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CMA Part 2
Financial Decision Making
SU 8.1 – The Capital Budgeting Process
• Capital budgeting is the process of planning
and controlling investment for long-term
projects.
– Will affect the company for many accounting
periods going forward
– Relatively inflexible once made
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SU 8.1 – The Capital Budgeting Process
– Predicting the need for future capital assets is one
of the more challenging tasks
• Affected by
–
–
–
–
Inflation
Interest rates
Cash availability
Market demands
– Production capacity is a key driver
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SU 8.1 – The Capital Budgeting Process
• Applications for capital budgeting
– Buying equipment
– Building facilities
– Acquiring a business
– Developing a product of product line
– Expanding into new markets
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SU 8.1 – The Capital Budgeting Process
• Important to correctly forecast future changes in
demand in order to have the correct capacity.
• Planning is crucial to anticipate changes in
capital markets, inflation, interest rates and
money supply.
• Consider the tax consequences.
– All decisions should be done on an after tax basis
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SU 8.1 – The Capital Budgeting Process
• Costs considered in capital budgeting
– Avoidable cost
• May be eliminated by ceasing or improving an activity.
– Common cost
• Shared by all options and is not clearly allocable.
– Deferrable cost
• May be shifted to the future.
– Fixed cost
• Does not very within relevant range.
– Imputed cost
• May not have a specific cash outlay in accounting
continued
– Incremental cost
• Difference in cost of two options.
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SU 8.1 – The Capital Budgeting Process
– Opportunity cost
• Maximum benefit forgone based on next alternative, including that of the
stockholders (which also establishes the firms hurdle rate).
– Relevant cost
• Vary with action.
• Constant cost don’t affect decision.
– Sunk cost
• Cannot be avoided.
– Weighted-average Cost of Capital
• Weighted average of the interest cost of debt (net of tax) and the costs
(implicit or explicit) of the components of equity capital to be invested in longterm assets. It is also the “hurdle rate”.
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SU 8.1 – The Capital Budgeting Process
• Stages in Capital Budgeting
1. Identification and definition
• Identify the strategy
• Define the projects
– Revenue, costs, and cash flow
– Most difficult stage
2. Search
• Each investment to be evaluated be each function
of the firms value chain.
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SU 8.1 – The Capital Budgeting Process
3. Information-acquisition
• Costs and benefits of the projects are enumerated
• Quantitative financial factors have highest priority
• Nonfinancial measures (quantitative and qualitative)
4. Selection
• Increase shareholder value. NPV, IRR..
5. Financing
• Debt or equity
6. Implementation and monitoring
• Feedback and reporting
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SU 8.1 – The Capital Budgeting Process
• Investment Ranking Steps
– Determine Net Investment Costs
• Gross cash requirement less cash recovered from trade or sale of existing
assets, adjusted for taxes
• Investment required includes funds to provide for increases in working capital,
i.e. additional receivables and inventories.
– Calculating estimated cash flows
•
•
•
•
Capture increase in revenue, decrease costs
Net cash-flow period by period from investment
Economic life of the investment
Depreciable life
– Comparing cash-flows to Net Investment Costs
• Evaluate the benefit
– Ranking investments
• NPV, IRR, Payback
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SU 8.1 – The Capital Budgeting Process
• Book Rate of Return =
GAAP NI from Investment
Book Value of Investment
– Also called accrual accounting rate of return
– Don’t use accrual accounting numbers, instead use cash flow
• Net Income is affected by company’s choices of accounting methods
– Also, do not compare project book rate to company’s book rate
of return for investments which could be distorted
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SU 8.1 – The Capital Budgeting Process
• Relevant Cash Flows
– Net initial investment
• New equipment cost
• Working capital requirements,
• After tax disposals proceeds
– Annual net cash flows
• After tax cash collections for operations
• Depreciation tax savings
– Project termination cash flows
• After tax disposal
• Working capital recovery
 See example on page 309
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SU 8.1 – The Capital Budgeting Process
• Other Considerations
– Inflation
• Raises hurdle rate
– Post-audits – Deterrent of bad projects.
•
•
•
•
Actual to expected cash flow
Identify sources of unrealistic estimates
Avoid premature evaluations of projects
Non-quantitative benefits
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SU 8.1 – The Capital Budgeting Process Practice
Question 1
The relevance of a particular cost to a decision is determined by
A
Riskiness of the decision.
B
Number of decision variables.
C
Amount of the cost.
D
Potential effect on the decision.
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SU 8.1 – The Capital Budgeting Process Practice
Question 1 Answer
Correct Answer: D
Relevance is the capacity of information to make a difference in a decision by
helping users of that information to predict the outcomes of events or to
confirm or correct prior expectations. Thus, relevant costs are those expected
future costs that vary with the action taken. All other costs are constant and
therefore have no effect on the decision.
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SU 8.1 – The Capital Budgeting Process Practice
Question 2
Lawson, Inc., is expanding its manufacturing plant, which requires an investment of
$4 million in new equipment and plant modifications. Lawson’s sales are expected to
increase by $3 million per year as a result of the expansion. Cash investment in
current assets averages 30% of sales; accounts payable and other current liabilities
are 10% of sales. What is the estimated total investment for this expansion?
A
$3.4 million.
B
$4.3 million.
C
$4.6 million.
D
$5.2 million.
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SU 8.1 – The Capital Budgeting Process Practice
Question 2 Answer
Correct Answer: C
The investment required includes increases in working capital (e.g., additional
receivables and inventories resulting from the acquisition of a new
manufacturing plant). The additional working capital is an initial cost of the
investment, but one that will be recovered (i.e., it has a salvage value equal to
its initial cost). Lawson can use current liabilities to fund assets to the extent
of 10% of sales. Thus, the total initial cash outlay will be $4.6 million {$4
million + [(30% – 10%) × $3 million sales]}.
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SU 8.1 – The Capital Budgeting Process Practice
Question 3
What is the net cash outflow at the beginning of the first year that
Dickins should use in a capital budgeting analysis?
A
$(170,000)
B
$(180,000)
C
$(192,000)
D
$(210,000)
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SU 8.1 – The Capital Budgeting Process Practice
Question 3 Answer
Correct Answer: D
Delivery and installation costs are essential to preparing the machine for its
intended use. Thus, the company must initially pay $210,000 for the machine,
consisting of the invoice price of $180,000, the delivery costs of $12,000, and
the $18,000 of installation costs.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments
• Risk analysis – Attempt to measure the variability of future returns from
proposed investment.
