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Management and Cost Accounting Student Manual

Mike Tayles, Colin Drury

Chapter 6

Joint and By-Product Costing - all with Video Answers

Educators

Chapter Questions

Problem 1

A company operates a process which produces three joint products: K, P and Z. The costs of operating this process during September amounted to $£ 117,000$. During the month the output of the three products was:
$$
\begin{array}{ll}
\text { K } & \text { 2,000 litres } \\
P & 4,500 \text { litres } \\
Z & 3,250 \text { litres }
\end{array}
$$
P is further processed at a cost of £9.00 per litre. The actual loss of the second process was 10 per cent of the input, which was normal. Products K and Z are sold without further processing.
The final selling prices of each of the products are:
$$
\begin{array}{ll}
\text { K } & £ 20.00 \text { per litre } \\
\mathrm{P} & £ 25.00 \text { per litre } \\
\mathrm{Z} & £ 18.00 \text { per litre }
\end{array}
$$
Joint costs ate attributed to products on the basis of output volume. The profit attributed to product P was:
(A) $€ 6,750$
(B) $€ 12,150$
(C) $€ 13,500$
(D) $€ 16,200$
(E) $€ 18,000$

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Problem 2

A company simultaneously produces three products (X, Y and Z) from a single process. X and Y are processed further before they can be sold; Z is a by-product that is sold immediately for $$\$6$$ per unit without incurring any further costs. The sales prices of X and Y after further processing are $$\$50$$ per unit and $$\$60$$ per unit respectively.
Data for October are as follows:
$$
\begin{aligned}
&\text { (\$) }\\
&\begin{array}{lr}
\hline \text { Joint production costs that produced } 2,500 \text { units of } X \text {, } & \\
3,500 \text { units of } Y \text { and } 3,000 \text { units of } Z & 140,000 \\
\text { Further processing costs for } 2,500 \text { units of } X & 24,000 \\
\text { Further processing costs for } 3,500 \text { units of } Y & 46,000
\end{array}
\end{aligned}
$$
Joint costs are apportioned using the final sales value method.
Calculate the total cost of the production of X for October.

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01:04

Problem 3

Charleville produces three products and one by-product. Output from the process for a month was as follows:
$$
\begin{array}{lcc}
\text { Product } & \begin{array}{c}
\text { Selling price } \\
\text { per unit }
\end{array} & \begin{array}{c}
\text { Units of } \\
\text { output from } \\
\text { process }
\end{array} \\
\hline 1 & £ 18 & 10,000 \\
2 & £ 25 & 20,000 \\
3 & £ 20 & 20,000 \\
4 \text { (by-product) } & £ 2 & 3,500
\end{array}
$$
Total output costs were £277,000.
What was the unit valuation for product 3 using the sales revenue basis for allocating joint cost?
(A) £4.70
(B) £4.80
(C) £5.00
(D) £5.10

Carson Merrill
Carson Merrill
Numerade Educator

Problem 4

Process Co. has two divisions, A and B. Division A produces three types of chemicals: products L, M and S, using a common process. Each of the products can either be sold by Division A to the external market at split-off point (after the common process is complete) or can be transferred to Division B for individual further processing into products LX, MX and SX.
In November, which is a typical month, Division A’s output was as follows:
$$
\begin{array}{ll}
\text { Product } & \text { (kg) } \\
\hline \mathrm{L} & 1,200 \\
\mathrm{M} & 1,400 \\
\mathrm{~S} & 1,800
\end{array}
$$
The market selling prices per kg for the products, both at split-off point and after further processing, are as follows:
$$
\begin{array}{llll}
& \mathbf{( \$ )} & & (\mathbf{S}) \\
\mathrm{L} & 5.60 & \mathrm{LX} & 6.70 \\
\mathrm{M} & 6.50 & \mathrm{MX} & 7.90 \\
\mathrm{~S} & 6.10 & \mathrm{SX} & 6.80
\end{array}
$$
The specific costs for each of the individual further processes are:
Variable cost of $\$ 0.50$ per $\mathrm{kg}$ of $L X$
Variable cost of $\$ 0.70$ per $\mathrm{kg}$ of MX
Variable cost of $\$ 0.80$ per $\mathrm{kg}$ of $S X$
Further processing leads to a normal loss of 5 per cent at the beginning of the process for each of the products being processed.
Required:
Calculate and conclude whether any of the products should be further processed in Division B in order to optimize the profit for the company as a whole.

