Managerial accounting ii

Edited by: I C C

Outline of Managerial Accounting II

PART 3
USING ACCOUNTING INFORMATION IN MAKING DECISIONS
Chapter 14. Decision Making: Relevant Costs and Benefits
Chapter 15. Cost Analysis and Pricing Decisions
Chapter 16 Capital Expenditure Decisions: Introduction.
Chapter 17. Further Aspects of Capital Expenditure Decisions.

Part 4
SELECTED TOPICS FOR FURTHER STUDY

Chapter 18. Cost Allocation: A Closer Look
Chapter 19. Analyzing Financial Statements
Chapter 20. Preparing The Statement of Cash Flows

Chapter 14 Decision Making: Relevant Costs & Benefits Edited by: I C C

CHAPTER 14
Decision Making: Relevant Costs and Benefits

After completing this chapter, you should be able to:

• Describe six steps in the decision-making process and the managerial
accountant’s role in that process.
• List and explain two criteria that must be satisfied by relevant
information.
• Identify relevant costs and benefits, giving proper treatment to sunk
cost, opportunity costs, and unit costs.
• Prepare analyses of various special decisions, properly identifying the
relevant costs and benefits.

Decision making is a fundamental part of management. Decisions about the
acquisition of equipment, mix of products, methods of production, and pricing
of products and services confront managers in all types of organizations. This
chapter covers the role of managerial accounting information in a variety of
common decisions,

The Managerial Accountant’s Role in Decision Making

The managerial accountant’s role in the decision-making process is to provide
relevant information to the managers who make the decisions. Production
managers typically make the decisions about alternative production processes
and schedules, marketing managers make pricing decisions, and specialists in
finance usually are involved in decisions about major acquisitions of
equipment. Al of these managers require information pertinent to their
decisions. The managerial accountant’s role is to provide information relevant
to the decisions faced by managers throughout the organization. Thus, the
managerial accountant needs a good understanding of the decisions faced by
those managers.

Prepared by: Prof. Shirdon, Edited & Printed by: SAHAL Stationery 4455061/9255353 Page 2


Managerial

Accountant

Designs and implements Managers who make
accounting information production, marketing,
system and finance decisions

Make substantive
economic decisions
affecting operations

Steps in the Decision-Making Process
Six steps characterize the decision-making process:
1. Clarify the decision problem. Sometimes the decision to be made is
clear. For example, if a company receives a special order for its product
at a price below the usual price, the decision problem is to accept or
reject the order. But the decision is seldom so clear and unambiguous.
Perhaps demand for a company’s most popular product is declining.
What exactly is causing this problem? Increasing competition? Declining
quality control? A new alternative product on the market? Before a
decision can be made, the problem needs to be clarified and defined in
more specific terms. Considerable managerial skill is required to define a
decision problem in terms that can be addressed effectively.
2. Specify the criterion. Once a decision problem has been clarified, the
manager should specify the criterion upon which a decision will be made.
Is the objective to maximize profit, increase market share, minimize cost,
or improve public service? Sometimes the objectives are in conflict, as in
a decision problem where production cost is to be minimized but
product quality must be maintained. In such cases, one objective is
specified as the decision criterion- for example cost minimization. The
other objective is established as a constraint- for example, product
quality must not fall below standard.



3. Identify the alternatives. If a machine breaks down, what are the
alternative courses of action? The machine can be repaired or replaced,
or a replacement can be leased. But perhaps repair will turn out to be
more costly than replacement. Determining the possible alternative is a
critical step in the decision process.

4. Develop a decision model. A decision model is a simplified
representation of the choice problem. Unnecessary details are stripped
away, and the most important elements of the problem are highlighted.
Thus, the decision model brings together the elements listed above the
criterion, the constraints, and the alternatives.
5. Collect the data. Although the managerial accountant often is involved
in step 1 through 4, he is chiefly responsible for step 5. Selecting data
pertinent to decisions is one of the managerial accountant’s most
important roles in an organization.
6. Select an alternative. Once the decision model is formulated and the
pertinent data are collected, the appropriate manager makes a decision.

Obtaining Information: Relevance. Accuracy. And Timeline

What criterion should the managerial accountant use in designing the
accounting information system that supplies data for decision making?
Three characteristics of information determine its usefulness.

Relevance Information is relevant if it is pertinent to a decision
problem. Different decisions typically will require different data. The
primary theme of this chapter is how to decide what information is
relevant to various common decision problems.

Accuracy Information that is pertinent to a decision problem must also
be accurate, or it will be 0f little use. This means the information must
be precise. Conversely, highly accurate but irrelevant data are of no
valve to a decision maker.

Timeliness Relevant and accurate data are of valve only if they are
timely, that is, available in time for a decision. Thus, timeliness is the
third important criterion for determining the usefulness of information

To summarize, the managerial accountant’s primary role in the decision-
making process is twofold:

1. Decide what information is relevant to each decision problem.
2. Provide accurate and timely data, keeping in mind the proper
balance between these often conflicting criteria.



Relevant Information
What makes information relevant to a decision problem? Four considerations
are important.

Bearing .on the future: The consequences of decisions are borne in the future,
not in the past. To be relevant to a decision, cost or benefit information must
involve a future event.

Different under Competing Alternative: Relevant information must involve
costs or benefits that differ among the alternative. Costs or benefits that are
the same across all the available alternatives have no bearing on a decision.

Need for Predictions: Since relevant information involves future events, the
managerial accountant must predict the amounts of the relevant costs and
benefits. In making these predictions, the accountant often will use estimates
of cost behavior based on historical data. There is an important and subtle
issue here. Relevant information must involve costs and benefits to be realized
in the future. However, the accountant’s predictions of these of these costs
benefits often are based on data from the past.

Unique versus Repetitive Decision: Unique decisions arise infrequently, or
rely once. Compiling data for unique decisions usually requires a special
analysis by the managerial accountant. The relevant information often will be
found in many diverse places in the organization’s overall information system.

In contrast, repetitive decisions are made over and over again, at either
regular or irregular intervals.

Importance of identifying Relevant Costs and Benefits
Why is it important for the managerial accountant to isolate the relevant costs
and benefit in a decision analysis? The reasons are twofold. First, generating
information is a costly process. The relevant data must be sought, and this
requires time and effort. By focusing on only the relevant information, the
managerial accountant can simplify and shorten the data gathering process.

Second, people can effectively use only a limited amount of information.
Beyond this they experience information overload, and their decision-making
effectiveness declines.



