Joint cost allocation in the sawmilling
industry: four methods for estimating raw
material costs.
Abstract
When processing a sawlog, four main product groups are produced: center boards, side
boards, chips, and sawdust. In this kind of joint production it is difficult to determine raw
material costs for the individual products. In this article we consider methods to allocate
joint costs to sawn products in the sawmilling industry. Joint cost accounting can be used
to allocate raw material costs and thus provide information that is crucial when
evaluating profitability in sawmilling. Four joint cost allocation methods are presented
and demonstrated. A base scenario is described resembling a typical Norwegian sawmill,
and the four joint costing methods are applied to the data. Then a second scenario is
introduced; we assume that the value of by-products increases and production efficiency
improves and then estimate raw material costs based on the set of new assumptions. All
four costing methods yield different results, and therefore the choice of costing method
affects profitability for the various product groups, although the aggregate profit is not
affected.
In Norway about eight million [m.sup.3] of roundwood are harvested annually, of which
about 50 percent is sawlogs. When processing a sawlog, four product groups will be
produced: center boards ([congruent to] 40 percent), side boards (15 percent), chips (35
percent), and sawdust (5 percent). In addition, kiln and drying results in 5 percent
reduced production volume. Center boards and side boards are referred to as main
products while chips and sawdust are considered low-value products and are referred to
as by-products.
By far the greater part of Norwegian sawmills are softwood sawmills using Norway
spruce (Picea abies (L.) Karst.) and Scots pine (Pinus svlvestris (L.)) as raw material.
Logs are sawn according to the Nordic practice, i.e., the main yield is sawn from the
center of the log, containing two or more pieces (Anonymous 1994, Juslin and Hansen
2003, Gjerdrum 2007). The thickness varies normally from 38 mm to 75 ram, and the
width from 75 mm to 225 mm. The side yield consists of boards with thickness from 16
mm to 32 mm, and width from 75 mm to 225 mm. Except for a minor portion of high
quality pine logs, the side boards are inferior to the center boards.
A typical sawlog small-end diameter distribution has a minimum of 12 cm and a
maximum of 40 cm, with an average of 17 to 22 cm. The log length distribution ranges
normally from 3.4 to 5.8 m, with an average of 4.5 to 5.0 m.
Most of the production costs in sawmilling are raw material costs. Companies have to
consider how they can best ascribe raw material costs (joint costs) generated up to the
split-off point to particular products. The split-off point in sawmilling is where the
sawlog is divided into center boards, side boards, chips, and sawdust. Joint costs were
described by Billera et al. (1981) as "... costs which cannot be readily identified with
individual products." They stated that joint costs are usually common in extractive,
agricultural, and chemical industries, as well as in industries where different grades of the
same product are obtained. If the costing system does not capture the consumption of
resources by products, costs will be distorted and there is a risk that managers decide to
produce unprofitable products.
The joint cost problem has been known for a long time in sawmilling. In 1992 the term
"sawmill paradox" was coined by Gronlund (1992), referring to the fact that when
processing a sawlog, a range of products (both main products and byproducts) are
produced. This is a typical joint production. Some of the products, such as sawdust, will
have a considerably lower sales value than both the raw material price and the sales value
of other wood products produced from the core of the sawlog. Furthermore, since the raw
material price is higher than the net revenue for chips and low-grade sawnwood (side
boards), the sawmill is apparently producing these products at negative net value. A
profit-maximizing softwood dimension or structural lumber sawmill should therefore
maximize production of center boards and minimize the production of low-grade
sawnwood (side boards), chips and sawdust. For these sawmills the side boards are
generally narrow and short, and thus of lower value per unit volume than the higher value
center boards. Clearly the situation will be different for hardwood sawmills where the
highest value lumber recovered is from the outer part of the log. However, what is
described here would apply to any type of mill, except that the product mix would vary.
There are indications that sawmill by-product prices will increase substantially. Due to
the emphasis on energy production based on renewable resources, to meet the EU's
binding target of a 20 percent share of renewable energies in overall EU energy
consumption by 2020 (Renewable Energy Technology Roadmap up to 2020 (EREC
2007)), increased demand results in an increased price for intermediate product (chips).
