,000. Total = $110,000. 2. Gasoline Allocation %: $50,000 / $110,000. 3. Allocated Cost to Gas: ($50,000/$110,000) × $400,000 = $181,818.18. 4. Cost per gallon of Gas (Old): $181,818.18 / 20,000 gallons = $9.0909 New Process: 1. Sales Value: Gas = 25,000×$2.50=$62,500; Oil = 22,500×$2.00=$45,000. Total = $107,500. 2. Gasoline Allocation %: $62,500 / $107,500. 3. Allocated Cost to Gas: ($62,500/$107,500) × $400,000 = $232,558.14. 4. Cost per gallon of Gas (New): $232,558.14 / 25,000 gallons = $9.3023 Change in Cost per Gallon: * $9.3023 (New) - $9.0909 (Old) = $0.2114 increase. The closest answer is an increase of $0.21. Distractor A is a sign error. Distractors C and D result from significant calculation errors, such as dividing the change in total allocated cost by the number of units, rather than calculating the per-unit cost in each scenario first.
7. Using the sales value at split-off method, what is the gross margin earned on the sale of planks for the month?
   Answer: $93,750 This is a multi-step problem. First, allocate joint costs to planks. Second, calculate the cost per plank. Third, find the cost of goods sold (COGS) for planks. Finally, calculate the gross margin for planks. 1. Calculate total sales value at split-off (based on production): * Planks: 80,000 units × $5.00/unit = $400,000 * Beams: 25,000 units × $16.00/unit = $400,000 * Total: $400,000 + $400,000 = $800,000 2. Allocate joint costs to planks: * Proportion for planks: $400,000 / $800,000 = 50% * Allocated cost: 50% × $600,000 = $300,000 3. Calculate cost per plank: * $300,000 / 80,000 planks produced = $3.75 per plank 4. Calculate COGS for planks: * 75,000 planks sold × $3.75/plank = $281,250 5. Calculate Revenue from planks: * 75,000 planks sold × $5.00/plank = $375,000 6. Calculate Gross Margin: * $375,000 (Revenue) - $281,250 (COGS) = $93,750 Distractor B ($75,000) incorrectly subtracts the total allocated cost from revenue ($375,000 - $300,000), ignoring the cost of unsold inventory. Distractor C ($84,677) incorrectly calculates the allocation based on units sold, a common error. Distractor D ($100,000) calculates the potential gross margin on all units produced ($5.00 - $3.75) × 80,000, not the actual gross margin on units sold.
8. What is the per-unit selling price of Lux?
   Answer: $10.00 This problem requires working backward from the allocated costs to find the sales price of Lux. 1. Determine the allocation ratio from the allocated costs: * Lux: $40,000; Standard: $80,000. The ratio is 1:2. This means the total sales value of Lux is half the total sales value of Standard. 2. Calculate the total sales value of Standard: * 20,000 units × $10/unit = $200,000 3. Use the ratio to find the total sales value of Lux: * Total Sales Value of Lux = 0.5 × Total Sales Value of Standard * Total Sales Value of Lux = 0.5 × $200,000 = $100,000 4. Calculate the per-unit selling price of Lux: * $100,000 / 10,000 units = $10.00 per unit Distractor A ($4.00) is the allocated cost per unit for Lux ($40,000 / 10,000 units). Distractor B ($5.00) is a calculation error. Distractor D ($8.00) is the allocated cost per unit for Standard ($80,000 / 10,000 units of Lux - incorrect denominator).
9. What is the sales price per unit for Gizmo at the split-off point?
   Answer: $15.00 This problem requires working backward from the allocated costs to find the sales price of Gizmo. 1. Determine the joint cost allocated to Widget: * Total Joint Cost: $240,000 * Allocated to Gizmo: $90,000 * Allocated to Widget: $240,000 - $90,000 = $150,000 2. Determine the allocation ratio: The ratio of allocated costs ($90,000 for Gizmo : $150,000 for Widget) must equal the ratio of total sales values. * Ratio: 90,000 / 150,000 = 0.6. So, Gizmo's total sales value is 60% of Widget's total sales value. 3. Calculate the total sales value of Widget: * 20,000 units × $12.50/unit = $250,000 4. Use the ratio to find the total sales value of Gizmo: * Total Sales Value of Gizmo = 0.6 × Total Sales Value of Widget * Total Sales Value of Gizmo = 0.6 × $250,000 = $150,000 5. Calculate the sales price per unit for Gizmo: * $150,000 / 10,000 units = $15.00 per unit. Distractor B ($9.00) is the cost per unit of Gizmo ($90,000 / 10,000 units), not its sales price. Distractor C ($25.00) results from incorrectly calculating the sales value of Gizmo as equal to the sales value of Widget ($250,000 / 10,000 units). Distractor D ($12.50) assumes the sales price is the same for both products.