– Informal method – NPV is calculated and reviewed.
– Risk-adjusted discount rates – Adjust rate of return upwards as project
becomes more risky.
– Certainty equivalent adjustments- from Utility theory – the point where you
are indifferent to a choice between a certain sum of money and the expected
value of a risky sum.
– Simulation analysis – Computer is used to generate many results based upon
various assumptions.
• Pilot plants
– Sensitivity analysis – An iterative process of recalculated returns based on
changing assumptions.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments
• Real (managerial or strategic) options
– Value of a real option – The difference between the projects NPV with
the option vs. without the option.
• Usually more valuable the later it is exercised.
– Types of real options:
•
•
•
•
•
•
•
Abandonment (Put option)
Follow-up investment
Wait and Learn (call option)
Flexibility option – vary an input
Capacity option – vary an output
New geographical markets
New product option – follow on products
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 1
Sensitivity analysis, if used with capital projects,
A
Is used extensively when cash flows are known with certainty.
B
Measures the change in the discounted cash flows when using the
discounted payback method rather than the net present value
method.
C
Is a “what-if” technique that asks how a given outcome will change if
the original estimates of the capital budgeting model are changed.
D
Is a technique used to rank capital expenditure requests.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 1 Answer
Correct Answer: C
After a problem has been formulated into any mathematical model, it may be
subjected to sensitivity analysis, which is a trial-and-error method used to
determine the sensitivity of the estimates used. For example, forecasts of
many calculated NPVs under various assumptions may be compared to
determine how sensitive the NPV is to changing conditions. Changing the
assumptions about a certain variable or group of variables may drastically
alter the NPV, suggesting that the risk of the investment may be excessive.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 2
When the risks of the individual components of a project’s cash flows are
different, an acceptable procedure to evaluate these cash flows is to
A
Divide each cash flow by the payback period.
B
Compute the net present value of each cash flow using the firm’s cost of
capital.
C
Compare the internal rate of return from each cash flow to its risk.
D
Discount each cash flow using a discount rate that reflects the degree of
risk.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 2 Answer
Correct Answer: D
Risk-adjusted discount rates can be used to evaluate capital investment
options. If risks differ among various elements of the cash flows, then
different discount rates can be used for different flows.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 3
Sensitivity analysis is used in capital budgeting to
A
Estimate a project’s internal rate of return.
B
Determine the amount that a variable can change without generating
unacceptable results.
C
Simulate probabilistic customer reactions to a new product.
D
Identify the required market share to make a new product viable and
produce acceptable results.
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SU 8.2 – Risk Analysis and Real Options
In Capital Investments Question 3 Answer
Correct Answer: B
After a problem has been formulated into any mathematical model, it may be
subjected to sensitivity analysis, which is a trial-and-error method used to
determine the sensitivity of the estimates used. For example, forecasts of
many calculated NPVs under various assumptions may be compared to
determine how sensitive the NPV is to changing conditions. Changing the
assumptions about a certain variable or group of variables may drastically
alter the NPV, suggesting that the risk of the investment may be excessive.
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SU 8.3 – Discounted Cash Flow Analysis
• Time Value of Money
–
–
–
–
Concept: A dollar received in the future is worth less than today.
Present Value (PV) – Value today of future payment
Future Value (FV) – Future value of an investment today.
Annuities – equal payments at equal intervals
• Ordinary annuity (in arrears)
• Annuity due (in advance) – PV & FV is always greater than ordinary
annuity
 See examples on page 310 through 312
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SU 8.3 – Discounted Cash Flow Analysis
– Hurdle rate
• Goal is for companies discount rate to be as low as
possible.
• WACC or Shareholder’s opportunity cost of capital.
• The lower the firm’s discount rate, the lower the
“hurdle” the company must clear to achieve
profitability
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SU 8.3 – Discounted Cash Flow Analysis
• Net Present Value (NPV)
– Project return in $$
– Positive NPV indicates a higher rate of return than
the company’s desired rate
 See example on 313
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SU 8.3 – Discounted Cash Flow Analysis
• Internal Rate of Return (IRR)
– Project return in %
– IRR shortcomings •
•
•
•
Directional changes of cash flows
Mutually exclusive projects
Varying rates of return
Multiple investments
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SU 8.3 – Discounted Cash Flow Analysis
• Cash flows and discounting
NPV = Cash flow0 + Cash flow1 + Cash flow2
(1 + r)0
(1 + r)1
(1 + r)2
Comparing Cash Flow Patterns – Page 315
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SU 8.3 – Discounted Cash Flow Analysis
• NPV vs IRR comparison
– Reinvestment rate NPV assumes the cash flow can be reinvested at projects
discount rate.
– Independent projects:
• NPV and IRR give same accept/reject decision if projects are independent.
• All acceptable independent projects can be undertaken.
– Mutually exclusive projects.
•
•
•
•
•
•
•
•
Cost of one greater than other
Timing, amounts, and direction of cash flow are different
Different useful lives
IRR provides 1 rate, NPV can be used with multiple rates.
Multiple investments. NPV is adaptable, IRR is not.
IRR assumes cash flow is reinvested at IRR rate.
NPV assumes reinvestment in the desired rate of return.
– NPV and IRR are most sound decision making tools for wealth maximization.
 NPV profile – Page 317
Select greatest NPV over greatest IRR
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SU 8.3 – Discounted Cash Flow Analysis
Question 1
The net present value (NPV) method of investment project analysis assumes
that the project’s cash flows are reinvested at the
A
Computed internal rate of return.
B
Risk-free interest rate.
C
Discount rate used in the NPV calculation.
D
Firm’s accounting rate of return.
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SU 8.3 – Discounted Cash Flow Analysis
Question 1 Answer
Correct Answer: C
The NPV method is used when the discount rate is specified. It assumes that
cash flows from the investment can be reinvested at the particular project’s
discount rate.
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SU 8.3 – Discounted Cash Flow Analysis
Question 2
The net present value of a proposed investment is negative; therefore, the
discount rate used must be
A
Greater than the project’s internal rate of return.
B
Less than the project’s internal rate of return.
C
Greater than the firm’s cost of equity.
D
Less than the risk-free rate.
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SU 8.3 – Discounted Cash Flow Analysis
Question 2 Answer
Correct Answer: A
The higher the discount rate, the lower the NPV. The IRR is the discount rate
at which the NPV is zero. Consequently, if the NPV is negative, the discount
rate used must exceed the IRR.