In the softwood sawmilling case, the problem is to decide when low-value side boards
should be further processed at the sawmill or chipped and sold for bioenergy. A
substantial part of the costs in sawmilling are joint costs, and in profit analysis joint costs
have to be included. This resembles the situation that faced the U.S. oil refining industry
in 1973/74. The prices of intermediate products were raised in order to cut back
production of gasoline and to increase production of fuel oil. The industry was requested
to provide the government with figures representing the loss associated with a change in
production from gasoline to home-heating fuel. To be able to do this, allocation of joint
costs was necessary because of the existence of joint production costs.
Previous research has been conducted on several industries--sawmilling, oil and gas--in
addition to developing a general theory on the topic of joint cost allocation. Johansson
and Rosling (2002) developed an approach to allocating joint costs in sawmilling based
on a linear programming model. The purpose of this model was to calculate the marginal
cost of center boards. This model was further developed by Johansson (2004) and has
been used for joint cost allocation in a Swedish pine mill. In Johansson's model, timber
costs (i.e., joint costs) include all costs before sawing the logs, minus revenue from
cellulose chips, bark and sawdust. Johansson (2004) suggested that marginal cost
estimates are useful only for center products, i.e., for products sold to regular customers
at negotiated prices and often further processed. For commercial side boards sold at fixed
market prices, marginal cost estimates are of little use since prices are given and the
volumes are consequences of the production of center boards.
A survey of accounting practices in the European oil and gas industry was conducted by
Coe et al. (1997). They stated that the accelerating pace of change in the energy industry
created uncertainty, and information on the accounting aspects of this dynamic
environment was needed. As early as 1977, Feller highlighted the need for management
accounting systems designed for handling joint costs in the oil refining industry. The oil
crisis in 1973 to 1974 had made by-products highly profitable, and other costing systems
were needed to allocate joint costs in a more appropriate way.
Billera et al. (1981) presented a unique procedure for allocating common costs from a
production process. This approach was suitable for allocating joint costs in a production
process yielding different products or services, or different grades of the same product.
The procedure enabled calculation of marginal unit costs for products produced and
finally a relative cost per unit product produced. This is the procedure implemented by
Johansson (2004).
Balachandran and Ramakrishnan (1981) also presented a way of allocating joint costs by
combining earlier joint cost allocation models developed by Moriarity (1975) and
Louderback (1976). Balachandran and Ramakrishnan (1981) used a combination of both
Moriarity (1975) and Louderback (1976) to provide a new approach called "prosperity to
contribute." A division's "prosperity to contribute" was calculated as the minimum cost of
each division acting independently of the company or together (internally) with the other
divisions in the company, minus the internal processing cost of each division. Each
division's relative share of the contribution was used as a distribution formula when joint
costs (i.e., purchasing raw material, joint production cost, etc.) were allocated.
Balachandran and Ramakrishnan (1981) also suggested a Shapley value-based scheme to
allocate joint costs. A more thorough discussion of game theoretical concepts and
Shapley value-based allocation can be found in Hamlen et al. (1977). The methods
presented by Balachandran and Ramakrishnan (1981) allocated joint costs to divisions
and not to products.
With semiconductor manufacturing as a setting, Gatti and Grinnell (2000) presented an
article in which they evaluated the effect of joint cost allocation in cases of productivity
and quality improvements. They presented methods called the physical quantities
approach and the market value approach. The conclusion was that joint cost allocation
based on market values are most sensitive to changes in productivity, and the most
comprehensive method in terms of reflecting the effects of improvements of product
quality.
Finally, Jang et al. (2006) proposed a method to allocate joint costs in the natural gas
industry. Natural gas is a joint product with crude oil and is usually processed and
transported via shared facilities to reduce net costs. The method was called the design
benefit method (DBM), and joint costs are allocated based on an ideal product's
utilization of real capital. Jang et al. (2006) focused on minimizing the total costs
connected to producing a number of products. The joint costs of utilizing specific
equipment were allocated to the products using a regression analysis to determine each of
the products' utilization of the equipment.
Theory and data
Joint cost allocation is comprehensively discussed in the cost accounting literature, but in
the practical accounting literature joint cost accounting has not been given much
attention. In Horngren's 12th edition of Cost Accounting, more emphasis is put on joint
cost allocation than in the previous editions. In addition to the methods referred to above,
Horngren et al. (2006) presented four joint cost allocation methods:
(1) Sales value at split-off point: the relative amount of cost is the same as the relative
amount of sales value.