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Problem 5

The marketing director of your company has expressed concern about product X, which for some time has shown a loss, and has stated that some action will have to be taken.
Product X is produced from material A, which is one of two raw materials jointly produced by passing chemicals through a process.
Representative data for the process are as follows:
$$
\begin{array}{ll}
\text { Output (kg) } & \\
\text { Material A } & 10,000 \\
\text { Material B } & 30,000 \\
\text { Process (f) } & \\
\text { Raw material } & 83,600 \\
\text { Conversion costs } & 58,000
\end{array}
$$
Joint costs are apportioned to the two raw materials according to the weight of output. Production costs incurred in converting material A into product X are £1.80 per kg of material A used. A yield of 90 per cent is achieved. Product X is sold for £5.60 per kg. Material B is sold without further processing for £6.00 per kg.
Required:
(a) Calculate the profit/loss per kg of product X and material B, respectively.
(b) Comment upon the marketing director’s concern, advising him whether you consider any action should be taken.
(c) Demonstrate an alternative joint cost apportionment for product X and comment briefly upon this alternative method of apportionment.

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Problem 6

A distillation plant, which works continuously, processes 1,000 tonnes of raw material each day. The raw material costs
£4 per tonne and the plant operating costs per day are £2,600. From the input of raw material the following output is produced:
$$
\begin{array}{ll}
& \text { (\%) } \\
\hline \text { Distillate X } & 40 \\
\text { Distillate Y } & 30 \\
\text { Distillate Z } & 20 \\
\text { By-product B } & 10
\end{array}
$$
From the initial distillation process, Distillate X passes through a heat process which costs £1,500 per day and becomes product X which requires blending before sale.
Distillate Y goes through a second distillation process costing £3,300 per day and produces 75 per cent of product Y and 25 per cent of product X1.
Distillate Z has a second distillation process costing £2,400 per day and produces 60 per cent of product Z and 40 per cent of product X2. The three streams of products X, X1 and X2 are blended, at a cost of £1,555 per day, to become the saleable final product XXX. There is no loss of material from any of the processes. By-product B is sold for £3 per tonne and such proceeds are credited to the process from which the by-product is derived. Joint costs are apportioned on a physical unit basis.
Required:
(a) Draw a flow chart, flowing from left to right, to show for one day of production the flow of material and the build up of the operating costs for each product.
(b) Present a statement for management showing for each of the products XXX, Y and Z, the output for one day, the total cost and the unit cost per tonne.
(c) Suggest an alternative method for the treatment of the income receivable for by-product B than that followed in this question (figures are not required).