IDENTIFYING RELEVANT COSTS AND BENEFITS
To illustrate how managerial accountants determine relevant costs and
benefits, we will consider several decisions faced by management of Worldwide
Airways. The airlines flies routes between the United States and Europe,
between various cities in Europe, and between the United States and several
Asian cities.

Sunk Costs
Sunk costs are costs that already have been incurred. They do not affect any
future cost and cannot be changed by any current or future action. Sunk costs
are irrelevant in decisions, as the following two examples show.

Book value of Equipment: At Paris Airport, Worldwide Airways has three-
year-old loader truck used to load in-flight meals onto airplanes. The box on
the truck can be lifted hydraulically to the level of a jumbo jet’s side doors. The
book value of this loader, defines as the asset’s acquisition cost less the
accumulated depreciation to date, is computed as follows:
Acquisition cost of older loader…………………..………….… $100,000
Less: Accumulated depreciation……………………..……...……$ 75,000
Book Value………………………………………………………$ 25,000

The loader has one year of useful life remaining, after which its salvage value
will be zero. However, it could be sold now for $5,000. In addition to the
annual depreciation of $5,000, Worldwide Airways annually incurs $80,000 in
variable costs to operate the loader. These include the costs of operator labor,
gasoline, and maintenances. A

The Airway’s ramp manager at Paris Airport faces a decision about replacement
of the loader. A new kind of loader uses a conveyor belt to move meals into an
airplane. The new loader is much cheaper than the old hydraulic loader and
costs less to operate. However, the new loader would be operable for only year
before it would need to be replaced. Pertinent data about the new loader are as
follows:
Acquisition cost of new loader………………………..… $15,000

Useful life…………………………………………….…… 1 year
Salvage value after one year……………………………….. 0
Annual depreciation………………………………..……… $15,000
Annual operating costs……………………………...………$45,000



The manager’s initial inclination is to continue using the old loader for another
year. He exclaims, “We can’t dump that equipment now. We paid $100,000 for
it, and we’ve only used it three years. If we get rid of that loader now, we’ll lose
$20,000, less its current salvage value of $5,000, amounts to a loss of $20.000.

Fortunately, the manager’s comment is overheard by the managerial
accountant in the company’s Airport. He points out to the ramp manager that
the book value of the old loader is a sunk cost. It cannot affect any future cost
the company might incur. To convince the ramp manager that the accountant
is right, he prepares the analysis shown below:

EXHIBIT 14-2 Equipment Replacement Decision: Worldwide Airways
Cost of Two Alternatives
(a) (b) (c)
Do not
Replace Replace
Old Old Differential
Loaders Loaders Costs
(1) Depreciation of old loader …………………………. $25,000
Sunk OR -0-
Cost
(2) Write-off of old loader’s book value …………… $25,000
(3) Proceeds from disposal of old loader …………. -0- (5,000) $5,000
Relevant (4) Depreciation (cost) of new loader ………………. -0- 15,000 (15,000)
data
(5) Operating costs ………………………………………….. 80,000 45,000 35,000
Total ………………………………………………………….. $105,000 $80,000 $25,000

Regardless, of which alternative is selected, the $25,000 book value of the old
loader will be an expense or loss in the next year. If the old loader is kept in
service, the $25,000 will be recognized as depreciation expense; otherwise, the
$25,000 cost will be incurred by the company as a write-off of the asset’s book
value. Thus, the current book value of the old loader is a sunk cost and
irrelevant to the replacement decision.

Notice that the relevant data in the equipment replacement decision are
items (3), (4), and (5). Each of these items meets the two tests of relevant
information:

1. The costs or benefits relate to the future
2. The costs or benefits differ between the alternatives

The proceeds from selling the old loader, item (1), will be received in the future
only under the “replace” alternative. Similarly, the acquisition cost
(depreciation) of the new loader, item (4) is a future cost incurred only under



the “replace” alternative. The operating cost, item (5), is also a future cost that
differs between the two alternatives.

Differential Costs: is shown in the above table by the column entitled
Differential Cost. This column shows the difference for each item between the
costs incurred under the two alternatives. The computation of differential
costs is a convenient way of summarizing the relative advantage of one
alternative over the other.

Irrelevant Future Costs and Benefits
At the headquarter, the manager of flight schedule, is in the midst of making a
decision about Atlanta to Honolulu route. The flight is currently nonstop, but,
he is considering a stop in San Francisco. He feels that the route would attract
additional passengers if the stop is made, there would also be additional
variable costs. His analysis is shown in the next table.

EXHIBIT 14-4 Flight Route Decision: Worldwide Airways
Revenue and Costs
under Two Alternatives
(a) (b) (c)

Relevant or With Stop
Irrelevant Nonstop in San Differential
Route* Franciscso* Amount+
Relevant (1) Passenger revenue …………………………… $240,000 $258,000 $(18,000)
Irrelevant (2) Cargo revenue ……………………………………. 80,000 80,000 -0-
Relevant (3) Landing Fee in San Francisco ………………. -0- (5,000) 5,000
Relevant (4) Use of airport gate facilities ………………… -0- (3,000) 3,000
Relevant (5) Flight crew cost …………………………………… (2,000) (2,500) 5,00
Relevant (6) Fuel ……………………………………………………… (21,000) (24,000) 3,000
Relevant (7) Meals and services …………………………….. (4,000) (4,600) 600
Irrelevant (8) Aircraft maintenance …………………………. (1,000) (1,000) -0-
Total revenue less costs ……………………. $292,000 $297,900 $5,900
*In columns (a) and (b) parentheses denote costs and numbers without parentheses are revenues.
+
In Column (c) parentheses denote differential items favoring option (b).

The analysis indicates that the preferable alternative is the route that includes
a stop in San Francisco. Notice that the cargo revenue (item 2) and the
aircraft- maintenance cost (item 8) are irrelevant to the flight-route decision.
Although these data do affect future cash flows, they do not differ between the
two alternatives. All of the other data differ between the two alternatives.



Opportunity Costs
Another decision confronting the manager of flight schedule is whether to add
two daily round-trip flights between Atlanta and Montreal. His initial analysis
of the relevant costs and benefits indicates that additional revenue from the
flights will exceed their costs by $30,000 per month. Hence, he is ready to add
the flights to the schedule. However, the Airways hanger manager in Atlanta,
points out that the flight manager has overlooked an important consideration.

The Airways currently has excess space in its hanger. A commuter airline has
offered to rent the hangar space for $40,000 per month. However, if the
Atlanta-to-Montreal flights are added to the schedule, the additional aircraft
needed in Atlanta will require the excess hangar space.