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SU 8.3 – Discounted Cash Flow Analysis
Question 3
Dr. G invested $10,000 in a lifetime annuity for his granddaughter Emily. The
annuity is expected to yield $400 annually forever. What is the anticipated
internal rate of return for the annuity?
A
Cannot be determined without additional information.
B
4.0%
C
2.5%
D
8.0%
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SU 8.3 – Discounted Cash Flow Analysis
Question 3 Answer
Correct Answer: B
The correct answer is 4.0%.
$10,000 = $400 ÷ IRR; IRR = 0.040 = 4.0%.
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SU 8.4 – Payback and Discounted Payback
• Payback period is the number of years it take
for an asset to pay for itself
– Pro
• Simple
– Cons
• No consideration for time value of money
• Does not consider cash flow after payback period
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SU 8.4 – Payback and Discounted Payback
• Constant cash flows
Payback =
Initial net investment
Annual expected cash flow
• Variable cash flows
– Cumulative calculation
See example on page 318
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SU 8.4 – Payback and Discounted Payback
• Discounted payback method
– Used to overcome the payback methods disregard for
time value of money
– Pro
• More conservative yet still simple
– Con
• Does not consider cash flow after payback period.
 See example
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SU 8.4 – Payback and Discounted Payback
• Other payback methods
– Bailout payback
• Considers salvage value
– Payback reciprocal
• 1 / payback
• Estimate of IRR
continued
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SU 8.4 – Payback and Discounted Payback
– Breakeven time
• Time require for discounted cash flows to equal 0
• Alternative is to consider the time required for the
present value of the cumulative cash inflows to equal
the present value of all the expected future cash flows
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SU 8.4 – Payback and Discounted Payback
Question 1
Which one of the following methods for evaluating capital projects is the
least useful from an investment analysis point of view?
A
Accounting rate of return.
B
Internal rate of return.
C
Net present value.
D
Payback.
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SU 8.4 – Payback and Discounted Payback
Question 1 Answer
Correct Answer: A
The accounting, or book, rate of return is an unsatisfactory means of
evaluating capital projects for two major reasons. Because the accounting
rate of return uses accrual-basis numbers, the calculation is subject to such
accounting judgments as how quickly to depreciate capitalized assets. Also,
the accounting rate of return is an average of all of a firm’s capital projects; it
reveals nothing about the performance of individual investment choices.
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SU 8.4 – Payback and Discounted Payback
Question 2
The payback reciprocal can be used to approximate a project’s
A
Profitability index.
B
Net present value.
C
Accounting rate of return if the cash flow pattern is relatively stable.
D
Internal rate of return if the cash flow pattern is relatively stable.
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SU 8.4 – Payback and Discounted Payback
Question 2 Answer
Correct Answer: D
The payback reciprocal (1 ÷ payback) has been shown to approximate the
internal rate of return (IRR) when the periodic cash flows are equal and the
life of the project is at least twice the payback period.
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SU 8.5 – Ranking Investment Projects
• Why should we rank investment projects?
– Capital rationing
• Reasons
– Lack of financial resources
– Control estimation bias
– Unwillingness to issue new equity (to raise new capital)
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SU 8.5 – Ranking Investment Projects
• Methods
– Profitability index =
NPV
Net Investment
 See example
– Internal capital markets – Internal funding
– Linear programming – Technique for optimizing
resource allocation.
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SU 8.5 – Ranking Investment
Projects Question 1
The profitability index approach to investment analysis
A
Fails to consider the timing of project cash flows.
B
Considers only the project’s contribution to net income and does not
consider cash flow effects.
C
Always yields the same accept/reject decisions for independent projects
as the net present value method.
D
Always yields the same accept/reject decisions for mutually exclusive
projects as the net present value method.
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SU 8.5 – Ranking Investment Projects Question
1 Answer
Correct Answer: C
The profitability index (excess present value index) of an investment is the
ratio of the present value of the future net cash flows (or only cash inflows) to
the net initial investment. It is a variation of the net present value (NPV)
method and facilitates the comparison of different-sized investments.
Because it is based on the NPV method, the profitability index will yield the
same decision as the NPV for independent projects. However, decisions may
differ for mutually exclusive projects of different sizes.
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SU 8.5 – Ranking Investment Projects
Question 2
The method that divides a project’s annual after-tax net income by the
average investment cost to measure the estimated performance of a capital
investment is the
A
Internal rate of return method.
B
Accounting rate of return method.
C
Payback method.
D
Net present value (NPV) method.
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SU 8.5 – Ranking Investment Projects
Question 2 Answer
Correct Answer: B
The accounting rate of return uses undiscounted net income (not cash flows)
to determine a rate of profitability. Annual after-tax net income is divided by
the average carrying amount (or the initial value) of the investment in assets.
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SU 8.5 – Ranking Investment Projects
Question 3
The technique that measures the estimated performance of a capital
investment by dividing the project’s annual after-tax net income by the
average investment cost is called the
A
Bail-out payback method.
B
Internal rate of return method.
C
Profitability index method.
D
Accounting rate of return method.
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SU 8.5 – Ranking Investment Projects
Question 3 Answer
Correct Answer: D
The accounting rate of return (also called the unadjusted rate of return or
book value rate of return) measures investment performance by dividing the
accounting net income by the average investment in the project. This method
ignores the time value of money.
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SU 8.6 – Comprehensive Examples
Please study the comprehensive page starting
on page 253
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CMA Part 2
Financial Decision Making
SU 9.1 – Marginal Analysis
•
•
•
Accounting Costs vs. Economic Costs
Accounting Costs = The total amount of money or goods expended in an endeavor.
It is money paid out at some time in the past and recorded in journal entries and
ledgers.
The economic cost of a decision depends on both the cost of the alternative
chosen and the benefit that the best alternative would have provided if chosen.
Economic cost differs from accounting cost because it includes opportunity cost.
– As an example, consider the economic cost of attending college. The accounting cost of
attending college includes tuition, room and board, books, food, and other incidental
expenditures while there. The opportunity cost of college also includes the salary or wage that
otherwise could be earning during the period. So for the two to four years an individual
spends in school, the opportunity cost includes the money that one could have been making
at the best possible job. The economic cost of college is the accounting cost plus the
opportunity cost.
– Thus, if attending college has a direct cost of $20,000 dollars a year for four years, and the lost
wages from not working during that period equals $25,000 dollars a year, then the total
economic cost of going to college would be $180,000 dollars ($20,000 x 4 years +
the interest of $20,000 for 4 years + $25,000 x 4 years).