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Problem 7

A chemical company carries on production operations in two processes. Materials first pass through process I, where a compound is produced. A loss in weight takes place at the start of processing. The following data, which can be assumed to be representative, relate to the month just ended:
$$
\begin{array}{lr}
\hline \text { Quantities (kg) } \\
\hline \text { Material input } & 200,000 \\
\text { Opening work in process (half processed) } & 40,000 \\
\text { Work completed } & 160,000 \\
\text { Closing work in process (two-thirds processed) } & 30,000
\end{array}
$$
$$
\begin{array}{ll}
\text { Costs }(€) & \\
\hline \text { Material input } & 75,000 \\
\text { Processing costs } & 96,000 \\
\text { Opening work in process: } & \\
\text { Materials } & 20,000 \\
\text { Processing costs } & 12,000
\end{array}
$$
Any quantity of the compound can be sold for £1.60 per kg. Alternatively, it can be transferred to process II for further processing and packing to be sold as Starcomp for £2.00 per kg. Further materials are added in process II such that for every kg of compound used, 2kg of Starcomp result.
Of the 160,000kg per month of work completed in process I, 40,000kg are sold as compound and 120,000kg are passed through process II for sale as Starcomp. Process II has facilities to handle up to 160,000kg of compound per month if required. The monthly costs incurred in process II (other than the cost of the compound) are:
$$
\begin{array}{lcc}
& \begin{array}{c}
120,000 \mathrm{~kg} \text { of } \\
\text { compound input }
\end{array} & \begin{array}{c}
160,000 \mathrm{~kg} \text { of } \\
\text { compound input }
\end{array} \\
\hline \text { Materials (f) } & 120,000 & 160,000 \\
\text { Processing costs }(f) & 120,000 & 140,000
\end{array}
$$
Required:
(a) Determine, using the average method, the cost per kg of compound in process I, and the value of both work completed and closing work in process for the month just ended.
(b) Demonstrate that it is worthwhile further processing 120,000kg of compound.
(c) Calculate the minimum acceptable selling price per kg, if a potential buyer could be found for the additional output of Starcomp that could be produced with the remaining compound.

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Problem 8

(a) Polimur Ltd operates a process that produces three joint products, all in an unrefined condition. The operating results of the process for October are shown below.
Output from process:
$$
\begin{array}{lr}
\text { Product A } & 100 \text { tonnes } \\
\text { Product B } & 80 \text { tonnes } \\
\text { Product C } & 80 \text { tonnes }
\end{array}
$$
The month’s operating costs were £1,300,000. The closing stocks were 20 tonnes of A, 15 tonnes of B and 5 tonnes of C. The value of the closing stock is calculated by apportioning costs according to weight of output. There were no opening stocks and the balance of the output was sold to a refining company at the following prices:
$$
\begin{array}{ll}
\text { Product A } & \text { E5 per kg } \\
\text { Product B } & \text { E4 per kg } \\
\text { Product C } & \text { \&9 per kg }
\end{array}
$$
Required:
Prepare an operating statement showing the relevant trading results for October.
(b) The management of Polimur Ltd have been considering a proposal to establish their own refining operations. The current market prices of the refined products are:
$$
\begin{array}{ll}
\text { Product A } & £, 17 \text { per kg } \\
\text { Product B } & £ 14 \text { per kg } \\
\text { Product C } & £, 20.50 \text { per kg }
\end{array}
$$
The estimated unit costs of the refining operation are:
$$
\begin{array}{|c|c|c|c|}
\hline & \begin{array}{c}
\text { Product A } \\
\text { (f per kg) }
\end{array} & \begin{array}{l}
\text { Product B } \\
\text { (E per kg) }
\end{array} & \begin{array}{l}
\text { Product C } \\
\text { (f per kg) }
\end{array} \\
\hline \text { Direct materials } & 0.50 & 0.75 & 2.50 \\
\hline \text { Direct labour } & 2.00 & 3.00 & 4.00 \\
\hline \text { Variable overheads } & 1.50 & 2.25 & 5.50 \\
\hline
\end{array}
$$
Prime costs would be variable. Fixed overheads, which would be £700,000 monthly, would be direct to the refining operation. Special equipment is required for refining product B and this would be rented at a cost, not included in the above figures, of £360,000 per month.
It may be assumed that there would be no weight loss in the refining process and that the quantity refined each month would be similar to October’s output shown in (a) above.
Required:
Prepare a statement that will assist management to evaluate the proposal to commence refining operations. Include any further comments or observations you consider relevant.