If worldwide Airways adds the Atlanta- to-Montreal flights, it will forgo the
opportunity to rent the excess hangar space for $40,000 per month. Thus, the
$40,000 in rent forgone is an opportunity cost of the alternative to add the new
flights. An opportunity cost is the potential benefit given up when the choice
of one action precludes a different action. The importance of opportunity costs,
they are just as relevant as out-of-pocket costs in evaluating decision
alternatives. In the Worldwide Airways case, the best action is to rent the
excess warehouse space to the commuter airline, rather than adding the new
flights. The analysis that supports this conclusion is shown below:

EXHIBIT 14-5 Decision to Add Flights: Worldwide Airways
(a) (b) (c)
Do Not
Add Add Differential
Flights Flights Amount
Additional revenue
from new flights
Less additional costs ………………………………………………… $30,000 -0- $30,000
Rental of excess
hanger space …………………………………………………………….. -0- $40,000 (40,000)
Total …………………………………………………………………………… $30,000 $40,000 $(10,000)
It is a common mistake for people to overlook or underweight opportunity
costs. The $40,000 hangar rental, which will be forgone if the new flights are
added, is an opportunity cost of the option to add the flights. It is a relevant
cost of the decision, and it is just as important as any out-of-pocket
expenditure.

Summary
Relevant costs and benefits satisfy the following two criteria:
1. They affect the future
2. They differ between alternatives.


Chapter 15 Cost Analysis & Pricing Decision Edited by: I C C

CHAPTER 15
COST ANALYSIS AND PRICING DECISIONS

AFTER COMPLETING THIS CHAPTER, YOU SHOULD BE ABLE TO:

• List and describe the four major influences on pricing decision.
• Explain and use the economic, profiting-maximizing price model.
• Set prices using cost-plus pricing formula.
• Determine prices using the time and material pricing approach.
• Set prices in special-order or competitive situations by analyzing the
relevant.

Setting the price for an organization’s product or services is one of the most
important decisions a manager faces. It is also one of the most difficult, due to
the number and variety of factors that must be considered. The pricing
decisions arises in virtually all types of organizations. Manufacturers set
prices for their goods they manufacture; merchandising companies set prices
for their goods; service firms set prices for such services as insurances policies,
train tickets, park admissions, and bank loans. Non-profit organizations often
set prices. For example, government units price vehicle registration, park-use
fees and utility services. Public utilities and TV cable companies face political
considerations in pricing their products and services, since their prices often
must be approved by a governmental commission.

In this chapter, we will study pricing decisions, with the emphasis on the role
of managerial accounting information. The setting for our discussion is Sydney
Sailing Supplies (SSS), a manufacturer of sailing supplies and equipment
located in Sydney, Australia.

MAJOR INFLUECES ON PRICING DECISIONS

Four major influences govern the prices set by Sydney Sailing Supplies:

1. Customer demand
2. Actions of competitors
3. Costs
4. Political, legal, and image related issues.



Customer Demand
The demands of customers are paramount importance in all phases of
business operations, from the design of a product to the setting of its price.
Product-design issues and pricing considerations are interrelated, so they must
be examined simultaneously. For example, if customers want a high-quality
sailboat, this will entail greater production time and more expensive raw
material. The result almost certainly will be a higher price. On the other hand,
management must be careful not to price its products out of the market.
Discerning customer demand is a critically important and continuous process.
Companies routinely obtain information from market research, such as
customer surveys and test-marketing campaign, and through feedback from
sales personnel. To be successful, SSS must provide the products its
customers want at a price they perceive to be appropriate.

Actions of competitors
Although Sydney Sailing Supplies’ managers would like the company to have
the sailing market to itself they are not so fortunate. Domestic and foreign
competitors are striving to sell their products to the same customers. Thus, as
SSS management designs products and sets prices, it must keep a watchful
eye on the firm’ competitors. If a competitor reduces its price on sales of a
particular type, SSS may have to follow suit to avoid losing its market share.
Yet the company cannot follow its competitors blindly either. Predicting
competitive reactions to its product-design pricing strategy is a difficult but
important task for Sydney Sailing Supplies management.

Costs
The role of costs in price setting varies widely among industries. In some
industries, prices are determined almost entirely by market forces. An example
is the agricultural industries, where grain and meat prices are market-driven.
Farmers must meet the market price. To make a profit, they must produce at a
cost below the market price. This is not always possible, so some periods of
loss inevitable result. In other industries, managers set prices at least partially
on the basis of production costs. For example, cost-based pricing is used in
the automobile, household appliance, and gasoline industries. Pricing are set
by adding a markup to production costs. Managers have some latitude in
determining the markup, so market forces influence prices as well. In public
utilities, such as electricity and natural gas companies, prices generally are set
by a regulatory agency of the state government. Production costs are of prime
importance in justifying utilities rates. Typically, a public utility will make a
request to the public. Utility Commission for a rate increase on the basis of its
current and projected production costs.



Balance of market Forces and Cost-Based Pricing: In most industries, both
market forces and cost considerations heavily influence prices. No
organization or industry can price its products below their production costs
indefinitely. And no company’s management can set prices blindly at cost plus
a markup with-out keeping an eye on the market. In most cases, pricing can
be viewed in either of the following ways,

How Are Prices Set?

Prices are determined Prices are based
on costs, subject to
by the market, subject Market
to the constraint that Costs the constraint that
forces the reaction of
costs must be covered
in the long run. customers and
competitors must
be heeded.

Political, Legal, and Image-Related Issues
Beyond the important effects on prices of market forces and costs are a range
of environmental consideration. In the legal area, managers must adhere to
certain laws. The law generally prohibits companies from discriminating
among their customers in setting prices. Also prohibited is collusion in price
setting, where the major firms in an industry all agree to set their prices at
high levels.

Political considerations also can be relevant. For example, if the firms in an
industry are perceived by public as reaping unfairly large profits, there may be
political pressure on legislators to tax those profits differentially or intervene in
some way to regulate the prices.

ECONOMIC PROFIT-MAXIMIZING PRICING
Companies are sometimes price takers, which mean their products’ prices are
determined totally by the market. Some agricultural commodities and precious
metals are examples of such products. In most cases, however, firms have



some flexibility in setting prices. Generally speaking, as the price of a product
or service is increased, the quantity demanded declines and vice versa.

