Solution manual cost accounting 14e by carter ch24

Expected value is the weighted average value of the events for a probability distribution, i.e., it is the average value of the events that are expected to occur.. The standard deviation

CHAPTER 24

DISCUSSION QUESTIONS

24-1

Q24-1 Before making a decision under conditions of

uncertainty, a manager should try to assess the

probabilities associated with alternative

possi-ble outcomes in order to determine the

proba-ble result of each alternative action Unless the

probabilities associated with possible outcomes

are determined, the effect of uncertainty cannot

be accounted for adequately, which may result

in inconsistent and unreliable decisions.

Q24-2 Expected value is the weighted average value

of the events for a probability distribution, i.e.,

it is the average value of the events that are

expected to occur.

Q24-3 The standard deviation of the expected value is

a measure of the variability of events within a

probability distribution and, as such, is viewed

as a measure of risk The larger the standard

deviation, the greater the risk that the actual

result will differ from the expected value.

Q24-4 The coefficient of variation relates the

stan-dard deviation for a probability distribution to

its expected value, thus allowing for

differ-ences in the relative size of different

probabil-ity distributions The coefficient of variation

provides a comparative measure of risk for

alternatives with different expected values.

Q24-5 A joint probability is the probability of the

simul-taneous occurrence of two or more events

(e.g., the probability of the occurrence of both

event A and event B, denoted as P(AB)),

whereas a conditional probability is the

proba-bility of the occurrence of one event given that

another event has occurred (e.g., the

probabili-ty of the occurrence of event A given that event

B has already occurred, denoted as P(AIB)) A

conditional probability implies that some

rela-tionship exists between the events.

Q24-6 Management should be interested in revising

probabilities as new information becomes

available, because new information may alter

the expected outcomes (i.e., probabilities)

enough to warrant making a different

deci-sion As a consequence, the revision of

prob-abilities may be necessary in order to provide

a basis for making the best decision.

Q24-7 Decision trees graphically portray alternatives

and their expected values and include a sequential decision dimension in the analysis They highlight decision points, alternatives, estimated results, related probabilities, and expected values They are especially useful in evaluating alternatives requiring sequential decisions that depend upon uncertain out- comes.

Q24-8 In a discrete probability distribution, the

possi-ble outcomes are limited to certain finite ues (e.g., 10, 11, 12, etc.) The number of shipments, orders, units of product, etc are events that could be described adequately by

val-a discrete probval-ability distribution For ience, the outcomes that occur in a discrete probability distribution are often limited to a fairly small number, but this need not neces- sarily be the case In contrast, the possible outcomes that may occur in a continuous probability distribution are infinite even within

conven-a limited rconven-ange Time, weight, volume, length, temperature, and economic value are exam- ples of continuous variables because they can take on an infinite number of values within a limited range (e.g., between 10 and

11 seconds times of 10.1 seconds, 10.53 onds, 10.926 seconds, etc could occur) Although such items are measured in discrete units, conceptually they can be subdivided into infinitely small units of measure (e.g., $2,

sec-$2.34, $2.627, $2.8935, etc.), and practically, the number of different discrete values an item may have without subdivision is large (e.g., the range of sales of $1 items between 10,000 and 20,000 units).

Q24-9 The normal distribution has the following

attractive properties:

(a) The normal distribution is symmetric and

it has only one mode This means that the expected value (which is the mean of the distribution) is equal to the most likely sin- gle event (the mode) Consequently, the single best guess is also the expected value.

(b) The relationship between the portion of

the area under the curve for any given

interval from the mean, as measured in

standard deviations, is constant for all

nor-mal distributions This makes it possible to

determine the probability of the

occur-rence of an event within any interval if the

mean and standard deviation are known.

Q24-10 Monte Carlo simulation is used to obtain a

probabilistic approximation of the outcome

of a business system or problem that

con-tains numerous stochastic variables, but can

be modeled mathematically Its procedure

utilizes statistical sampling techniques and

is computer oriented.

Q24-11 A normal distribution is a symmetrical

distri-bution The expected value (the mean) and

the most likely event (the mode) are equal.

Since the most likely event would be used

even when the distribution of probable

out-comes is not considered specifically, and

since the most likely event and the expected

value are the same for a normal distribution,

the expected net present value would be the

same whether probability analysis is

incorpo-rated or not Nevertheless, probability

analy-sis should be incorporated into the capital

expenditure evaluation because it provides a

way for management to evaluate risk.