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SU 9.1 – Marginal Analysis
• Explicit vs. Implicit Costs
– Implicit cost, also called an imputed cost, implied
cost, or notional cost, is the opportunity cost equal to
what a firm must give up in order to use factors which
it neither purchases nor hires.
– An explicit cost is a direct payment made to others in
the course of running a business, such as wage, rent
and materials.
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SU 9.1 – Marginal Analysis
• Accounting vs. Economic Profit
 See Tutorial at http://www.khanacademy.org/economics-financedomain/microeconomics/firm-economic-profit/economic-profit-tutorial/v/economic-profitvs-accounting-profit
• Accounting Profit = book income exceeds book
expenses
• Economic Profit = includes Accounting Profit +
Implicit costs
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SU 9.1 – Marginal Analysis
• Marginal Revenue and Marginal Cost
– Marginal Revenue is the additional or incremental revenue
of one additional unit of output.
– See that Marginal Revenue is $540 between generating 4
vs. 5 units of output.
– Marginal Cost is the additional or incremental cost
incurred of one additional unit of output.
• Note that while cost decrease over some range they will at some
point begin to increase due to the process becoming lest efficient.
• Profit Maximization is where MR = MC
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SU 9.1 – Short-Run Profit Maximization
• Pure Competition is a market structure in which a very
large number of firms sell a standardized product into
which entry is very easy in which the individual seller has
no control over the product price and in which there is
no non-price competition; a market characterized by a
very large number of buyers and sellers.
– Examples : Agricultural products such as potatoes and wheat
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SU 9.1 – Short-Run Profit Maximization
•
A Monopoly is a market structure in which one firm sells a unique product into
which entry is blocked in which the single firm has considerable control over
product price and in which non-price competition may or may not be found.
– Examples / Importance
1. Public utilities: gas, electric, water, cable TV, and local telephone service companies,
are often pure monopolies.
2. First Data Resources (Western Union), Wham-O (Frisbees), and the DeBeers diamond
syndicate are examples of "near" monopolies. (See Last Word.)
3. Manufacturing monopolies are virtually nonexistent in nationwide U.S. manufacturing
industries.
4. Professional sports leagues grant team monopolies to cities.
5. Monopolies may be geographic. A small town may have only one airline, bank, etc.
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SU 9.1 – Short-Run Profit Maximization
• Monopolistic Competition is a market structure
in which many firms sell a differentiated product
into which entry is relatively easy in which the
firm has some control over its product price and
in which there is considerable non-price
competition.
– Examples are grocery stores and gas stations
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SU 9.1 – Short-Run Profit Maximization
• Oligopoly is a market structure in which a few
firms sell either a standardized or differentiated
product into which entry is difficult in which the
firm has limited control over product price
because of mutual interdependence (except
when there is collusion among firms) and in
which there is typically non-price competition.
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SU 9.1 – Short-Run Profit Maximization
• Law of Demand states that all other things remaining
unchanged, people demand (buy) more of any good /
service if the price of that good / service falls and
demand (buy) less if the price increases.
– Usually represented by a negatively-sloped demand curve
which slows that the quantity demanded (quantity of a
particular good people intending to buy) declines as price
rises and increases as price rises.
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SU 9.1 – Short-Run Profit Maximization
• Elasticity of demand measures how responsive a
products demand is to changes in its price level.
– When we have inelastic demand, a consumer will pay
almost any price for the good.
– Elastic demand therefore means that demand for the
product will vary when its price changes. Generally goods
which have elastic demand tend to have many substitutes,
so if the price of one good increases too much I will
substitute out towards a similar good which is cheaper.
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SU 9.1 – Short-Run Profit Maximization
• Calculating Price elasticity of demand
– Price elasticity of demand is calculated as the percentage change in quantity demanded
divided by the percentage change in price.
– There are a number of factors that can determine the price elasticity of demand for a
good or service.
– For example, the demand for luxury items tend to be more elastic than the demand for
necessities. For items that are essential, you tend to be less responsive to changes in
price. An example of this would be the demand for diamonds tends to be more price
elastic than the demand for electricity.
– Price elasticity of demand is also affected how large a percentage of your total income
an item is. We tend to be more elastic in regards to price changes for items that make up
a larger percentage of our incomes. For example, if the price of a pack of gum goes up
by 10%, I probably wouldn't even notice. On the other hand, if the price of a car I'm
considering purchasing goes up by 10%, I would definitely notice and I would probably
reconsider the purchase.
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SU 9.1 – Short-Run Profit Maximization
• A third factor that influences the price elasticity of demand is the time
frame allowed for response. We tend to be more responsive to changes in
price in the long run than in the short run. For example, if the price of gas
were to go up overnight to $10/gallon I would still have to put gas in my
car tomorrow morning because I have to go to work and I have to go to
school. But if the price of gas were to stay at $10/gallon for a year, then I
have more options. I could move closer to work, start carpooling, or trade
in my car for a hybrid with better gas mileage so that I don't have to buy as
much gas. So in the long run, demand tends to be more elastic than in the
short run.
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SU 9.1 – Short-Run Profit Maximization
Price Elasticity Example
Antoinette has a beauty salon. She services 100
customers per day. Her usual fee is $50. She wants to
expand her business. If she lowers her price (gives
everyone a coupon for $10 off), she expects to get an
extra 10 customers per day. Calculate the price
elasticity of demand. Did she make the correct
decision?
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SU 9.1 – Short-Run Profit Maximization
Price Elasticity Example Answer
A)
Percentage change in quantity demanded = 10% (100 customers increased to 110 customers)
B)
Percentage change in price = -20% ($50 reduced to $40)
A/B = 10%/-20% = -0.5
The price elasticity of demand for this service is -0.5, and a price elasticity of demand less than 1
means that a good is inelastic, meaning that quantity demanded is relatively unresponsive to a
change in price.
So you could argue that she made the wrong decision, as the price decrease did not greatly affect
demand. She might have been better choosing another strategy, such as better advertising or her
services.
You could also argue that she is reducing the price by 20% in return for a 10% increase in volume.
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SU 9.1 – Short-Run Profit Maximization
Price Elasticity Defined
A product with elasticity of 1.2 has elastic demand. What this means is that
for every 1% rise in the price, demand will fall by 1.2% (similarly, a 1% fall in
the price will lead to a 1.2% rise in demand).