(2) Physical measurement: the relative physical part of one product at split-off point is
used as the cost allocation key.
(3) Net realizable value (NRV): final sales value for one product minus separable costs
(costs connected directly to that product), relative to total net realizable value, is used as a
key to allocate joint costs to each product.
(4) Constant gross margin percentage NRV: the gross margin is deducted from a
product's total revenue using the gross margin percentage. The remaining amount is the
total production cost for that product. Separable cost is then deducted, and the cost
remaining is the joint cost for each product.
These are the basic methods for joint cost allocation and many articles on joint cost
allocation originate from them. For example Gatti and Grinnell (2000) used the sales
value at split-off point method and the NRV method to measure and calculate product
profitability in a case of quality and productivity improvements in a semiconductor
manufacturing company producing memory devices.
Using data from the Norwegian sawmilling industry, examples showing how joint costs
allocation procedures affect products' contribution margins are provided. In addition,
illustrations are presented to demonstrate how quality and productivity improvements
influence products' profitability. The joint cost allocation methods presented in this
article come from findings in Tunes et al. (2006) and from theoretical examples derived
in Horngren (2006) and Gatti and Grinnell (2000). The examples presented do not
consider further processing of the lumber in planer mills. Planer shavings are therefore
not mentioned as a product since the value of that residue is being captured in the planing
mill.
Horngren et al. (2006) stated that the sales value at split-off point method should be used
when the sales price of the product is available (even if further processing is done) and
presented four reasons for this: firstly, it measures the value of the joint product
immediately at the end of the joint process; secondly, there are no anticipations of
subsequent management decisions; thirdly, it is meaningful to allocate joint costs based
on relative revenues; and fourthly, because of its simplicity compared to the other
methods described above.
In the sawmilling industry, sales prices at the split-off point are usually not available
because the main products (i.e., center boards and side boards) are often used as inputs in
value-added production, for example planed, precut or pressure treated. When the sales
prices of products at the split-off point are not available and the physical measurement
methods are unsuitable, other methods should be used. These are presented by Horngren
et al. (2006) as the NRV method and the constant gross margin percentage NRV method.
According to Horngren et al. (2006) the NRV method measures products' income better
than the gross margin percentage NRV method. The NRV method is also perceived as
better than the physical measurement method. However, there are instances when
physical measurement methods are preferred. Market price based methods (i.e., the sales
value at split-off point method) are for instance difficult to use in the context of rate and
price regulations because exact prices of products do not exist, or can be difficult to
obtain. In addition, the concepts of future income and costs are of great importance. The
idea is that only expected future revenues and costs are taken into consideration when the
decisions are made on whether a joint product or main product should be processed
further or sold at the split-off point. Horngren et al. (2006) emphasized that joint costs
incurred up to the split-off point are irrelevant, because these costs would have been
incurred whether the product is sold at the split-off point or processed further. Joint costs
up to the split-off point are frequently not available (these are not only raw material costs
and labor costs, but include a range of costs such as depreciations, house rent and
administration). This is one of the reasons why Horngren et al. (2006) suggested that
further processing should depend on product revenue attainable beyond the split-off
point.
Joint cost allocation in the sawmilling industry
In Tunes et al. (2006), methods for joint cost allocation in use by the Norwegian
sawmilling industry were surveyed. No clear methods of joint cost allocation were found,
but the study showed that several methods for product calculation were in use. One of the
interviewed sawmills used an approximation to the physical measurement method to
allocate costs, i.e., the total costs of by-products (chips and sawdust) were allocated to the
main products. Product costing for sawdust and chips was not made; instead by-products'
joint costs were allocated to the main products. The total cost of chips and sawdust was
apportioned equally to center boards and side boards. The result is that center boards and
side boards will have an additional cost on top of their calculated product cost. Other
techniques such as cost per timber class and sawing pattern were used. This method
provides a total cost for the yield of products derived from a fixed sawing pattern for a
specific timber class in a time period. Obviously, none of these methods allocate costs to
products.