Q24-12 A mutiperiod problem expands the analysis

from a single variable to multiple variables

(i.e., the cash flows from each period are

treated as different random variables) As a

consequence, the expected net present value

of a capital expenditure proposal is treated as

a random variable drawn from a multivariate

probability distribution The variance for a

multivariate distribution is computed by

sum-ming the variances for each variable if the

variables are independent, or by summing

the standard deviations and squaring the total

if the variables are perfectly correlated

(squaring the total incorporates the

interac-tion between the dependent variables) To

consider the time value of money in a

mutiperiod capital expenditure proposal, the

periodic variances and the periodic standard

deviations should be discounted at the

com-pany’s weighted average cost of capital.

Q24-13 Cash flows are independent if the

magni-tude of cash flows in one period is not in any

way affected by the magnitude of cash flows

in another period Independent cash flows might be expected to occur when a capital expenditure relates to the production of an established product or service; the demand for which is expected to vary in response to temporary changes in consumer tastes and preferences or the capacity to purchase, which are uncorrelated between periods Q24-14 Cash flows are perfectly correlated if the mag-

nitude of cash flows in a subsequent period is dependent upon the magnitude of cash flows

in a preceding period Perfectly correlated cash flows might be expected to occur if a capital expenditure relates to the production of

a new product or the entrance of a product into a new market In such a case, consumer acceptance of the product in one period might

be expected to have a direct bearing an the level of sales in the following period.

Q24-15 If the periodic cash flows are neither

independent nor perfectly correlated, the variance of the net present value of a capital expenditure can be computed by (a) dividing the period cash flows into independent and dependent components; (b) computing the periodic variances for the independent cash flows and then discounting and summing to get the variance for the net present value of the independent cash flows; (c) computing the periodic variances for the dependent cash flows, taking the square root of each variance to get the periodic standard devia- tions, discounting and summing the periodic standard deviations, and squaring the total

to get the variance for the net present value

of the dependent cash flows; and (d) adding the variance for the net present value of the independent cash flows to the variance of the net present value of the dependent cash flows.

Q24-16 MADM stands for multi-attribute decision

model, and it is an expenditure evaluation tool that explicitly incorporates both quanti- tative and nonquantitative factors into the decision analysis Traditional economic eval- uation tools do not incorporate qualitative factors into the decision model, yet most of the benefits to be derived from investments

in new technologies are strategic and cult to quantify MADM attempts to remedy this problem by giving weight to noneco- nomic variables.

Volume Value Probability Value

E24-2

Cost to purchase thermocouplers:

Units needed annually (18,000 ÷ (1 – 10)) 20,000 Unit cost × $15 Total estimated cost if thermocouplers purchased $300,000 Weighted average unit cost (expected value) to manufacture thermocouplers:

Manufacturing yields an estimated savings of $26,300 ($300,000 – $273,700), subject to the accuracy of estimated data If data are accurate, manufacturing appears desirable; assuming that the savings represents an acceptable rate of return on additional invested capital, there is no better alternative use of limited available facilities and equipment, and quality and production schedule demands can be met.

Table of expected values of possible strategies (000s omitted):

Expected Purchases/Sales 100 120 140 180 Value

(2) The expected value of perfect information is the difference between the average

contribution margin using the best strategy (ordering 30,000 hot dogs) and the probabilities and average contribution margin if Wurst knew in advance what the sales level would be each Saturday.

Average contribution margin if Wurst knew sales level:

$2,000 × 1 $ 200

$4,000 × 2 800

$6,000 × 4 2,400

$8,000 × 3 2,400 $5,800 Average contribution margin using expected value

Contribution margin improved by $1,800

Since the contribution margin would be improved by $1,800, Wurst could afford

to pay up to $1,800 for “perfect” information.

E24-6

Prior Probability × Conditional Posterior

Since the expected value of not moving exceeds that of moving, the manager should not move the stereo store to the shopping mall ($42,000 > 40,000).

CGA-Canada (adapted) Reprint with permission.

Market demand increases (.3)

Market demand increases (.3) Market demand remains same (.5)

Market demand remains same (.5) Market demand declines (.2)

Market demand declines (.2)

$ 30,000

25,000

–5,000

$ 50,000 –10,000

The firm should make the sub-assembly rather than buy it because the expected value of making the sub-assembly is $26,000, which is greater than the expected value of buying ($24,500).

CGA-Canada (adapted) Reprint with permission.

High demand (.4)

High demand (.4) Medium demand (.3)

Medium demand (.3) Low demand (.3)

Expected Value

1 $300,000 expected profit – $10,000 cost of applying for rezoning.

2 $100,000 expected profit – $10,000 cost of applying for rezoning.

The land developer should bid on parcel B, and, if successful, apply for rezoning because the expected value of this alternative is greater than any other.