Total Revenue, Demand, and marginal Revenue Curves
The trade-off between a higher price and a higher sales quantity can be shown
in the shape of the firm’s total revenue curve, which graphs the functional
relationship between total sales revenue and quantity sold. SSS total revenue
curve for its two-person sailboat, the Wave Dater, is displayed as Fig (A) shown
below. The total revenue curve increases throughout its range, but the rate of
increase declines as monthly sales quantity increase. To see this, notice that
the increase in total revenue when the sales quantity increases from zero to a
units is greater than the increase in total revenue when the sales quantity
increases from a units to b units.
Closely related to the total revenue curve are two other curve, which are
graphed in panel (B). The demand curve shows the relationship between the
sales price and the quantity of units demanded. The demand curve decreases
throughout its range, because any decrease in the sale price brings about an
increase in the monthly sales quantity. The demand curve is also called the
average revenue curve, since it shows the average price at which any
particular quantity can be sold.



Total Revenue, Demand, and Marginal Revenue Curve
EXHIBIT 15-1 Total Revenue, Demand, and Marginal Revenue Curves

Dollars Total revenue

Curve is increasing throughout
its range, but at a declining
rate

Quantity sold
0 a b per month

(A) Total revenue curve
Dollars per unit

Demand (or average revenue)

Marginal
revenue

Quantity sold
per month
(B) Demand (or average revenue) curve and marginal revenue curve



EXHIBIT 15-1 (CONTINUED) Total Revenue, Demand, and Marginal Revenue Curve

Quantity
Sold
Per Unit Total Revenue Changes in
Month Sales Price per Month Total Revenue
10 ………… $1,000 …………… $10,000
………… $9,500
20 …………. 975 …………… 19,500
………… 9,000
30 …………. 950 …………… 28,500
………… 8,500
40 …………. 925 ………….. 37,000
………… 8,000
50 …………. 900 …………… 45,000
………… 7,500
60 …………. 875 …………… 52,500

Related to Related to Related to
demand total revenue marginal revenue
curve curve curve
(C) Totaled price, quantity, and revenue data

The marginal revenue curve shows the change in total revenue that
accompanies a change in the quantity sold. The marginal revenue curve is
decreasing throughout its range to show that total revenue increases at a
declining rate as monthly sales quantity increases.

A tabular presentation of the price, quality, revenue data for SSS is displayed
in panel (C). Study this table carefully to see how the data relate to the graphs
shown in panel A and B of the exhibit. No matter what approach a manager
take to the pricing decision, a good understanding of the relationship will lead
to better decisions. Before we can fully use the revenue data, however, we
must examine the cost side of SSS business

Total Cost and Marginal Cost Curve
Understanding cost behavior is important in many business decisions, and
pricing is no exception. How does total cost behave as the number of boats
produced and sold by SSS changes? Panel (A) of displays the firm’s total cost
curve, which graphs the relationship between total cost and the quantity
produced and sold each month.



Total cost increases throughout its range. The rate of increase in total cost
declines as quantity increases from zero to c units. To verify this, notice that
the increase in total costs when quantity increases from zero to a units is
greater than the increase in total costs when quantity increases from a units to
b units.

The rate of increase in total costs increases as quantity increases from c units
upward. To verify this, notice that the increase in total costs as quantity
increases from c units to d units is less than the increase in total costs as
quantity increases from d units to c units.

Closely, related to the total cost curve is the marginal cost curve, which is
graphed in panel (B). the marginal cost curve shows the change in total cost
that accompanies a change in quantity produced and sold. Marginal cost
declines as quantity increases from zero to c units; then it increases as
quantity increases beyond c units.

Price Elasticity
The impact of price changes on sales volume is called price elasticity.
Demand is elastic if a price increase has a large negative impact on sales
volume, and vice versa. Demand is inelastic if price changes have little or no
impact on sales quantity. Cross-elasticity refers to the extent to which a
change in a product’s price affects the demand for other substitute products.
For example, if SSS raises the price of its two-person sailboat, there may be an
increase in demand for substitute recreational craft, such as small powerboats,
canoes, or windsurfers.

Measuring price elasticity and cross-elasticity is an important objective of
market research. Having a good understanding of these economic concepts
helps managers to determine the profit-maximizing price.

ROLE OF ACCOUNTING PRODUCT COSTS IN PRICING
Most managers base prices on accounting product costs, at least to some
extent. There are several reasons for this. First, most companies sell
many products or services. There simply is not time enough to do a
thorough demand and managerial-cost analysis for every product or
service. Managers must rely on a quick and straight forward method for
setting prices, and cost-based pricing formulas provide it. Second, even
though market considerations ultimately may determine the final
product price, a cost-based pricing formula gives the manager a place to
start. Finally, and most importantly, the cost of a product or service
provides a floor below which the price cannot be set in the long run



Cost-Plus Pricing

Price = cost + (markup percentage × cost)
Cost-based pricing formulas typically have the follow general form.

Such a pricing approach often is called cost-plus pricing, because the price is
equal to cost plus a markup. Depending on how cost is defined, the markup
percentage may differ. Several different definitions of cost, each combined with
a different markup percentage, can result in the same price for a product or a
service.

The following table illustrates how SSS management could use several different
cost-plus pricing formulas and arrive at a price of $925 for the Wave Darter.
Cost-plus formula (1) is based on variable manufacturing cost. Formula (2) is
based on absorption (or full) manufacturing cost, which includes an allocated
portion of fixed cost manufacturing costs. Formula (3) is based on all costs;
both variable and fixed costs of the manufacturing, selling, and administrative
functions. Formula (4) is based on all variable costs, including variable
manufacturing, selling, and administrative costs. Notice that all four pricing
formulas are based on a linear representation of the cost function, in which all
costs are categorized as fixed or variable.


Chapter 16 Capital Expenditure Decisions: Introduction Edited by: I C C

CHAPTER 16
Capital Expenditure Decisions: An Introduction

AFTER COMPLETING THIS CHAPTER, YOU SHOULD BE ABLE TO:

• Explain the importance of the time value of money in capital-budgeting
decisions.
• Compute the future value and present value of cash flows occurring over
several time periods.
• Use the net-present value method and internal-rate-of-return method to
evaluate an investment proposal.
• Compare the net-present value and internal-rate-of-return method, and
state the assumptions underlying each method.

Managers in all organizations periodically face major decisions that involve
cash flows over several years. Decisions involving the acquisition of machinery,
vehicles, buildings, or land are examples of such decisions.

Decisions involving cash inflows and outflows beyond the current year
are called capital-budgeting decision. Managers encounter two types of
capital-budgeting decisions.