10. Using the sales value at split-off method, what is the cost of goods sold for Product A?
    Answer: $75,000 This is a multi-step calculation: allocate joint costs, find the per-unit cost, and then calculate the cost of goods sold (COGS). 1. Calculate total sales value at split-off (based on production): * Product A: 20,000 units × $10/unit = $200,000 * Product B: 20,000 units × $20/unit = $400,000 * Total Sales Value: $200,000 + $400,000 = $600,000 2. Allocate joint costs to Product A: * Proportion for A: $200,000 / $600,000 = 1/3 * Allocated Cost: (1/3) × $300,000 = $100,000 3. Calculate cost per unit for Product A: * $100,000 / 20,000 units produced = $5.00 per unit 4. Calculate COGS for Product A: * 15,000 units sold × $5.00/unit = $75,000 Distractor A ($100,000) is the total joint cost allocated to Product A, not the COGS. Distractor C ($112,500) is the COGS if the allocation were based on units sold (A sales val=15k*$10=150k, B sales val=18k*$20=360k. Total=510k. Allocation A = (150/510)*300k = $88,235. This distractor is not derived this way. Let's see... Maybe it uses the wrong cost per unit? $150k (revenue) 75% sales rate = $112,500. Not logical.) Let's try physical units. Allocation is 50/50, $150k to A. Cost/unit = $150k/20k = $7.50. COGS = 15k $7.50 = $112,500. This is a very plausible distractor. Distractor D ($150,000) is the revenue from selling Product A (15,000 units × $10), or the allocated cost if using physical units.
11. Using the sales value at split-off method, what is the total cost assigned to the Paste produced?
    Answer: $75,000 The cost of normal spoilage is absorbed by the cost of good units produced. The allocation is based on the sales value of these good units. The information about the 5% loss is irrelevant for the calculation itself, as the good output quantities are given. 1. Calculate the total sales value at split-off for the good units produced: * Paste: 19,000 kg × $6/kg = $114,000 * Liquid: 28,500 kg × $4/kg = $114,000 * Total Sales Value: $114,000 + $114,000 = $228,000 2. Determine the allocation proportion for Paste: * $114,000 (Paste) / $228,000 (Total) = 50% 3. Allocate the joint cost to Paste: * $150,000 (Total Joint Costs) × 50% = $75,000 Distractor A ($60,000) incorrectly uses the physical measure (kilograms) for allocation: (19,000 kg / (19,000 kg + 28,500 kg)) × $150,000 = 40% × $150,000 = $60,000. Distractor B ($71,250) incorrectly attempts to account for the spoilage by reducing the joint cost pool by 5% before allocation (50% × ($150,000 × 95%)). Distractor C ($114,000) confuses the total sales value of Paste with its allocated joint cost.
12. Riverside Lumber processes logs through a joint cutting process that yields three products: Premium boards, Standard boards, and Wood chips. Joint processing costs for the week were $84,000. At split-off, 2,000 board feet of Premium boards can be sold for $25 per board foot, 5,000 board feet of Standard boards can be sold for $15 per board foot, and 1,500 tons of Wood chips can be sold for $40 per ton. If the company uses the relative sales value method and allocates $37,800 to Standard boards, what was the total sales value used in the allocation calculation?
    Answer: $165,000 Working backwards from the allocation: If Standard boards received $37,800 of the $84,000 total joint costs, then Standard boards represent $37,800 ÷ $84,000 = 0.45 or 45% of total sales value. Since Standard boards' sales value is 5,000 × $15 = $75,000, and this represents 45% of total sales value, then: Total sales value = $75,000 ÷ 0.45 = $166,667. The closest answer is C at $165,000. Let me verify by calculating all product values: Premium boards: 2,000 × $25 = $50,000; Standard boards: 5,000 × $15 = $75,000; Wood chips: 1,500 × $40 = $60,000. Total = $185,000. With this total, Standard's allocation would be ($75,000 ÷ $185,000) × $84,000 = $34,054, not $37,800. So the total must be different. If Standard gets $37,800 out of $84,000, that's 45%. So $75,000 ÷ 0.45 = $166,667 ≈ $165,000.
13. Using the relative sales value method, what amount of joint costs will be included in the ending inventory valuation for Premium gasoline?
