24
DISCUSSION CHAPTER QUESTIONS
Q24-1. Before making a decision under conditions of
uncertainty, a manager should try to assess the
probabilities associated with alternative possible outcomes in order to determine the probable 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 standard deviation for a probability distribution to
its expected value, thus allowing for differences in the relative size of different probability 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 simultaneous 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 probability of the occurrence of one event given that
another event has occurred (e.g., the probability of the occurrence of event A given that event
B has already occurred, denoted as P(AIB)). A
conditional probability implies that some relationship 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 decision. As a consequence, the revision of probabilities 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 outcomes.
Q24-8. In a discrete probability distribution, the possible outcomes are limited to certain finite values (e.g., 10, 11, 12, etc.). The number of
shipments, orders, units of product, etc. are
events that could be described adequately by
a discrete probability distribution. For convenience, the outcomes that occur in a discrete
probability distribution are often limited to a
fairly small number, but this need not necessarily be the case. In contrast, the possible
outcomes that may occur in a continuous
probability distribution are infinite even within
a limited range. Time, weight, volume, length,
temperature, and economic value are examples 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 seconds, 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,
$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 single event (the mode). Consequently, the
single best guess is also the expected
value.
24-1
24-2
Chapter 24
(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 normal distributions. This makes it possible to
determine the probability of the occurrence 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 contains 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 distribution. 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 outcomes 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 incorporated or not. Nevertheless, probability analysis 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 summing 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 interaction 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 companys weighted average cost of capital.
Q24-13. Cash flows are independent if the magnitude 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 magnitude 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 deviations, 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 quantitative and nonquantitative factors into the
decision analysis. Traditional economic evaluation 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 difficult to quantify. MADM attempts to remedy
this problem by giving weight to noneconomic variables.
24-2
Chapter 24
24-3
EXERCISES
E24-1
(1)
Monthly
Sales
Volume
3,000
6,000
9,000
12,000
15,000
(2)
xi
Income or
(Loss)
Conditional
Value
$(35,000)
5,000
30,000
50,000
70,000
P(xi)
Probability
.05
.15
.40
.30
.10
1.00
(1)
xi
E(x)
Income or
(Loss)
Expected
Value
$(1,750)
750
12,000
15,000
7,000
$33,000
(2)
(3)
(4)
2
(xi E(x))
(xi E(x))
P(xi)
Difference
Income
from
or (Loss)
Expected
Conditional
Value
Value
($33,000)
(2) Squared
Probability
$(35,000)
$(68,000)
$4,624,000,000
.05
5,000
(28,000)
784,000,000
.15
30,000
(3,000)
9,000,000
.40
50,000
17,000
289,000,000
.30
70,000
37,000
1,369,000,000
.10
Variance ...........................................................................
Standard deviation ( ) = $576,000,000 = $24, 000
Coefficient = Standard deviation( ) = $24, 000
of variation Expected value (E( x )) $33, 000 = .727
(5)
P(xi)(xi E(x))2
(3) (4)
$231,200,000
117,600,00
3,600,000
86,700,000
136,900,000
$576,000,000
24-4
E24-2
(1)
Chapter 24
(2)
Monthly
Sales
Volume
10,000
11,000
12,000
13,000
14,000
15,000
(2)
(1)
Unit
Contribution
Margin
$10
10
10
10
10
10
(3)
xi
Conditional
Value
(1) (2)
$100,000
110,000
120,000
130,000
140,000
150,000
(4)
P(xi)
Frequency
Based
Probability
9/60 = .15
15/60 = .25
18/60 = .30
9/60 = .15
6/60 = .10
3/60 = .05
60/60 = 1.00
(1)
xi
(5)
E(x)
Expected
Value
(3) (4)
$ 15,000
27,500
36,000
19,500
14,000
7,500
$119,500
(2)
(3)
(4)
(5)
(xi E(x))
(xi E(x))2
P(xi)
P(xi)(xi E(x))2
Deviation from
Conditional
$119,500
Value
Expected Value
(2) Squared
Probability
(3) (4)
$100,000
$(19,500)
$380,250,000
.15
$ 57,037,500
110,000
(9,500)
90,250,000
.25
22,562,500
120,000
500
250,000
.30
75,000
130,000
10,500
110,250,000
.15
16,537,500
140,000
20,500
420,250,000
.10
42,025,000
150,000
30,500
930,250,000
.05
46,512,500
2)..............................................................................