In 2004, Johansson published a linear programming (LP) model that calculated marginal
costs of center boards. The model is based on the work of Billera et al. (1981). It can be
extended in order to also include marginal cost estimates for side boards and by-products.
Other industries too use LP models for solving their production planning problems. A
refinery faces the same challenge as other industries in dealing with a great proportion of
joint costs, and in Nyiramucyo and Sahabanik (2006), a description of the LP model in
use at a Norwegian oil refinery was presented. This LP model is used to calculate the
amounts of raw oil qualities that need to be purchased from different geographical
locations in order to ensure that stocks are appropriate.
Scenario I: Base scenario
The four joint cost allocation methods presented by Horngren et al. (2006) can be
explained using examples from the sawmilling industry.
A sawmill purchases sawlogs for 450 NOK/[m.sup.3]. (1) The sawlogs are used to
produce center boards, side boards, chips and sawdust. The yield and sales value of each
product is presented in Table 1. The lumber volume dimensions are represented in dry,
rough condition, and the yield percentages are fractions of the total roundwood "green"
solid wood equivalent (physical volume). Hence there will be a certain amount of
shrinkage. This is the usual practice to express the yield in Norwegian sawmills, and we
have therefore used this method.
Dealing with shrinkage this way means that shrinkage is treated as a component of yield
or a pseudo-product. Since the volume of center boards and side boards are measured in
dry conditions, and chips in green condition, calculating the transforming of low grade
lumber to chips, or the opposite, is not straightforward. When calculating marginal
changes, however, as shown in Tables 6, 7, 8, and 9, the shrinkage issue can be ignored.
An alternate convention would be to report the fractional yield of all products in green
(full swollen) condition and adjust the dry, rough price for the boards to reflect an
equivalent green, rough price. Doing this, the shrinkage issue falls out.
Example 1: The physical measurement method.--Results using the physical measurement
method are presented in Table 2. Using this method resulted in high gross margin for
center boards and a negative gross margin for all the byproducts.
Example 2: The sales value method.--Results using the sales value method are presented
in Table 3. When using the sales value method, none of the product groups have a
negative gross margin. The gross margin for center boards has decreased, while the gross
margin for the other product groups has increased, except for side boards.
Example 3: The net realizable value (NRV) method.--As seen from Table 4, center
boards' gross margin is further reduced, but the gross margin of side boards has increased
when using the NRV method. The other product groups have about the same gross
margin.
Example 4: The constant gross margin percentage NR V method.--When it comes to the
constant gross margin percentage NRV method, an overall gross margin for all joint
products must be computed (cf. estimation below). An example of how joint costs are
allocated can then be presented using the fourth method of Horngren et al. (2006).
There is a fundamental difference between the four methods presented above, and Gatti
and Grinnell (2000) argue that in practice, there are two approaches to joint cost
allocation. The physical measurement method allocates joint costs in proportion to some
measure of the physical quantities of products, while the three other methods rely on
some measure of market value to make the allocation of joint costs. When using the
physical measurement method, shrinkage, which can be considered a non-existent
product or a pseudo-product, will be charged a part of the joint costs. If one of the other
methods is used, shrinkage will not be given any amount of the joint costs because a
market value for shrinkage is of course not available. Another result when using the
physical measurement method is that some of the products are apparently produced with
negative net income. When using the other methods, all (excluding shrinkage) are
produced with a positive net income
Based on the amount of joint cost allocated to each product group, decisions regarding
which product to produce can be made. The mill would seek to produce as much center
boards as possible, compared to any other product, regardless of joint cost accounting
method. Consequently, joint cost allocation will never affect the amount of center boards
produced; it is profitable to produce as many center boards as possible. Of course the
different qualities of center boards produced have to be planned to fit customers' needs
and stocks. However, joint cost allocation is highly important in cases of equal income of
products. A price increase for chips is likely in the present situation in the bioenergy
market, and hypothetically the market price of chips could equal the price of low value
side boards. Consequently, different joint cost allocation methods will influence decisions
concerning which product to produce.
Using the physical measurement method or the sales value method obviously affects the
gross margin for a single product, but the overall gross margin is the same for both
methods.