The rule is:
Elasticity > 1 : elastic (% change in demand is greater than % change in price e.g. luxury
goods such as cars etc.)
Elasticity < 1 : inelastic (% change in demand is less than % change in price e.g. essential
goods such as food)
Elasticity = 1 : unitary elastic (% change in demand is equal to the % change in price)
Basically a firm producing an inelastic good can increase revenue by raising the price, as the
fall in demand is more than offset by the increased revenue on the remaining demand.
73
SU 9.1 – Short-Run Profit Maximization
Price Elasticity Defined
• Infinite or perfectly elastic - If it were “perfectly” elastic,
demand would be infinite at all prices less than $3. A perfectly
elastic demand graph is a vertical line. And, when the price is
at $3, you can not tell from the graph what the demand is
since the line is vertical. The demand could be at any value.
• Perfectly price inelastic - means that the quantity demanded
will not change when price changes. Vertical demand curve
• Also, perfectly price elastic means if price changes, quantity
demanded changes totally, Horizontal Demand Curve
74
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
•
CVP = Break-even analysis
– Allows us to analyze the relationship between revenue and fixed and variable expenses
– It allows us to study the effects of changes in assumptions about cost behavior and the
relevant ranges (in which those assumption are valid) may affect the relationships
among revenues, variable costs, and fixed costs at various production levels
– Cost-volume-profit analysis is a tool to predict how changes in costs and sales levels
affect income; conventional CVP analysis requires that all costs must be classified as
either fixed or variable with respect to production or sales volume before CVP analysis
can be used.
– It considers the effects of:
• Sales volume
• Sales price
• Product mixes
• What else……?
75
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• CVP analysis is done with what assumptions?
–
–
–
–
–
Cost and revenue relationships are predictable
Unit selling prices are constant
Changes in inventory are insignificant
Fixed costs remain constant over relevant range
Total variable cost change proportional with volume
Continued
76
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
– The revenue (sales) mix is constant
– All costs are either fixed or variable (long-term all costs are
considered as variable)
– Volume is the sole revenue driver and cost driver
– The breakeven point is directly related to costs and
inversely related to the budgeted margin of safety and the
contribution margin
– Time value of money is ignored
77
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Fixed Costs
– Total fixed cost remains unchanged in amount when volume of activity varies
from period to period within a relevant range.
– The fixed cost per unit of output decreases as volume increases (and vice
versa).
– When production volume and cost are graphed, units of product are usually
plotted on the Horizontal axis and dollars of cost are plotted on the vertical
axis.
– Fixed cost is represented by a horizontal line with no slope (cost remains
constant at all levels of volume within the relevant range).
– Intersection point of line on cost (vertical) axis is at fixed cost amount.
– Likely that amount of fixed cost will change when outside of relevant range.
78
Monthly Basic
Telephone Bill per
Local Call
SU 9.2 – Cost-Volume-Profit (CVP) Analysis – Theory
Fixed Costs
Monthly Basic
Telephone Bill
C1
Number of Local Calls
Total fixed costs
remain constant as
activity increases.
Number of Local Calls
Cost per call
declines as
activity increases.
79
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Variable Costs
– Total variable cost changes in proportion to changes in volume
of activity.
– Variable cost per unit remains constant but the total amount of
variable cost changes with the level of production.
– When production volume and cost are graphed
– Variable cost is represented by a straight line starting at the zero
cost level.
– The straight line is upward (positive) sloping. The line rises as
volume increases.
80
Cost per Minute
SU 9.2 – Cost-Volume-Profit (CVP) Analysis - Theory
Total Costs
C1
Minutes Talked
Total variable costs
increase as
activity increases.
Minutes Talked
Cost per Minute
is constant as
activity increases.
81
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Mixed Costs
– Include both fixed and variable cost components.
– When volume and cost are graphed,
• Mixed cost is represented by a straight line with an upward (positive)
slope.
• Start of line is at fixed cost point (or amount of total cost when volume
is zero) on cost (vertical) axis. As activity level increases, mixed cost
line increases at an amount equal to the variable cost per unit.
– Mixed costs are often separated into fixed and variable
components when included in a CVP analysis.
82
Scatter Diagrams
P1
Total Cost in
1,000’s of Dollars
Draw a line through the plotted data points so that about equal
numbers of points fall above and below the line.
20
* *
* *
10
* ** *
**
Estimated fixed cost = 10,000
0
0
1
2
3
4
5
Activity, 1,000’s of Units Produced
6
83
Scatter Diagrams
P1
Total Cost in
1,000’s of Dollars
Unit Variable Cost = Slope =
20
10
0
* *
* *
Δ in cost
Δ in units
* ** *
**
Horizontal distance is the
change in activity.
0
1
2
3
4
5
Activity, 1,000’s of Units Produced
6
84
Vertical
distance is
the change
in cost.
High-Low Method
• The following is not in this Study Unit, but it is
important to know and be able to calculate.
85
The High-Low Method
The following relationships between units
produced and total cost are observed:
Using these two levels of activity, compute:
 the variable cost per unit.
 the total fixed cost.
86
High-Low Method
High activity level - December
Low activity level - January
Change in activity
Units
67,500
17,500
50,000
Cost
$ 29,000
20,500
$ 8,500
 Variable cost per unit is determined as follows:
 Fixed costs are determined as follows:
Total cost = $17,525 + $0.17 per unit produced
87
Contribution Margin and its Measures
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 200,000
140,000
$ 60,000
24,000
$ 36,000
Unit
$ 100
70
$ 30
Contribution margin is the amount by which revenue
exceeds the variable costs of producing the revenue.
Total contribution margin is $60,000 and the
contribution margin per unit sold is $30.
88
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Breakeven point is the level of output where total
revenues equals total expenses; the point at which
all fixed costs have been covered and operating
income is zero.
– What is the break-even point and where is it on a
graph on the next page?
89
CVP Graph
Break-Even Point
90
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• BEP = output level at which Total Rev = Total Exp
– It is also the point at which all fixed cost have been
covered and operating income is zero
Revenue
Var. Cost
Gross Margin
Fixed Cost
Oper. Income
$100,000
$ 80,000
$ 20,000
$ 20,000
$ 0
91
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Other terms and definitions
– Margin of safety is the excess of “budgeted” sales over BE Sales
– Mixed costs (See slide 11) are costs that have both a fixed and variable
component. For example, the cost of operating an automobile includes some
fixed costs that do not change with the number of miles driven (e.g., operating
license, insurance, parking, some of the depreciation, etc.) Other costs vary
with the number of miles driven (e.g., gasoline, oil changes, tire wear, etc.).