$184,750,000
Variance (
Standard deviation ( ) = Variance ( 2 ) = $184,750,000 = $13, 592
Standard deviation ( )
$13, 592
Coefficient
= .114
=
=
of variation Expected value (E( x )) $119, 500
Chapter 24
24-5
E24-3
Cost to purchase thermocouplers:
Units needed annually (18,000 (1 .10)) ........................................
Unit cost................................................................................................
Total estimated cost if thermocouplers purchased..........................
20,000
$15
$300,000
Weighted average unit cost (expected value) to manufacture thermocouplers:
Estimated
per Unit Variable
Cost
$10
12
14
16
Probability
.1
.3
.4
.2
Weighted Average
Unit Cost
(Expected Value)
$ 1.00
3.60
5.60
3.20
$13.40
Estimated variable manufacturing cost (18,000 units $13.40) ....
Additional fixed manufacturing cost ................................................
Total estimated cost if thermocouplers manufactured ...................
$241,200
32,500
$273,700
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.
24-6
Chapter 24
E24-4
Table of expected values of possible strategies (000s omitted):
Purchases/Sales
100
120
140
180
Probability
100
$25
15
5
(15)
.1
120
$25
40
301
10
.3
140
$25
40
55
35
.4
180
$25
40
55
85
.2
Expected
Value
$25.0
37.5
42.52
32.5
1Contribution
margin for ordering 140,000 units and selling 120,000 units:
Sales (120,000 $1.25) ........................................................................
Cost of units ($50,000 + (140,000 $.50)) .........................................
$150,000
120,000
$ 30,000
2Expected
value for purchasing 140,000 units:
$ 5 .1..................................................................................................
30 .3..................................................................................................
55 .4 .................................................................................................
55 .2..................................................................................................
$
.5
9.0
22.0
11.0
$42.5
Jessica Company should purchase 140,000 units for December, according to the expected
value decision model, because this number of units produces the largest expected
value, $42,500.
E24-5
(1)
Payoff table of expected values of possible strategies
Sales
Order
10,000
20,000
30,000
40,000
Probability
1Contribution
10,000
$2,000
(1,000)
(4,000)
(7,000)
20,000
$2,000
4,000
1,0001
(2,000)
5 50 = .1 10 50 = .2
30,000
$2,000
4,000
6,000
3,000
40,000
$2,000
4,000
6,000
8,000
Expected
Contribution
Margin
$2,000
3,500
4,0002
2,500
20 50 = .4 15 50 = .3
margin for ordering 30,000 hot dogs and selling 20,000 hot dogs:
Sales (20,000 $.50) ............................................................................
$10,000
Cost of hot dogs (30,000 $.30) ........................................................
9,000
Contribution margin.............................................................................
$ 1,000
Chapter 24
24-7
E24-5 (Concluded)
2Expected
contribution margin for ordering 30,000 hot dogs:
$(4,000) .1.....................................................................................
$ 1,000 .2 ....................................................................................
$ 6,000 .4 ....................................................................................
$ 6,000 .3 ....................................................................................
Expected value.....................................................................................
(2)
$ (400)
200
2,400
1,800
$4,000
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........................................................
$4,000 .2........................................................
$6,000 .4........................................................
$8,000 .3........................................................
Average contribution margin using expected value
decision rule to determine best strategy (from 1)
Contribution margin improved by...............................
$ 200
800
2,400
2,400
$5,800
4,000
$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
(1)
Demand
30,000
40,000
50,000
60,000
(2)
Prior
Probability
.10
.10
.50
.30
1.00
(3)
Conditional
Probability
.20
.50
.20
.10
1.00
(4)
Prior
Probability
Conditional
Probability
(2) (3)
.02
.05
.10
.03
.20
(5)
Posterior
Probability
(4) (4) Total
.10
.25
.50
.15
1.00
Chapter 15
24-8
E24-7
Payoffs
Expected
Value
$100,000
$ 30,000
Market demand remains same (.5)
50,000
25,000
Market demand declines (.2)
25,000
Market demand increases (.3)
$40,000
Moving cost
Move to
Mall
5,000
$ 50,000
10,000
$ 40,000
Do not
move
Market demand increases (.3)
80,000
$ 24,000
Market demand remains same (.5)
40,000
20,000
Market demand declines (.2)
10,000
$42,000
2,000
$ 42,000
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.