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Problem 9

C Ltd operates a process which produces three joint products. In the period just ended costs of production totalled £509,640. Output from the process during the period was:
$$
\begin{array}{ll}
\text { Product W } & 276,000 \mathrm{~kg} \\
\text { Product X } & 334,000 \mathrm{~kg} \\
\text { Product Y } & 134,000 \mathrm{~kg}
\end{array}
$$
There were no opening stocks of the three products. Products W and X are sold in this state. Product Y is subjected to further processing. Sales of Products W and X during the period were:
$$
\begin{array}{ll}
\text { Product W } & 255,000 \mathrm{~kg} \text { at } £ 0.945 \text { per kg } \\
\text { Product X } & 312,000 \mathrm{~kg} \text { at } £ 0.890 \text { per kg }
\end{array}
$$
During the period 128,000kg of Product Y were further processed. The balance of the period production of the three products W, X and Y remained in stock at the end of the period. The value of closing stock of individual products is calculated by apportioning costs according to weight of output.
The additional costs in the period of further processing Product Y, which is converted into Product Z, were:
$$
\begin{array}{lr}
\text { Direct labour } & £ 10,850 \\
\text { Production overhead } & £ 7,070
\end{array}
$$
A total of 96,000kg of Product Z were produced from the 128,000kg of Product Y. A by-product, BP, is also produced which can be sold for £0.12 per kg. 8,000kg of BP were produced and sold in the period.
Sales of Product Z during the period were 94,000kg, with a total revenue of £100,110. Opening stock of Product Z was 8,000kg, valued at £8,640. The FIFO method is used for pricing transfers of Product Z to cost of sales.
Selling and administration costs are charged to all main products when sold, at 10 per cent of revenue.
Required:
(a) Prepare a profit and loss account for the period, identifying separately the profitability of each of the three main products.
(b) C Ltd has now received an offer from another company to purchase the total output of Product Y (i.e. before further processing) for £0.62 per kg. Calculate the viability of this alternative.
(c) Discuss briefly the methods of, and rationale for, joint cost apportionment.

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Problem 10

A fish processing company has a contract to purchase all the fish caught by a fishing vessel. The processor removes the head and skeleton, which are waste (Process 1), and is then able to sell the fish fillets which remain. The waste is estimated to be 40 per cent by weight of the fish bought and is sold at $30 \mathrm{p}$ per $\mathrm{kg}$ for animal food.
The fish fillets are inspected for quality and three categories are identified (standard, special and superior). Half the catch is expected to be of standard quality. Of the remainder there is twice as much special as superior.
For one contract period, the vessel contains a total of $36,000 \mathrm{~kg}$ of whole fish and the contract price is $f 1.50$ per $\mathrm{kg}$, irrespective of quality. The labour cost for Process 1 is $£ 28,000$ for this quantity.
As an alternative to sale as fresh produce, the fillets of fish may be cooked and coated in breadcrumbs (Process 2). The process of cooking the fillets and coating them in breadcrumbs costs $10 \mathrm{p}$ per $\mathrm{kg}$ for material and $60 \mathrm{p}$ per $\mathrm{kg}$ for labour. Current market prices of fresh fillets and the breadcrumbed alternatives are;
$$
\begin{array}{|c|c|c|}
\hline \text { Category } & \text { Fresh } & \begin{array}{c}
\text { (f per kg) } \\
\text { Breadcrumbed }
\end{array} \\
\hline \text { Superior } & 7.50 & 8.70 \\
\hline \text { Special } & 6.80 & 7.50 \\
\hline \text { Standard } & 4.00 & 5.20 \\
\hline
\end{array}
$$
In Process 1 the overhead costs are recovered based on 120 per cent of labour costs; one-third of these overheads are variable. In Process 2 the overhead rate set is 180 per cent of labour costs, one-quarter being variable.
Required:
(a) An often quoted phrase used in management accounting is ‘different costs for different purposes’. To demonstrate the appropriateness of this phrase, list and briefly describe three purposes of preparing product costs in a manufacturing organization.
(b) Prepare statements of total net profit or loss per period for each category of fish if all sales are in the fresh state (i.e. after Process 1) and on the assumption that the total net cost is shared between the three categories based on:
(i) weight;
(ii) market value.
(c) If a loss was revealed for a category under either (b) (i) or (ii) above, explain how the management should react.
(d) Determine for each category whether it is profitable for the company to further process the fillets, and make brief comments.