– Revenue or sales mix is the composition of total revenues in terms of various
products
– Sensitivity analysis (See slide 12) examines the effect on the outcome of not
achieving the original forecast or of changing an assumption. Since many
decisions must be made due to uncertainty, probabilities can be assigned to
different outcomes (“what-if”).
92
C1
SU 9.2 – Cost-Volume-Profit (CVP) Analysis - Theory
Total Utility
Cost
Mixed costs contain a fixed portion that is incurred even when the
facility is unused, and a variable portion that increases with
usage. Utilities typically behave in this manner.
Variable
Cost per KW
Activity (Kilowatt Hours)
Fixed Monthly
93 Charge
Utility
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
94
•
•
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
Unit Contribution Margin (UCM) is an important term used with break-even point
or break-even analysis is contribution margin. In equation format it is defined as
follows:
Contribution Margin = Revenues – Variable Expenses
The contribution margin for one unit of product or one unit of service is defined
as:
– Contribution Margin per Unit = Revenues per Unit (Sales price) – Variable
Expenses per Unit
– Expressed in either percentage of the selling price (contribution margin ratio)
or dollar amount
– Slope of total cost curve plotted so that volume is on the x-axis and dollar
value is on the y-axis
95
SU 9.2 – Cost-Volume-Profit (CVP) Analysis Theory
• Break-even point in units
Fixed costs
UCM
• Break-even point in dollars
Fixed costs
CMR
96
A1
Contribution Margin Ratio
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Contribution
margin ratio
Contribution
margin ratio
=
=
Total
$ 200,000
140,000
$ 60,000
24,000
$ 36,000
Unit
$ 100
70
$ 30
Contribution margin per unit
Sales price per unit
$30 per unit
$100 per unit
=
30%
97
P2
Computing the Break-Even Point
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 200,000
140,000
$
60,000
24,000
$
36,000
Unit
$ 100
70
$ 30
How much contribution margin must Rydell Company have to
cover its fixed costs (break-even)?
Answer: $24,000
How many units must Rydell sell to cover its fixed costs (breakeven)?
Answer: $24,000 ÷ $30 per unit = 800 units
98
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 1
Cost-volume-profit (CVP) analysis is a key factor in many decisions,
including choice of product lines, pricing of products, marketing
strategy, and use of productive facilities. A calculation used in a CVP
analysis is the breakeven point. Once the breakeven point has been
reached, operating income will increase by the
A
Gross margin per unit for each additional unit sold.
B
Contribution margin per unit for each additional unit sold.
C
Fixed costs per unit for each additional unit sold.
D
Variable costs per unit for each additional unit sold.
99
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 1 Answer
Correct Answer: B
At the breakeven point, total revenue equals total fixed costs plus the
variable costs incurred at that level of production. Beyond the
breakeven point, each unit sale will increase operating income by the
unit contribution margin (unit sales price – unit variable cost) because
fixed cost will already have been recovered.
Incorrect Answers:
A: The gross margin equals sales price minus cost of goods sold, including fixed cost.
C: All fixed costs have been covered at the breakeven point.
D: Operating income will increase by the unit contribution margin, not the unit
variable cost.
100
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 2
One of the major assumptions limiting the reliability of breakeven
analysis is that
A
Efficiency and productivity will continually increase.
B
Total variable costs will remain unchanged over the relevant range.
C
Total fixed costs will remain unchanged over the relevant range.
D
The cost of production factors varies with changes in technology.
101
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 2 Answer
Correct Answer: C
One of the inherent simplifying assumptions used in CVP analysis is that
fixed costs remain constant over the relevant range of activity.
Incorrect Answers:
A: Breakeven analysis assumes no changes in efficiency and productivity.
B: Total variable costs, by definition, change across the relevant range.
D: The cost of production factors is assumed to be stable; this is what is
meant by relevant range.
102
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 3
The margin of safety is a key concept of CVP analysis. The margin of
safety is the
A
Contribution margin rate.
B
Difference between budgeted contribution margin and breakeven
contribution margin.
C
Difference between budgeted sales and breakeven sales.
D
Difference between the breakeven point in sales and cash flow
breakeven.
103
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 3 Answer
Correct Answer: C
The margin of safety measures the amount by which sales
may decline before losses occur. It is the excess of budgeted
or actual sales over sales at the BEP.
Incorrect Answers:
A: The contribution margin rate is computed by dividing contribution margin
by sales. The contribution margin equals sales minus total variable costs.
B: The margin of safety is expressed in revenue or units, not contribution
margin.
D: Cash flow is not relevant.
104
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 4
The breakeven point in units increases when unit costs
A
Increase and sales price remains unchanged.
B
Decrease and sales price remains unchanged.
C
Remain unchanged and sales price increases.
D
Decrease and sales price increases.
105
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory Question 4 Answer
Correct Answer: A
The breakeven point in units is calculated by dividing total fixed costs by the unit
contribution margin. If selling price is constant and costs increase, the unit
contribution margin will decline, resulting in an increase of the breakeven point.
Incorrect Answers:
B: A decrease in costs will cause the unit contribution margin to increase, lowering the breakeven
point.
C: An increase in the selling price will increase the unit contribution margin, resulting in a lower
breakeven point.
D: Both a cost decrease and a sales price increase will increase the unit contribution margin, resulting
in a lower breakeven point.
106
Remember
Computing the Break-Even Point
We have just seen one of the basic CVP relationships
– the break-even computation.
Fixed costs
Break-even point in units =
Contribution margin per unit
Unit sales price less unit variable cost
($30 in previous example)
107
Remember
Computing the Break-Even Point
The break-even formula may also be
expressed in sales dollars.
Fixed costs
Break-even point in dollars =
Contribution margin ratio
Unit contribution margin
Unit sales price
108
SU 9.2 – Cost-Volume-Profit (CVP) Analysis –
Theory
• Review:
– What is the difference between gross margin and
contribution margin
– Effect of an increase in CM
– Effects on BEP by changes in CM
109
SU 9.3 – CVP Analysis – Basic Calculations
• CVP Applications
– Target Operating Income
– Multiple products
– Choice of products
• Degree of Operating Leverage (DOL)
110
SU 9.3 – CVP Analysis – Basic Calculations
Question 1
Which of the following would decrease unit a contribution margin the
most?
A
A 15% decrease in selling price.