CGA-Canada (adapted) Reprint with permission.

Successful (.6)

Successful (.5) Unsuccessful (.4)

Unsuccessful (.5)

Unsuccessful (.2)

Apply

for Rezoning

Expected Value

for Rez oning

Expected net present value $ 1,775*

*The difference in the results is due to rounding in the present value tables.

σσ = 7 496 , units

Present

Standard deviation of NPV $3,791*

*The difference in the results is due to rounding in the present value tables.

Standard Deviation of NPV for

dependent cash flows $6,846.00

Variance of NPV for dependent cash flows = ($6,846) 2 = $46,867,716

Variance of NPV for independent cash flows $ 3,126,940

Variance of NPV for dependent cash flows 46,867,716

Variance of total NPV of investment $49,994,656

(1) The 95% confidence interval for the net present value is a range between a low

of –$20,000 ($30,000 expected NPV – (2 × $25,000 standard deviation)) and a high

of $80,000 ($30,000 expected NPV + (2 × $25,000 standard deviation)).

(2) There is a 88493 probability that the NPV of the investment will be positive, i.e.,

the 5 area above the mean plus the 38493 area below the mean (determined from the table of Z values in Exhibit 24-8 of the text for ( µµ – x) ÷ σσ = ($30,000

expected NPV – 0) ÷ $25,000 = 1.20 σσ).

Direct materials (60,000 units × $25) $1,500,000 Direct labor (60,000 units × $8.80 per

hour most likely rate × 2 hours) 1,056,000 Variable overhead (60,000 units ×

($.40 supplies + $.35 materials handling + $1.25 heat, light, and power)

× 2 hours) 240,000 Promotion fee (60,000 units × $6) 360,000 3,156,000 Contribution margin $2,844,000 Additional fixed costs:

Supervisor salary $ 28,000 Equipment lease rentals 150,000 178,000 Annual pretax advantage of introducing new

product $2,666,000

(2) Expected value approach:

Sales in Units Probability Expected Value 50,000 25 12,500

Supervisor salary $ 28,000 Equipment lease rentals 150,000 178,000 Expected annual pretax advantage $2,743,250

(3) In this situation, Monte Carlo simulation could be used A linear equation for the

net advantage would have to be developed that included the two variable items (sales volume and hourly direct labor costs) treated as independent stochastic variables The probability distributions for sales volume and hourly direct labor cost would be simulated and pairs of values would be selected for entry into the equation, using a random number generator The net pretax advantage would be calculated and recorded, and then a new set of values for the stochastic vari- ables would be determined and reentered into the equation A large number of iterations would be calculated and recorded to determine the approximate distribution of the net pretax advantage The distribution would have a calculat-

ed mean (which would be interpreted as the expected annual net pretax tage) and a standard deviation (which could be interpreted as a measure of the product’s risk).

Plan 2

Urban service calls (850 calls × 60% urban × $450 per call) $229,500 Rural service calls (850 calls × 40% rural × $350 per call) 119,000 Parts ($60 expected value per call × 850 calls) 51,000 Estimated total cost of Plan 2 $399,500

Plan 3

Employee salaries (9 employees × $24,000 average salary) $216,000 Employee fringe benefits ($216,000 employee wages × 35%) 75,600 Preventive maintenance parts (200 calls per employee ×

9 employees × $15 in parts per call) 27,000 Repair parts ((850 calls × (1 – 30%)) ×

($60 expected value per call × (1 – 20%))) 28,560 Estimated total cost of Plan 3 $347,160

Rejected During Assembly Rejected During Performance Testing

Hourly cost to = Direct labor + Variable overhead

Maximum amount Cost of rejections Cost of rejections

Number for quality = during assembly + during performance ×

of lots

= ($140 + $300) × (1,000,000 units ÷ 1,000 units per lot)

= $440,000

(

(

( (

(1) The payoff table of expected contribution margins for Kenton Clothiers’ shirt

order sizes follows:

Possible Actions Contribution Margin (Conditional Value) Contribution Margin

* 100 shirts at the regular $30 sales price × $7 CM per shirt = $700 CM

** (100 shirts at the regular $30 sales price × $8 CM per shirt) – (100 shirts at the

$15 reduced price × $7 loss per shirt) = $100 CM

*** (.12 probability × $(500)) + (.48 probability × $1,000) + (.36 probability × $2,500) + (.04 probability × $4,000) = $1,480 CM

(2) The best strategy for Kenton Clothiers would be to order 300 shirts each year

because it would result in the largest contribution margin over time The cient of variation for the best strategy (i.e., purchasing 300 shirts each year) is 615 determined as follows:

E

996 795

of variation