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Problem 11

A company manufactures two joint products in a single process. One is sold as a garden fertilizer, the other is a synthetic fuel which is sold to external customers but which can also be used to heat greenhouses in which the company grows fruit and vegetables all year round as a subsidiary market venture. Information relating to the previous 12 -month period is as follows:
(i) 1,600,000kg of garden fertilizer were produced and then sold at $€ 3.00$ per $\mathrm{kg}$. Joint costs are apportioned between the garden fertilizer and the synthetic fuel on a physical units (weight) basis. The fertilizer has a contribution to sales ratio of 40 per cent after such apportionment. There are no direct costs of fertilizer sales or production.
(ii) The synthetic fuel represents 20 per cent of the total weight of ourput from the manufacturing process. A wholesaler bought $160,000 \mathrm{~kg}$ at $£ 1.40$ per $\mathrm{kg}$ under a long-term contract which stipulates that its availability to him will not be reduced below $100,000 \mathrm{~kg}$ per annum. There is no other external market for the fuel. Fixed administrative, selling and distribution costs incurred specifically as a result of the fuel sales to the wholesaler totalled $€ 40,000$. That part of the fuel production which was sold to the wholesaler incurred additional variable costs for packaging of $£ 1.20$ per $\mathrm{kg}$.
(iii) The remaining synthetic fuel was used to heat the company greenhouses. The greenhouses produced $5 \mathrm{~kg}$ of fruit and vegetables per $\mathrm{kg}$ of fuel. The fruit and vegetables were sold at an average price of 60.50 per $\mathrm{kg}$. Total direct costs of fruit and vegetable production were $f 520,000$. Direct costs included a fixed labour cost of $f 100,000$ which is avoidable if fruit and vegetable production ceases, the femainder being variable with the quantity produced.
A notional fuel charge of $£ 1.40$ per $\mathrm{kg}$ of fuel is made to fruit and vegetable production. This notional charge is in addition to the direct costs detailed above.
(iv) Further company fixed costs were apportioned to the products as follows:
$$
\begin{array}{lr}
\hline \text { Garden fertilizer } & 720,000 \\
\text { Synthetic fuel } & 18,000 \\
\text { Fruit and vegetables } & 90,000
\end{array}
$$
The above data were used to produce a profit and loss analysis for the 12-month period for each of three areas of operation viz:
1. garden fertilizer;
2. synthetic fuel (including external sales and transfers to the greenhouses at £1.40 per kg);
3. fruit and vegetables (incorporating the deduction of any notional charges).
Required:
(a) Prepare a summary statement showing the profit or loss reported in each of the three areas of operation detailed above.
(b) Calculate the percentage reduction in the fixed costs of £40,000 which would have been required before the synthetic fuel sales for the previous 12-month period would have resulted in a net benefit to the company.
(c) Calculate the net benefit or loss which sales of fruit and vegetables caused the company in the previous 12-month period.
(d) Advise management on the fruit and vegetable price strategy for the coming year if fruit and vegetable production/sales could be expanded according to the following price/demand pattern:
$$
\begin{array}{llllll}
\text { Sales }(000 \mathrm{~kg}) & 1,200 & 1,300 & 1,400 & 1,500 & 1,600 \\
\text { Average selling price } / \mathrm{kg}(f) & 0.50 & 0.495 & 0.485 & 0.475 & 0.465
\end{array}
$$
All other costs, prices and quantities will remain unchanged during the coming year. The wholesaler will continue to purchase all available synthetic fuel not used in the greenhouses.