    Answer: $34,560 First, calculate total sales values at split-off: Regular gasoline: 240,000 × $2.80 = $672,000; Premium gasoline: 180,000 × $3.20 = $576,000; Jet fuel: 120,000 × $4.50 = $540,000. Total sales value = $1,788,000. Joint cost allocation to Premium gasoline = ($576,000 ÷ $1,788,000) × $1,080,000 = 0.3221 × $1,080,000 = $347,865. Premium gasoline unit cost = $347,865 ÷ 180,000 gallons = $1.932 per gallon. Ending inventory quantity = 10% × 180,000 = 18,000 gallons. Joint costs in ending inventory = 18,000 × $1.932 = $34,776. The closest answer is B at $34,560. Let me verify: $576,000/$1,788,000 = 0.32215. 0.32215 × $1,080,000 = $347,922. $347,922 ÷ 180,000 = $1.9329 per gallon. 18,000 × $1.9329 = $34,792. This is very close to option B ($34,560). The small difference may be due to rounding in the calculation process.
14. What was the total joint cost incurred by FarmFresh Co. for this process?
    Answer: $150,000 This problem requires working backward from a known allocated cost amount to find the total joint cost. 1. Calculate the total sales value at split-off for each product: * Apple Juice: 40,000 quarts × $1.50/quart = $60,000 * Apple Sauce: 25,000 jars × $2.40/jar = $60,000 2. Calculate the total sales value of all joint products: * $60,000 (Juice) + $60,000 (Sauce) = $120,000 3. Determine the allocation proportion for apple sauce: * Proportion = $60,000 (Sauce) / $120,000 (Total) = 50% 4. Use the proportion and the allocated cost to find the total joint cost: * Allocated Cost to Sauce = Total Joint Cost × Proportion for Sauce * $75,000 = Total Joint Cost × 50% * Total Joint Cost = $75,000 / 0.50 = $150,000 Distractor A ($120,000) is the total sales value, not the total joint cost. Distractor B ($125,000) results from a calculation error, perhaps using a physical unit measure incorrectly. Distractor D ($75,000) is the cost allocated to one product, not the total.
15. Using the sales value at split-off method, what is the amount of joint cost allocated to Product B?
    Answer: $180,000 The sales value at split-off method allocates joint costs based on the relative market value of the products at the point of separation, calculated using units produced. 1. Calculate the total sales value at split-off for each product produced: * Product A: 10,000 units × $15/unit = $150,000 * Product B: 15,000 units × $20/unit = $300,000 2. Calculate the total sales value of all joint products: * $150,000 (A) + $300,000 (B) = $450,000 3. Determine the allocation proportion for Product B: * $300,000 / $450,000 = 2/3 4. Allocate the joint cost to Product B: * $270,000 (Total Joint Costs) × (2/3) = $180,000 Distractor B ($189,000) is incorrect because it uses the sales value of units sold (A: 8,000×$15=$120k; B: 14,000×$20=$280k; Total=$400k. Allocation = ($280k/$400k)×$270k = $189,000). Distractor C ($162,000) is incorrect because it uses the physical measure of units produced (Total units = 25k; B's share = 15k/25k = 60%. Allocation = 60%×$270k = $162,000). Distractor D ($90,000) is the amount allocated to Product A, not Product B (($150k/$450k)×$270k).
16. What was the market price per unit of product A at the split-off point?
    Answer: $20.00 This problem requires multiple backward calculations, starting from the final cost per unit of one product to find the initial market price of the other. 1. Calculate the total joint cost allocated to Product A: * 8,000 units × $12.00/unit = $96,000 2. Calculate the total joint cost allocated to Product B: * $132,000 (Total Joint Cost) - $96,000 (Allocated to A) = $36,000 3. Calculate the total sales value of Product B: * 4,000 units × $15/unit = $60,000 4. Determine the ratio of sales values. It must equal the ratio of allocated costs: * Cost of A / Cost of B = Sales Value of A / Sales Value of B * $96,000 / $36,000 = Sales Value of A / $60,000 5. Solve for the total sales value of Product A: * Sales Value of A = ($96,000 / $36,000) × $60,000 = (8/3) × $60,000 = $160,000 6. Calculate the market price per unit of Product A: * $160,000 / 8,000 units = $20.00 per unit Distractor A ($9.00) is the cost per unit of Product B ($36,000 / 4,000 units). Distractor B ($12.00) is the cost per unit of Product A, not its selling price. Distractor C ($15.00) is the selling price of Product B, not Product A.