Acceptance-or-Rejection Decisions: These decisions occur when managers
must decide whether or not they should undertake a particular capital
investment project. In such a decision, the required funds are available or
readily obtainable, and management must decide whether the project is
worthwhile. For example, the controller for the city Mountainview is faced with
a decision as to whether to replace one of the city’s oldest street-cleaning
machines. The funds are available in the city’s capital budget. The question is
whether the cost savings with the new machine will justify the expenditure.
The analysis of acceptance-or-rejection decisions is the focus of this chapter.

Capital-Rationing Decisions: in these decisions, managers must decide
which of several worthwhile projects makes the best use of limited investment
funds.



CONCEPT OF PRESENT VALVE
Before we can study the capital-budgeting methods used to make decisions
such as those faced in the city of Mountainview, we first must examine the
basic tools used in those methods. The fundamental concept in a capital-
budgeting decision analysis is the time value of money. Would you rather
receive a $100 gift check from a relative today, or would you rather a receive
letter promising the $100 in a year? Most of us would rather have the cash
now. There are two possible reasons for this attitude. First, if we receive the
money today, we can spend it on that new sweater now instead of waiting a
year. Second, as an alternative strategy, we can invest the $100 received today
at 10 percent interest. Then, at the end of one year, we will have $110. Thus,
there is a time value associated with money. A $100 cash flow today is not the
same as a $100 cash flow in one year, two years, or ten years.

Component Interest: Suppose you invest $100 today (time o) at 10 percent interest
for one year. How much will you have after one year? The answer is $110, as the
following analysis shows.
$100 $100+ (.10)($100) =$110

Time

Time 0 1 year Time 1

The $110 at time 1(end of one year) is composed of two parts, as shown below:

Principal. Time 0 amount…………………………………….. $100
Interest earned during year 1 (.10 X $100) ……………………. 10
Amount at time 1……………………………………………… $ 110

Thus, the $110 at time 1 consist of the $100 at time 0, called principal, plus
the $10 of interest earned during the year.



Now suppose you leave your $110 invested during the second year. How much
will you have at the end of two years? As the following analysis shows, the
answer is $121

$100 $100 + (.10)($100) = $110 $110 + (.10)($110) = $121

Time

Time 0 Year 1 Time 1 Year 2 Time 2

We can break down the $121 at time 2 into two parts as follows:

Amount at time 1…………………………………………….….. $110

Interest earned during year 2 (.10 X $110) …………………. 11

Amount at time 2……………………………………….……… $ 121

Notice that you earned more interest in year 2 ($11) than you earned in year 1
($10). Why? During year 2, you earned 10% interest on the original principal
of $100 and you earned 10% interest on the year 1 interest of $10. When
interest is earned on prior periods’ interest, we call the phenomenon compound
interest. How about if your invested fund grow over five years period? Give an
example…..

As the number of years in an investment increases, it becomes more difficult to
compute the future valve of the investment using the method shown above.
Fortunately, the simplest formula shown below may be used to compute the
future value of any investment.

F = P (1+r) (1)
Where P denotes principal
r. denotes interest rate per year
n. denotes number of years

Using formula (1) to compute the future value after five years of your $100
investment, we have the following computation.



F = P(1+r)
= $100(1 + .10)

= $100(1.6105) = $161.05

The value of (1 + r) is called the accumulation factor. The values of (1 + r), for
various combinations of r and n, are tabulated in separate tables at the of
chapter..

Use formula (1) and the tabulated values in Table 1 to compute the future
value after 10 years of an $800 investment that earns interest at the rate of
12% per year.

Present value: In the discussion above, we computed the future value of an
investment when the original principal is known. Now consider a slightly
different problem. Suppose you know how much money you want to
accumulate at the end of a five-year investment. Your problem is to determine
how much your initial investment needs to be in order to accumulate the
desired amount in five years. To solve this problem, we start with formula (1).

F = P (1+ r)
Now divide each side of the preceding equation by (1 + r)
P=F 1…. (2)

(1 + r)
In formula (2), P denotes what is commonly referred to as the present value of
the cash flow F , which occurs after n years when the interest rate is r,

Let’s try out formula (2) on your investment problem, which we analyzed in the
example earlier. Suppose you did not know the value of the initial investment
required if you want to accumulate $16.05 at the end of five years in an
investment that earns 10% per year. We can determine the present value of
the investment as follows:
1
P=F ----------
(1+r)
1
= $161.05 -----------
( 1 + .10)
= $161.05 (..6209) = $100



Thus, as we knew already, you must invest $100 now in order to accumulate
$161.05 after five years in an investment earning 10 percent per year. The
present value of $100 and the future value of 161.05 at time 5 are economically
equivalent, giver that the annual interest rate is 10 percent. If you are
planning to invest the $100 received now, then you should be indifferent
between receiving the present value of $100 now receiving the future value of
$161.05 at the end five years.

When we used formula (2) to compute the present valve of the $161,05 cash
flow at time 5, we used a process called discounting. The interest rate used
when we discount a future cash flow to compute its present value is called the
discount rate. The value of 1/(1 + r), which appears in formula (2), is called
discount factor. Discount factors, factor, for various combinations of r and n,
are tabulated in table 3.

Suppose you want to accumulate $18,000 to buy a new car in four years,
and you can earn interest at rate of 8 percent per year on an investment you
make now. How much do you need to invest now? Use formula (2) and the
discount factor in Table 3 to compute the present value of the required $18,000
amount needed at the end of four years.

Present Value of a Cash-flow Series: the present value problem we just
solved involved only a single future cash flow. Now consider a slightly different
problem. Suppose you just won $5,000 in the state lottery. You want to spend
some of the cash now, but have decided to have save enough to rent a beach
during spring break of each of the next three years. You would like to deposit
enough in a bank account now so that you can withdraw $1000 from account
at the end of each of the next three years. The

Money in the bank account will earn 8 percent per year. The question, then, is
how much do you need to deposit? Another way of asking the same question
is, what is the of a series of three $1000 cash flows at the end of each of the
next three years, given that the discount the discount rate is 8 percent.?

Present
Value? $1,000 $1,000 $1,000
._____________._____________._____________.______________ Time
0 1 2 3

One way to figure out the answer to the question is to compute the present
value of each of the three $1,000 cash flows and add the three present value
amounts. We can use formula (2) for these calculations as shown in the panal



A ………. Notice that the present value of each of the $1,000 cash flows is
different, because the timing of the cash flows is different. The earlier the cash
flow will occur, the higher is its present value.