Scenario 2: Improved production efficiency and product quality
Due to the high amount of sawlogs processed at a sawmill, a slight increase in the yield
of high quality sawn products (center boards and side boards) will contribute
substantially to a sawmill's profitability. In the following, examples of quality
improvements are given. The yield of side boards was increased from 13 percent to 14
percent and the yield of chips was decreased from 32 percent to 31 percent, all other
conditions remaining the same. As expected and shown in Tables 6, 7, 8, and 9, the
overall gross margin will increase when using the physical measurement method, the
sales value method, the NRV method and the constant gross margin NRV method. One
notable observation is that, when it comes to the physical measurement method and due
to the negative gross margin of chips, a yield decrease in chips will result in an improved
overall gross margin due to a less negative gross margin for chips (Table 6 compared to
Table 2).
As seen in Table 6, gross margin of the profitable side boards increase whereas it
decreases for chips. This is due to the yield increase for sideboards and yield decrease for
chips.
In Table 7 the same pattern as in Table 3 is revealed; all products (except from shrinkage)
receive a positive gross margin. Compared to the base scenario, both side boards' and
center boards' gross margins have increased and chips' gross margin has decreased.
In Table 8 the gross margin for center boards decreases compared to the sales value
method, and as in the base scenario the use of the NRV method results in a considerable
increase of sideboards' gross margin.
When it comes to the constant gross margin NRV method under the quality improvement
scenario, a new overall gross margin percentage has to be calculated due to changes in
the sales value for all products (cf. estimation below). The total joint cost and separable
cost will still be the same.
As expected, in Table 9 the gross margin of center boards and side boards has increased
due to quality improvements, compared to Table 5 (base scenario).
The consequence when using the sales value based approaches (the sales value method,
the NRV method and the constant gross margin NRV method) and due to the yield
increase of side boards (the quality improvement scenario), is that a smaller amount of
the timber costs will be charged center boards. In other words, the yield of center boards
is the same and they have the same sales value, but due to the distribution formula their
share of the costs will be lower. Consequently, the gross margin for center boards will
increase. However, the overall gross margin is the same for all four methods.
Discussion
Johansson (2004) argued that marginal cost estimates are useful only for center products,
i.e., for products sold to regular customers at negotiated prices and often further
processed. In addition to allocating joint costs to the main products, which is fundamental
for main product calculation, it is also important to allocate costs to by-products. Due to
technological changes and increased demand for low value products for energy or
innovative products, such as wood fiber composites, it is likely that the sawmilling
industry will start applying joint cost allocation. There are examples of other by-products
that have influenced sawmills' revenues considerably. For example the bark market,
where traditionally most of the bark has been used for heating and for drying
semifinished products. In the last years, the market for bark for garden and sanitary
purposes has increased rapidly, and most sawmills have to decide, based on economic
calculations, whether they are better off selling bark to bark retailers or using it internally
for heating and drying. In Norway it is the sawlog volume under bark which is paid for,
and most sawmills therefore consider bark a "free product." An alternate treatment would
be to partition out the bark values per unit of raw material input, and to treat raw material
costs to a "wood-only" cost basis.
The recent increase in demand for chips and sawdust due to high energy prices influences
profitability in sawmilling. The present situation resembles the situation in the oil
industry in 1973/74 when a shortage of crude oil made by-products highly profitable.
Consequently, the oil industry had to invent new costing systems to allocate joint costs in
a more appropriate way. The situation in the oil refining industry in 1973 resulted in
reconsiderations of the joint cost allocation methods in use in the oil industry (Feller
1977), and sawmills facing the same situation today should also evaluate methods for
better joint cost allocation. The value of by-products increases and the producers have to
calculate when it is profitable to produce chips instead of side boards. When the demand
for chips for bioenergy increases, the sawmills will have to consider to whom they should
sell the chips in order to get the highest net revenue. Unlike bark, chips have to bear their
share of the joint costs and the preferred joint cost allocation method will therefore
influence calculations on chips' profitability. The sawmill will then have to decide
whether chips or side boards should be produced.
Previous research indicates that the North European forest products market is integrated
and products, such as coniferous sawnwood, are traded in international markets (cf.