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Problem 12

Amongst its products a chemical company markets two concentrated liquid fertilizers - type P for flowers and type Q for vegetables. In the current year total sales are expected to be restricted by forecast sales of type $Q$ which are limited to 570,000 litres for the year. At this level the plant capacity will be under-utilized by 20 per cent. The fertilizers are manufactured jointly as follows:
Mixing: Raw materials $A$ and B are mixed together in equal amounts and filtered. After filtering there is a saleable residue, $X$, amounting to 5 per cent of the input materials.
Distillation: The mixed materials are heated and there is an evaporation loss of 10 per cent. The remaining liquid distils into one-third each of an extract $P$, an extract $Q$ and a by-product $Y$.
Blending: Two parts of raw material $C$ are blended with one part of extract $P$ to form the fertilizer type $P$. One part of raw material $D$ is blended with one part of extract $Q$ to form the fertilizer type $Q$.
Fertilizer type $P$ is filled into 3-litre cans and labelled. Fertilizer type $Q$ is filled into 6-litre preprinted cans. Both are then ready for sale. The costs involved are as under:
$$
\begin{array}{lc}
\begin{array}{l}
\text { Raw } \\
\text { material }
\end{array} & \begin{array}{c}
\text { Cost per } \\
\mathbf{1 0 0} \text { litres } \\
(\boldsymbol{\epsilon})
\end{array} \\
\hline \text { A } & 25 \\
\text { B } & 12 \\
\text { C } & 20 \\
\text { D } & 55
\end{array}
$$
$$
\begin{array}{lc}
\text { Cans } & \begin{array}{c}
\text { Cost each } \\
(\boldsymbol{\epsilon})
\end{array} \\
\hline \text { 3-litre } & 0.32 \\
\text { 6-litre } & 0.50
\end{array}
$$
$$
\begin{array}{lc}
\text { Labels } & \begin{array}{c}
\text { Cost } \\
\text { per } 1,000 \\
\text { (f) }
\end{array} \\
\hline \text { For 3-litre cans } & 3.33
\end{array}
$$
Manufacturing costs:
Per 100 litres of input processed
$$
\begin{array}{lccc}
& \begin{array}{c}
\text { Direct } \\
\text { wages } \\
(\boldsymbol{t})
\end{array} & \begin{array}{c}
\text { Variable } \\
\text { overhead } \\
(\boldsymbol{t})
\end{array} & \begin{array}{c}
\text { Fixed } \\
\text { overhead } \\
\text { per year } \\
(\boldsymbol{t})
\end{array} \\
\hline \text { Mixing } & 2.75 & 1.00 & 6,000 \\
\text { Distilling } & 3.00 & 2.00 & 20,000 \\
\text { Blending } & 5.00 & 2.00 & 33,250
\end{array}
$$
The residue $X$ and by-product $Y$ are both sold to local companies at $£ 0.03$ and $€ 0.04$ per litte respectively. Supplies are collected in bulk by the buyers using their own transport. The sales revenue is credited to the process at which the material arises.

Product costs are apportioned entirely to the two main products on the basis of their output from each process.
No inventories of part-finished materials are held at any time.
The fertilizers are sold through agents on the basis of list price less 25 per cent. Of the net selling price, selling and distribution costs amount to $131 / 3$ per cent and profit to 20 per cent. Of the selling and distribution costs 70 per cent are variable and the remainder fixed.
Required:
(a) Calculate separately for the fertilizers type $\mathrm{P}$ and type $\mathrm{Q}$ for the current year:
(i) total manufacturing cost;
(ii) manufacturing cost per litre;
(iii) list price per litre;
(iv) profit for the year.
(b) Calculate the break-even price per litre to manufacture and supply an extra 50,000 litres of fertilizer type Q for export and which would incur variable selling and distribution costs of $£, 2,000$.
(c) State the price you would recommend the company should quote per litre for this export business, with a brief explanation for your decision.

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