In looking the example, we obtained the $2,577 total present value by adding
three present value amounts. Each of these amounts is the result of
multiplying $1,000 by a discount factor. Notice that we can obtain the same
final results by adding the three discount factors first, and then multiplying by
$1,000. This approach is taken in the example panel B…… The sum of the
three discount factors is called an annuity discount factors, because a series of
equivalent cash flows is called an annuity. Annuity discount factors for
various combinations of r and n are tabulated in Table 4.

Now let’s verify that $2,577 is the right amount to finance your three
spring-break vacations. Example C shows how your bank account will change
over the three-year period as you earn interest and then withdraw $1,000 each
year.

Future Value of Cash-Flow Series: To complete our discussion of present
value and future value concepts, let’s consider the series of $1000 rental
payments. Suppose the owner invested each $1000 rental payment in a bank
account that pays 8 percent interest per year. How much will the owner
accumulate at the end the three-year period? An equivalent question is, what
is the future value of the three-year series of $1000 cash flows, given an
annual interest rate of 8 percent? Example 5a answers the question in two
ways. First, three separate future-value calculations are made using formula
(1). Notice that the $1000 cash flow at time 1 is multiplied by (1.08)3, since it
has two years to earn interest. The $1000 cash flow at time 2 has only one
year to earn interest, and the time 3 cash flow has no time to earn interest.

Second, the three-year annuity accumulation factor is used. This factor is the
sum of the three accumulation factors used in the first part. The annuity
accumulation factors for various combinations of r and n are tabulated in
Table 2.

Using the Table correctly: when using the tables in the appendix to solve
future-value and present-value problems, be sure to select the correct table.
Table 1 is used to find the future value of a single cash flow, and Table 3 is
used to find the present value of a single cash flow. Table 2 is used in finding
the future value of a series of identical cash flow. Be careful not to confuse
future value with present value or to confuse a single cash flow with a series of
identical cash flows.



DISCOUNTED-CASH-FLOW ANALYSIS

With our review of future-value and present-value tools behind us, we can
return to the main issue of how to evaluate capital-investment projects. Our
discussion will be illustrated by several discussions made by the
Mountainreview city government. The controller of Mountainreview routinely
advises the mayor and city council on major capital-investment decisions.

Currently under consideration is the purchase of a new street cleaner. The
controller has estimated that the city’s old street-cleaning machine would last
another five years. A new street cleaner, which also would last for five years,
can be purchased for $50,470. It would cost the city $14,000 less each year to
operate the new equipment than it costs to operate the old machine. The
expected cost savings with the new machine are due to lower expected
maintenance costs. Thus, the new street cleaner will cost $50,470 and save
$70,000 over its five-year life ($70,000 = $14,000 savings per year). Since the
$70,000 in cost savings exceeds the $50,470 acquisition cost, one might be
tempted to conclude that the new machine should be purchased. However,
this analysis is flawed, since it does not account for the time value of money.
The $50,470 acquisition cost will occur now, but the cost savings are spread
over a five-year period. It is a mistake to add cash flows occurring at different
points in time. The proper approach is to use discounted-cash-flow analysis,
which takes account of the timing of the cash flows. There are two widely used
methods of discounted-cash-flow analysis: the net-present-value method and
the internal-rate-of-return method.

Net-Present-Value Methods
The following four steps comprise a net-present-value analysis of an
investment proposal.
1. Prepare a table showing the cash flows during each year of the proposed
investment.
2. Compute the present value of each cash flow, using a discount rate that
reflects the cost of acquiring investment capital. This discount rate is
often called the hurdle rate or minimum desired rate of return.
3. Compute the net present value, which is the sum of the present values
of the cash flows.
4. If the net present value (NPV) is positive, accept the investment proposal.
Otherwise, reject it.

Example 6 displays these four steps for the Mountainview controller’s street-
cleaner decisions. In step (2) the controller used a discount rate of 10%.
Notice that the cost savings are $14,000 in each of the years 1 through 5.



Thus, the cash flows in those years comprise a five-year, $14,000 annuity. The
controller used the annuity discount factor to compute the present value of the
five years of cost savings.

The net-present-value analysis indicates that the city should purchase the new
street cleaner. The present value of the cost savings exceeds the new
machine’s acquisition cost.

Net-Present-Value Method
Mountainview City Government
Purchase of Street Cleaner
(r = .10, n = 5)
Step 1
Time 0 Time 1 Time 2 Time 3 Time 4 Time 5

Acquisition Cost $(50,470)

Annual cost savings $14,000 $14,000 $14,000 $14,000 $14,000

Step 2 Present value of annuity = $14,000(3.791)

Annuity discount factor for r = .10
And n = 5 from Table 4

Present Value $(50,470) $53,074

Step 3 Net Present Value $2,604

Step 4 Accept proposal, since net present value is positive

Internal-Rate-of-Return Method
An alternative discounted-cash-flow method analyzing investment proposals is
the internal-rate-of-return method. An asset’s internal-rate-of-return is the
true economic return earned by the asset over its life. Another way of stating
the definition is that an asset’s internal rate of return (IRR) is the discount rate
that would be required in a net-present-value analysis in order for the asset’s
net present value to be exactly zero.



What is the internal rate of return on Mountainreview’s proposed street-
cleaner acquisition? Recall that the asset has a positive net present value, given
that the city’s cost of acquiring investment capital is 10 present. Would you
expect the asset’s IRR to be higher or lower than 10 percent? Think about this
question intuitively. The higher the discount rate used in a net-present-value
analysis, the lower the present value of all the future cash flows will be. This is
true because a higher discount rate means that it is even more important to
have the money earlier instead of later. Thus, a discount rate higher than 10
percent would be required to drive the new street cleaner’s net present value
down to zero.

Finding the Internal Rate of Return: How can we find this rate? One way is
trail and error. We could experiment with different discount rates until we find
the one that yields a zero net-present value. We already know that a 10
percent discount rate yields a positive NPV. Let’s try 14 percent. Discounting
the five-year, $14,000 cost-savings annuity at 14 percent yields a negative NPV
of $2,408.

(3.433)($14,000) - $50,470 = ($2,408)

Annuity discount factor for r = 14 and n = 5. (From Table 4 )

What does the negative NPV at a 14 percent discount rate mean? We increased
the discount rate too much. Therefore, the street cleaner’s internal rate of
return must lie between 10 percent and 14 percent. Let’s try 12 percent:

(3,605)($14,000) - $50,470 = 0

Annuity discount factor for r = 14 and n = 5. (From Table 4 )

That’s it. The new street cleaner’s internal rate of return is 12 percent. With a
12 percent discount factor, the investment proposal’s net present value is zero,
since the street’s cleaner’s acquisition cost is equal to the present value of the
cost savings.