Hanninen 1998, Thorsen 1998, Stordal and Nyrud 2003). Wood products markets are in
general not subject to trade barriers and the main constraint to trade is simply the cost of
transportation. The result is an increased focus on production and cost efficiency. The
sawmilling industry is a mature industry, and, for most sawmills, an increase in
production efficiency will have to be made incrementally by making small improvements
throughout the production facility. For example through using better sawing equipment to
reduce the saw kerfs, i.e., the amount of sawdust is reduced, which leads to an increased
amount of all the higher value products (chips, side boards and center boards).
In recent years, scanning equipment for measuring the sawlogs has improved. The aim is
to get a three-dimensional picture of the sawlog so that the highest possible yield can be
achieved when processing it. Many aspects have to be considered, and use of 3-D
technology has made it possible to take many variables (taper, crooks, exact diameter
etc.) into account. In the end a complete picture of the shape &the sawlog is provided.
These calculations lead to reduced overcut size and increased utilization of the sawlog,
and in turn increased yield of the highest value sawnwood products.
Gatti and Grinnell (2000) focused on the causal relationship between cost associated with
higher quality input factors and increased value of the output. The sawmilling industry is
clearly affected by this causal relationship. To obtain an increased yield of high quality
sawn products, the sawmilling industry has to use more effective production equipment
(for example 3-D scanning), buy high quality raw material, use highly skilled labor etc.
All these elements lead to increased costs and in turn increased revenues. The base and
quality improvement scenarios in this article illustrate the effect of increasing the amount
of high value products.
The software optimization programs available for the sawmilling industry have improved
simultaneously with the development of 3-D scanning. It is in fact possible for the
sawmills to calculate an optimal primary breakdown based on (1) the sales value of final
products, (2) a physical optimization, or (3) a combination of both methods. In addition,
it is possible to add costs, for example joint costs, direct costs and overhead costs. Thus,
the choice of joint cost allocation method will have considerable influence on which
products the sawmills decide to produce. The result is that a net profit optimization for
each product produced can be made. This way of thinking can be considered a product
optimization method. The challenge is to make good cost estimates, i.e., using
appropriate joint cost, overhead cost and allocation methods. However, the sawmills
interviewed by Tunes et al. (2006) that had the possibility to add costs to their
optimization procedures did not utilize the opportunities which lie in the software when it
comes to addition of cost estimates to products or product groups.
Conclusions
In addition to influencing product profitability, joint costs also affect other parts of a
company's product costing, for example transfer pricing decisions and inventory
valuation. In the case of production of semifinished products sold internally, it is
important to determine the transfer prices of products, because one unit's income is
another unit's costs. For example, costs allocated to products will make up the income for
the sawing part of the sawmill, while they are the purchasing costs for the planing part of
the sawmill. There are three basic methods to determine transfer prices: cost based,
market based and negotiated transfer prices. When using cost based transfer pricing, the
share of joint costs allocated to a product is determined by the joint cost allocation
method used, and is crucial in determination of a product's net profit. Further, transfer
pricing is vital in determination of a production unit's profitability, both production units
that are placed at the same site and production units located at different geographical
locations. In any case, cost allocation has to be included in profit analyses to reveal the
places or parts of the production which are profitable
Inventory valuation is another area influenced by transfer pricing decisions. For example,
in insurance related questions, it is of great importance to estimate the value of
inventories as correctly as possible. In the case of cost based inventory valuation, the
insurance premium will be affected by the method used to allocate costs. In a fire
situation for example, the loss covered by the insurance company will depend on the cost
allocation method used if the insurance company makes use of a cost based insurance
premium. Due to variation in weather conditions and building activity during the year, a
sawmill is forced to have a high amount of timber in stock during the summer period.
Also, the amount of sawnwood in stock will vary during the year due to fluctuations in
building activity. Consequently, a lot of sawnwood can be damaged and the selected joint
cost allocation method will have a considerable influence on the insurance premium. The
most important side of inventory valuation is still the requirements for the financial
accounts. Norwegian sawmills are obliged (by law) to present ordinary financial
accounts, including inventory valuation, but in the Norwegian sawmilling industry there
are fundamental differences in the accounting systems used for financial reports and
management accounting systems used for product costing and transfer pricing decisions.
Data from financial accounts are used to a certain degree in management accounts, and
improved management accounts could also contribute to financial accounts reports. In
any case, cost allocation in general and joint cost allocation in particular is unalterable in
financial and management accounting.