17. Using the sales value at split-off method, what amount of joint cost is allocated to Zinc?
    Answer: $450,000 The value of the by-product must first be deducted from the total joint costs. The remaining net joint cost is then allocated to the main products based on their relative sales values at split-off. 1. Calculate the net joint cost to be allocated: * Total Joint Cost: $1,000,000 * Less: NRV of By-product (Lead): $100,000 * Net Joint Cost: $900,000 2. Calculate the total sales value at split-off for the main products: * Copper: 50,000 lbs × $15/lb = $750,000 * Zinc: 30,000 lbs × $25/lb = $750,000 * Total Sales Value: $750,000 + $750,000 = $1,500,000 3. Determine the allocation proportion for Zinc: * $750,000 (Zinc) / $1,500,000 (Total) = 50% 4. Allocate the net joint cost to Zinc: * $900,000 (Net Joint Cost) × 50% = $450,000 Distractor A ($500,000) incorrectly allocates the gross joint cost ($1,000,000 × 50%) without deducting the by-product's value. Distractor B ($337,500) incorrectly uses a physical measure (pounds) for allocation (30,000 lbs / 80,000 total lbs) × $900,000. Distractor C ($550,000) incorrectly adds the by-product's value to the joint costs before allocating (($1,000,000 + $100,000) × 50%).
18. What proportion of the joint costs should be allocated to Product P2?
    Answer: 37.2% This question asks for the allocation proportion, not the final dollar amount. This requires calculating the total sales value for all products and the specific sales value for P2. 1. Calculate the total sales value at split-off for each product: * P1: 10,000 units × $12/unit = $120,000 * P2: 20,000 units × $8/unit = $160,000 * P3: 15,000 units × $10/unit = $150,000 2. Calculate the total sales value of all joint products: * $120,000 + $160,000 + $150,000 = $430,000 3. Determine the allocation proportion for Product P2: * Proportion = (Sales Value of P2) / (Total Sales Value) * Proportion = $160,000 / $430,000 = 0.37209... * Rounded to one decimal place, this is 37.2%. Distractor A (33.3%) would be the answer if all three products had equal sales value. Distractor B (44.4%) incorrectly uses the physical measure of units (20,000 units / (10k+20k+15k=45k units) = 44.4%). Distractor C (40.0%) results from a miscalculation, perhaps rounding the sales values before calculating the ratio ($160k / ($120k+$160k+$120k) or similar error).
19. Management is considering an advertising campaign that is expected to increase the selling price of Product M to $15, with no change in production volumes or other prices. If the campaign is successful, what would be the allocated joint cost per unit for Product N?
    Answer: $4.50 This is a sensitivity analysis question. The student must calculate the allocation based on the new selling price for Product M and determine the resulting cost per unit for Product N. 1. Calculate the new total sales value at split-off using the new price for M: * Product M: 10,000 units × $15/unit (new price) = $150,000 * Product N: 20,000 units × $7.50/unit = $150,000 * New Total Sales Value: $150,000 + $150,000 = $300,000 2. Allocate joint costs to Product N based on the new values: * Proportion for N: $150,000 (N) / $300,000 (Total) = 50% * Allocated Cost to N: 50% × $180,000 = $90,000 3. Calculate the new cost per unit for Product N: * $90,000 / 20,000 units = $4.50 per unit Distractor B ($6.00) is the cost per unit if allocation is based on physical units ((20,000/30,000) × $180,000 = $120,000; $120,000/20,000 units = $6.00). Distractor C ($5.00) is the cost per unit for Product N before the price change for Product M (Original SV: M=$120k, N=$150k, Total=$270k. Allocation N = ($150k/$270k)×$180k = $100k. Cost/unit = $100k/20k=$5.00). Distractor D ($9.00) is the new cost per unit for Product M ($90,000 / 10,000 units), not Product N.
20. Using the sales value at split-off method, what is the joint cost assigned to Product R?
    Answer: $45,000 This question includes irrelevant data (machine hours) to test the student's focus on the correct allocation base for the specified method. 1. Calculate the total sales value at split-off for each product: * Product R: 10,000 units × $6/unit = $60,000 * Product S: 5,000 units × $12/unit = $60,000 2. Calculate the total sales value of all joint products: * $60,000 (R) + $60,000 (S) = $120,000 3. Determine the allocation proportion for Product R: * $60,000 / $120,000 = 50% 4. Allocate the joint cost to Product R: * 50% × $90,000 = $45,000 Distractor B ($36,000) incorrectly uses machine hours as the allocation base (2,000 hours / 5,000 total hours = 40%; 40% × $90,000 = $36,000). Distractor C ($54,000) is the amount that would be allocated to Product S if using machine hours (60% × $90,000). Distractor D ($60,000) is the total sales value of Product R, not its allocated cost.

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