Chapter 17 Further Aspects of Capital Expenditure Decisions Edited by: I C C

CHAPTER 17

COST ALLOCATION: A CLOSER LOOK

After completing this chapter, you should be able to:
 Allocate service department costs using the direct method, step-down
method, or reciprocal-service method.
 Use the dual approach to service department cost allocation
 Explain the difference between two-stage cost allocation with departmental
overhead rates and activity-based costing.
 Describe the purposes for which joint cost allocation is used and those for
which it is not.

In earlier chapters we studied cost allocation and explored its role in an
organization’s overall managerial- accounting system. We also examined
several purposes of cost allocation. The goal of cost allocation is to ensure that
all costs incurred by the organization ultimately are assigned to its products or
services. In addition to that, the allocation of all costs to departments serve to
make departmental managers aware of the costs incurred to produce services
their department use.

This chapter is divided into two sections, each of which explores a particular
cost allocation topic in greater detail. These are:

• Service department cost allocation
• Joint product cost allocation

Service Department Cost Allocation
A service department is a unit in an organization that is not involved directly in
producing the organization’s goods or services. However, a service department
does provide a service that enables the organization’s production process to
take place. For example, the Maintenance Department in an automobile plant
does not make automobiles, but if it did not exist, the production process
would stop when the manufacturing machines broke down.

Service departments are important in nonmanufacturing organizations also.
For example, a hospital’s Personnel Department is responsible for staffing the



hospital with physicians, nurses, lab technicians, and other employees without
it the hospital would have no staff to provide medical care.

A service department such as the Maintenance Department or the Personnel
Department must exist in order for an organization to carry out its primary
function. Therefore, the cost of running a service department is part of the cost
incurred by the organization in producing goods or services.

To see how service department cost allocation fits into the overall picture of
product and service costing, it may be helpful to review the following three
types of allocation processes:

1. Cost distribution. Cost in various cost pools are distributed to all
departments, including both service and production departments.
2. Service department cost allocation. Service department costs are
allocated to production departments
3. Cost application. Costs are assigned to the goods or services produced
by the organization.

It is the second type of allocation process listed above that we are focusing on
now. The context for our discussion is Riverside Clinc.

The clinc is organized into three service departments and two direct-patient-
care departments as shown below. Since the clinic is not a manufacturing
organization, we refer to direct-patient-care departments instead of production
departments. These two departments, Orthopedics and Internal Medicine,
directly provide the health care that is the clinc’s primary objective. Thus, the
clinc’s direct-patient-care departments are like the production departments in
a manufacturing firm.

Organization Chart for Riverside Clinc
EXHIBIT 1

Patient Personnel Admin/Acc.
Records Department Department
Service Department
Departments

Direct-patient-care Orthopedics Internal
Department Department Medicine
Department



Notice that the Personnel Department and the Administration and Accounting
Department provide services to each other. When this situation occurs, the
two service departments exhibit reciprocal services.

EXHIBIT TWO provides some of the details of our illustration is consumed of service department cost
allocation. Panel A shows the proportion of each of the departments using its services. Panel B shows
the allocation bases, which are used to determine the proportion shown in panel A.

Patient Records: The service output of the Patient Records Department is
consumed only by the Orthopedic and Internal Medicine Department. Annual
patient load is the allocation base used to determine that 30 percent of the
Patient Records Department’s services were consumed by Orthopedics and 70
percent by Internal Medicine.

Personnel: The Personnel Department serves each of the clinic’s other
departments, including the other two service departments and the direct-
patient-care departments. The allocation base used to determine the
proportions of the Personnel Department’s. For example, 5 percent of the
clinic’s employees (excluding those in the Personnel Department) work in the
Patient Records Department.

Administration and Accounting: This service department provides services
only to the Personnel Department, the Orthopedics Department, and the
Internal Medicine Department. A variety of services only to the Personnel
Department, Orthopedics Department, and the Internal Medicine Department.
A variety of services are provided, such as computer support, patient billing,
and general administration. Since larger amounts of these services are
provided to larger using departments, departmental size is the allocation base
used to determine the proportion of service output consumed by each using
department.

EXHIBIT 2: Provision of Services by Service Departments
User of Services Provider of Services
Patient Recoder Personnel Administration
Accounting

Service Patient Recoder - 5% -
Departments Personnel - - 5%
Administration - 20% -
Accounting

Direct-care Orthopedics 30% 25% 35%
departments Internal Medicine 70% 50% 60%
(A) Percentage of Service output consumed by using departments



Service Department Allocation base

Patient Records…………………………………………. Annual patient load

Personnel ……………………………………………….. Number of employee

Adminstration and Accounting ………………..……….. Size of Department (sq.m space)

(B) Allocation bases

Service Variable Cost Fixed Cost Total Cost to Be
Departments Allocated

Patient Recoder $24,000 $76,000 $100,000
Personnel 15,000 45,000 60,000
Administration
Accounting 47,500 142,500 190,000

TOTAL $86,500 $263,500 $35,000
(C) Service department costs

There are two widely used methods of service department cost allocation, the
direct method and step-down method. These methods are discussed and
illustrated next, using the data for Riverside Clinic.

Direct Method
Under the direct method, each service department’s costs are allocated among
only the direct-patient-care that consume part of the service department’s
output. This method ignores the fact that some service departments provide
services to other service departments. Thus, even though Riverside Clinic’s
Personnel Department provides services to two other service departments, none
of its costs are allocated to these departments. Exhibit – 3 presents Riverside
Clinic’s service department cost allocation under the direct method.

Notice that the proportion of each service department’s costs to be allocated to
each direct-patient-care department is determined by the relative proportion of
the service department’s output consumed by each direct-patient-care
department (see exhibit 2)



Step-Down Method
As stated above, the direct method ignores the provision of services by one
service department to another service department. This shortcoming is
overcome partially by the step-down method of service department cost
allocation.

Under this method, the managerial accountant first chooses a sequence in
which to allocate the service department’s costs. A common way to select the
first service department in the sequence is to choose the one that serves the
largest number of other service departments. The service departments are
ordered in this manner, with the last service department being the one that
serves the smallest number of other service departments. Then the managerial
accountant allocates each service department’s costs among the direct-patient-
care departments and all of the other service departments that follow it in the
sequence. Note that the ultimate cost allocations assigned to the direct-
patient-care departments will differ depending on the sequence chosen.