B
A 15% increase in variable expenses.
C
A 15% decrease in variable expenses.
D
A 15% decrease in fixed expenses.
111
SU 9.3 – CVP Analysis – Basic Calculations
Question 1 Answer
Correct Answer: A
Unit contribution margin (UCM) equals unit selling price
minus unit variable costs. It can be decreased by either
lowering the price or raising the variable costs. As long as
UCM is positive, a given percentage change in selling
price must have a greater effect than an equal but
opposite percentage change in variable cost. The example
below demonstrates this point.
Continued
112
SU 9.3 – CVP Analysis – Basic Calculations
Question 1 Answer
Original:
UCM = SP – UVC
= $100 – $50
= $50
Lower Selling Price:
UCM = (SP × .85) – UVC
= $85 – $50
= $35
Higher Variable Cost:
UCM = SP – (UVC × 1.15)
= $100 – $57.50
= $42.50
Since $35 < $42.50, the lower selling price has the greater effect.
113
SU 9.3 – CVP Analysis – Basic Calculations
Question 2
The breakeven point in units sold for Tierson Corporation is 44,000. If fixed
costs for Tierson are equal to $880,000 annually and variable costs are $10
per unit, what is the contribution margin per unit for Tierson Corporation?
A
$0.05
B
$20.00
C
$44.00
D
$88.00
114
SU 9.3 – CVP Analysis – Basic Calculations
Question 2 Answer
Correct Answer: B
The breakeven point in units is equal to the fixed costs divided by
the contribution margin per unit. Thus, the UCM is $20.00
($880,000 ÷ 44,000 units).
115
SU 9.3 – CVP Analysis – Basic Calculations
Question 3
A manufacturer contemplates a change in technology that would reduce
fixed costs from $800,000 to $700,000. However, the ratio of variable costs
to sales will increase from 68% to 80%. What will happen to breakeven level
of revenues?
A
B
C
D
Decrease by $301,470.50.
Decrease by $500,000.
Decrease by $1,812,500.
Increase by $1,000,000.
116
SU 9.3 – CVP Analysis – Basic Calculations
Question 3 Answer
Correct Answer: D
The original breakeven level was:
Breakeven point
= Fixed costs ÷ Contribution margin ratio
= $800,000 ÷ (1.0 – .68)
= $2,500,000
The new level is:
Breakeven point
= Fixed costs ÷ Contribution margin ratio
= $700,000 ÷ (1.0 – .80)
= $3,500,000
Thus, there is an increase of $1,000,000 ($3,500,000 – $2,500,000).
117
SU 9.4 – CVP Analysis – Target Income
Calculations
• Target Operating Income
Fixed costs + Target operating income
UCM
• Target Net Income
Fixed costs + Target net income / (1.0 – tax rate)
UCM
118
Computing Sales (Dollars) for a
Target Net Income
To convert target net income to before-tax
income, use the following formula:
Before-tax income =
Target net income
1 - tax rate
119
SU 9.4 – CVP Analysis – Target Income
Calculations Question 1
The data below pertain to the forecasts of XYZ Company for the upcoming year.
Total Cost
Unit Cost
$1,000,000
$25
Raw materials
160,000
4
Direct labor
280,000
7
80,000
2
Sales (40,000 units)
Factory overhead:
Variable
Fixed
Selling and general expenses:
360,000
Variable
120,000
Fixed
225,000
3
Continued
120
SU 9.4 – CVP Analysis – Target Income
Calculations Question 1
How many units does XYZ Company need to produce and
sell to make a before-tax profit of 10% of sales?
A.
65,000 units.
B.
36,562 units.
C.
90,000 units.
D.
25,000 units.
121
SU 9.4 – CVP Analysis – Target Income
Calculations Question 1 Answer
Correct Answer: C
Revenue minus variable and fixed expenses equals net income.
If X equals unit sales, revenue equals $25X, total variable expenses
equal $16X ($4 + $7 + $2 + $3), total fixed expenses equal $585,000
($360,000 + $225,000), and net income equals 10% of revenue. Hence, X
equals 90,000 units.
$25X - $16X -$585,000
=
$25X × 10%
6.5X
=
$585,000
X
=
90,000 units
122
SU 9.4 – CVP Analysis – Target Income
Calculations Question 2
The data below pertain to the forecasts of XYZ Company for the upcoming year.
Total Cost
Unit Cost
$1,000,000
$25
Raw materials
160,000
4
Direct labor
280,000
7
80,000
2
Sales (40,000 units)
Factory overhead:
Variable
Fixed
Selling and general expenses:
360,000
Variable
120,000
Fixed
225,000
3
Continued
123
SU 9.4 – CVP Analysis – Target Income
Calculations Question 2
Assuming that XYZ Company sells 80,000 units, what is the
maximum that can be paid for an advertising campaign while still
breaking even?
A.
$135,000
B.
$1,015,000
C.
$535,000
D.
$695,000
124
SU 9.4 – CVP Analysis – Target Income
Calculations Question 2 Answer
Correct Answer: A
The company will break even when net income equals zero. Net income is equal to
revenue minus variable expenses and fixed expenses, including advertising. Thus, if X
equals advertising cost, the equation is
80,000)($25) – (80,000)($16) – $585,000 – X
=
0
$2,000,000 – $1,280,000 – $585,000 – X
=
0
X
=
$135,000
125
SU 9.4 – CVP Analysis – Target Income
Calculations Question 3
For one of its divisions, Buona Fortuna Company has fixed costs of $300,000
and a variable-cost percentage equal to 60% of its $10 per unit selling price. It
would like to earn a pre-tax income of $90,000 per year from the division.
How many units will Buona Fortuna have to sell to earn a pre-tax income of
$90,000 per year?
A
65,000 units.
B
75,000 units.
C
77,250 units.
D
97,500 units.
126
SU 9.4 – CVP Analysis – Target Income
Calculations Question 3 Answer
Correct Answer: D
Buona Fortuna’s unit contribution margin is $4 ($10 unit price – $6 unit variable cost).
By treating desired profit as an additional fixed cost, the target unit sales can be
calculated as follows:
Target unit sales = (Fixed costs + Target operating income) ÷ UCM
= ($300,000 + $90,000) ÷ $4
= 97,500
127
Computing a Multiproduct
Break-Even Point
• The CVP formulas can be modified for use when a company sells
more than one product.
• The unit contribution margin is replaced with the contribution
margin for a composite unit.
• A composite unit is composed of specific numbers of each product
in proportion to the product sales mix.