Exhibit 3: Direct Method of Service Department Cost Allocation:
Direct-Patient-Care Departments Using Service
Provider of Cost to be Orthopedics Internal medicine
Service Allocated
Proportion Allocated Proportion Allocated
Patient Records $100,000 3/10 $ 30,000 7/10 $ 70,000
Personnel 60,000 25/75 20,000 50/75 40,000
Administration
and Accounting 190,000 35/95 70,000 60/95 120,000
TOTAL $350,000 $ 120,000 $230,000

Grand
Total = $350,000

The step-down method is best explained by way of an illustration. Riverside
Clinic’s Personnel Department serves two other service departments: Patient
Records, and Administration and Accounting. The Administration and
Accounting Department serves only one other service department: Personnel.
Finally, the Patient Records Department serves no other service department.
Thus, Riverside Clinic’s service department sequence is as follows:



(1) (2) (3)

Personnel Administration Patient
And Accounting Records

In accordance with this sequence, each service department’s costs are allocated
to the other departments as follows:

Cost Allocated from To these Departments This
Service Department

Personnel……………………………………… - Administration/Accounting

• Patient Records
• Orthopedics
• Internal Medicine

Administration/ Accounting …………………. - Orthopedics


Patient Records ………………………….…... - Orthopedics


Note that even though Administration and Accounting serves Personnel, there is no cost
allocation in that direction. This results from Personnel’s placement before Administration and
Accounting in the allocation sequence. Moreover, no costs are allocated from Patient Records to
either of the other service departments, because Patient Records does not serve those
departments.

Exhibit-4 presents the results of applying the step-down method at Riverside Clinic. First, the
Personnel Department’s $60,000 in cost is allocated among the four departments using its
services. Second, the cost of the Administration and Accounting Department is allocated. The
total cost to be allocated is the department.s original $190,000 plus the the $12,000 allocated
from the Personnel Department. The new total of $202,000 is allocated to the Orthopedics and
Internal Medicine Departments according to the relative proportions in which these two
departments use the services of the Adminstration and Accounting Department. Finally, the
Patient Records Department’s cost is Allocated.



Exhibit-4. Step-Down method of Service Department Cost Allocation: Riverside Clinic
Service Departments Direct-Patient-Care Deparments
Personnel Administration/ Patient Orthopedic Internal
Accounting Records Records
Costs prior $190,000
to allocation $60,000 $100,000

Allocation of
Personnel $60,000 12,000 (20/100) $3,000 $15,000 (25/100) $30,000 (50/100)
Department costs (5/100)

Allocation of
Administration/Acc. $202,000 $74,421 (35/95) $127,579 (60/95)
Department costs

Allocation of
Patient Records $103,000 $30,900 (30/100) $72,100 (70/100)
Department costs
Total cost allocated to each department $120,321 $229,679
Total cost allocated to direct-patient-care departments = $ 350,000

SECTION TWO: Joint Product Cost Allocation
A joint production process results in two or more products, which are termed
joint products. The cost of the input and the joint production process is called
a joint product cost. The point in the production process where the
individual products become separately identifiable is called the split-off point.
To illustrate, International Chocolate Company produces cocoa powser and
cocoa butter by processing cocoa beans in the joint production process shown
exhibit-5.

As the diagram shows, cocoa beans are processed in 1-ton batches. The beans
cost $500 and the joint process costs $600, for a total joint cost of $1,100. The
process results is 1,500 kgs of cocoa butter and 500 kgs of cocoa powder.
Each of these two joint products can be sold at the split-off point or processed
further. Cocoa butter can be separately processed into the instant cocoa mix.

….



Cocoa butter Separable Tanning cream
sales value: process sales value:
$750 for costing $3,000 for 500
1,500 kgs $1,560 kgs

Cocoa beans
costing $500
Joint production
per 1 ton
process costing Cocoa Separabl Instant cocoa
batch
$600 per ton powder sales e process mix sales
value: $500 costing value: $2,000
for 500 kgs $800 for 500 kgs

Total joint cost: $1,100 per 1 ton batch

Physical-Units Method: This method allocates joint product costs on the
basis of some physical characteristic of the joint products at the split-off point.
Panal A of exhibit 6 illustrates this allocation method for International
Chocolate Company using the weight of the joint products as the allocation
basis.

Relative-Sale-Value Method: This approach to joint cost allocation is based
on the relative sales value of each joint product at the split-off point. In the
International Chocolate Company illustration, these joint products are cocoa
butter and cocoa powder. This method is illustrated in Exhibit 6 (panel B)

Net-Realizable-value Method: Under this method, the relative value of the
final products is used to allocate the joint cost. International Chocolate
Company’s final products are tanning cream and instant cocoa mix. The net
realizable value of each final product is its sales value less any separable costs
incurred after the split-off point. The joint cost is allocated according to the
relative magnitudes of the final product’s net realizable values. Panel C of
Exhibit 6 illustrates this allocation method.

Notice how different the cost allocations are under the three methods,
particularly the physical-units method. Since the physical-units approach is
not based on the economic characteristics of the joint products, it is the least
preferred of the three methods.



EXHIBIT 6: Methods for Allocating Joint Product Costs

Joint Joint Weight at Relative Allocation of
Cost Product Split-off Point Preportion Joint Cost
Cocoa butter ……. 1,500 kgs……….……. ¾ ……………………..$ 825

$1,100 Cocoa powder……. 500 kgs…………… 1/4 ……………………. 275

Total joint cost allocated…………………………… ………….……… $ 1,100

(A) Physical-unit method

Joint Joint Sales Value at Relative Allocation of
Cost Product Split-off Point Proportion Joint Cost
Cocoa butter ………. $750…………. ………. 3/5 …………………….. $660

$1,100 Cocoa Powder………. 500 ………………..… 2/5 ……………………… 440

Total joint cost allocated…………………………….………………… $ 1,100

(B) Relative-sales-value method

Sales Value Separable Net
Joint Joint of final Cost Realizable Relative Allocation of
Cost Product product Processing Value Proportion joint Costs
Cocoa butter $3,000 $1,560 $1,440 6/11 $600
$1,100 Cocoa Powder 2,000 800 1,200 5/11 500
Total joint cost allocated…………………………………………….. $1,100
(C) Net-realizable-value method

*
Sales value of separable cost Net Calculating of relative proportions:
final product - of processing = realizable $1,440 + $1,200 = $2,640
value
$1,000 - $1,500 = $1,440 (1,440 + 2,640) = 6/11
2,000 - 800 = 1,200 (1,200 + 2,640) = 5/11


Managerial accounting ii

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