• Sales mix is the ratio of the volumes of the various products.
128
SU 9.5 – CVP Analysis – Multi-Product
Calculations
• Multiple Products (or Services)
– S = FC + VC = Calculated Weighted Average Contribution
Margin
129
SU 9.5 – CVP Analysis – Multi-Product
Calculations
• Choice of Product decisions – When resources are
limited companies have to choose which products to
produce
• A breakeven analysis of the point where the same
operating income or loss will result
130
SU 9.5 – CVP Analysis – Multi-Product
Calculations
• Special Orders (usually lower price than std.)
– The assumption are that idle capacity is sufficient to
manufacture extra units of a special order.
131
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 1
Moorehead Manufacturing Company produces two products for which the data
presented to the right have been tabulated. Fixed manufacturing cost is applied
at a rate of $1.00 per machine hour. The sales manager has had a $160,000
increase in the budget allotment for advertising and wants to apply the money
to the most profitable product. The products are not substitutes for one
another in the eyes of the company’s customers.
Per Unit
XY-7
BD-4
Selling price
$4.00
$3.00
Variable manufacturing cost
2.00
1.50
Fixed manufacturing cost
.75
.20
Variable selling cost
1.00
1.00
Continued
132
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 1
Suppose Moorehead has only 100,000 machine hours that can be made
available to produce additional units of XY-7 and BD-4. If the potential increase
in sales units for either product resulting from advertising is far in excess of this
production capacity, which product should be advertised and what is the
estimated increase in contribution margin earned?
A
Product XY-7 should be produced, yielding a contribution margin of $75,000.
B
Product XY-7 should be produced, yielding a contribution margin of $133,333.
C
Product BD-4 should be produced, yielding a contribution margin of $187,500.
D
Product BD-4 should be produced, yielding a contribution margin of $250,000.
133
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 1 Answer
Correct Answer: D
The machine hours are a scarce resource that must be allocated to the product(s) in a
proportion that maximizes the total CM. Given that potential additional sales of either product
are in excess of production capacity, only the product with the greater CM per unit of scarce
resource should be produced. XY-7 requires .75 hours; BD-4 requires .2 hours of machine time
(given fixed manufacturing cost applied at $1 per machine hour of $.75 for XY-7 and $.20 for BD4). XY-7 has a CM of $1.33 per machine hour ($1 UCM ÷ .75 hours), and BD-4 has a CM of
$2.50 per machine hour ($.50 ÷ .2 hours). Thus, only BD-4 should be produced, yielding a CM
of $250,000 (100,000 × $2.50). The key to the analysis is CM per unit of scarce resource.
Incorrect Answers:
A: Product XY-7 actually has a CM of $133,333, which is lower than the $250,000 CM for product BD-4.
B: Product BD-4 has a higher CM at $250,000.
C: Product BD-4 has a CM of $250,000.
134
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 2
Product A accounts for 75% of a company’s total sales revenue and has
a variable cost equal to 60% of its selling price. Product B accounts for
25% of total sales revenue and has a variable cost equal to 85% of its
selling price. What is the breakeven point given fixed costs of
$150,000?
A
$375,000
B
$444,444
C
$500,000
D
$545,455
135
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 2 Answer
Correct Answer: B
Using the relationship: sales = total variable costs + total fixed costs, the combined breakeven
point can be calculated as follows:
S
S
=
=
0.75S(0.60) + 0.25S(0.85) + $150,000
0.45S + 0.2125S + $150,000
S – 0.6625S
=
$150,000
0.3375S
S
=
=
$150,000
$444,444
Incorrect Answers:
A: This amount is based on the contribution margin of Product A only rather than a weighted average.
C: This amount is based on half of the required sales at B’s contribution margin.
D: This amount is based on an unweighted average of the two contribution margins.
136
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 3
Von Stutgatt International’s breakeven point is 8,000 racing bicycles and
12,000 5-speed bicycles. If the selling price and variable costs are $570 and
$200 for a racer, and $180 and $90 for a 5-speed respectively, what is the
weighted-average contribution margin?
A
$100
B
$145
C
$179
D
$202
137
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 3 Answer
Correct Answer: D
Contribution margin equals selling price minus variable costs.
The product contribution margins are:
= $370
Racer:
$570 – $200
= $90
5-Speed:
$180 – $90
The sales mix is:
Racer:
8,000 ÷ (8,000 + 12,000) = 40%
5-Speed:
12,000 ÷ (8,000 + 12,000) = 60%
Multiply the CM by the sales mix for each product, and add the results.
Weighted-average CM = ($370 × 40%) + ($90 × 60%)
= $148 + $54
= $202
138
SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 3 Answer
Incorrect Answers:
A: The sales mix dictates how much of the total CM will come from sales of each
product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the
UCM for racers must be added to 60% of the UCM for 5-speeds to get the weightedaverage CM.
B: The sales mix dictates how much of the total CM will come from sales of each
product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the
UCM for racers must be added to 60% of the UCM for 5-speeds to get the weightedaverage CM.
C: The sales mix dictates how much of the total CM will come from sales of each
product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the
UCM for racers must be added to 60% of the UCM for 5-speeds to get the weightedaverage CM.
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SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 4
Catfur Company has fixed costs of $300,000. It produces two products, X and Y.
Product X has a variable cost percentage equal to 60% of its $10 per unit selling price.
Product Y has a variable cost percentage equal to 70% of its $30 selling price. For the
past several years, sales of Product X have averaged 66% of the sales of Product Y.
That ratio is not expected to change. What is Catfur’s breakeven point in dollars?
A
$300,000
B
$750,000
C
$857,142
D
$942,857
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SU 9.5 – CVP Analysis – Multi-Product
Calculations Question 4 Answer
Correct Answer: D
A helpful approach in a multiproduct situation is to make calculations based on the
composite unit, i.e., 2 units of Product X and 3 units of Product Y (a 66% ratio). The
selling price of this composite unit is $110 [(2 × $10) + (3 × $30)]. The UCM of the
composite unit is $35 {[2 × ($10 – $6)] + [3 × ($30 – $21)]}. Consequently, the
breakeven point in composite units is 8,571.43 ($300,000 FC ÷ $35 UCM), and the
breakeven point in sales dollars is $942,857 (8,571.43 × $110).
Incorrect Answers:
A: This amount equals the fixed costs.
B: This amount assumes a 40% contribution margin ratio.
C: This amount assumes a 35% contribution margin ratio.
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