Chapter 24
24-9
E24-8
Payoffs
Expected
Value
$ 50,000
$ 20,000
Medium demand (.3)
30,000
9,000
Low demand (.3)
10,000
3,000
High demand (.4)
$26,000
$ 26,000
Make
Buy
High demand (.4)
35,000
$ 14,000
Medium demand (.3)
30,000
9,000
Low demand (.3)
5,000
$24,500
1,500
$ 24,500
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.
24-10
Chapter 24
E24-9
Expected
Payoff
Successful (.6)
Expected
Value
$ 200,000
$ 120,000
0
0
$120,000
el
A
Unsuccessful (.4)
Bi
d
on
Pa
rc
$ 120,000
Successful (.5)
$ 290,0001
$ 145,000
lB
90,000 2
45,000
pl
y
fo
r
Unsuccessful (.5)
$190,000
Successful (.8)
$ 190,000
Ap
arce
on P
Re
Bid
zo
n
in
g
$190,000
Do
No
or
ly f
pp
tA
$152,000
ing
zon
Re
$ 100,000
Unsuccessful (.2)
1$300,000
2$100,000
$ 100,000
$
$
0
0
expected profit $10,000 cost of applying for rezoning.
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.
Chapter 24
24-11
E24-10
55,000 units 45,000 units 10, 000 units
= 7, 496 units
=
(.667 2)
1.334
(1)
=
(2)
$193, 750 fixed cos t
= 38, 750 units to breakeven
$5 CM per unit
50, 000 units at mean 38, 750 units to breakeven
= 1 .5
7, 496 units in s tan dard deviation
The probability of making a profit is equal to the area under the normal curve
above the breakeven point, which is approximately 93% (.43 for the area between
the breakeven point and the mean, which is the area for an interval of 1.5 standard deviations from the mean found in Exhibit 24-8 of the textbook, plus .50 for
the area above the mean).
E24-11
(1)
(2)
(3)
(4)
Expected Value
Present Value
of After-Tax
Present
of Expected
Net Cash
Value
After-Tax
(Outflow)
of $1
Net Cash Flow
Year
Inflow
@10%
(2) (3)
0
$(20,000)
1.000
$(20,000)
1
5,000
.909
4,545
2
5,000
.826
4,130
3
5,000
.751
3,755
4
5,000
.683
3,415
5
5,000
.621
3,105
6
5,000
.564
2,820
Expected net present value.............................
$ 1,770
OR
(1)
(2)
(3)
(4)
Expected Value
Present
Present Value
of After-Tax
Value of
of Expected
Net Cash
Annuity
After-Tax
(Outflow)
of $1
Net Cash Flow
Year
Inflow
@10%
(2) (3)
0
$(20,000)
1.000
$(20,000)
1 6
5,000
4.355
21,775
Expected net present value.............................
$ 1,775*
*The difference in the results is due to rounding in the present value tables.
24-12
E24-12
(1)
Chapter 24
(2)
(3)
(4)
(5)
Present
Value of
Periodic
Present
Periodic
$1 at 12%
Standard
Value of
Variance
Squared
Year
Deviation
$1@12%
(2) (2)
(3) (3)
0
0
1.000
0
1.000000
1
$500
.893
$250,000
.797449
2
500
.797
250,000
.635209
3
500
.712
250,000
.506944
4
500
.636
250,000
.404496
5
500
.567
250,000
.321489
6
500
.507
250,000
.257049
7
500
.452
250,000
.204304
8
500
.404
250,000
.163216
Variance of net present value .....................................................
(6)
Present
Value of
Variance
(4) (5)
0.00
$199,362.25
158,802.25
126,736.00
101,124.00
80,372.25
64,262.25
51,076.00
40,804.00
$822,539.00
Standard deviation of net present value = $822, 539 = $906.94
E24-13
(1)
(2)
Periodic
Standard
Year
Deviation
0
0
1
$1,000
2
1,000
3
1,000
4
1,000
5
1,000
Standard deviation
(3)
(4)
Present Value
Present
of Standard
Value of
Deviation
$1 @ 10%
(2) (3)
1.000
0
.909
$909
.826
826
.751
751
.683
683
.621
621
of NPV .................... $3,790
OR
(1)
(2)
Periodic
Standard
Year
Deviation
0
0
1-5
$1,000
Standard deviation
(3)
(4)
Present
Present Value
Value of
of Standard
Annuity of
Deviation
$1@ 10%
(2) (3)
1.000
0
3.791
$3,791
of NPV .................... $3,791*
*The difference in the results is due to rounding in the present value tables.
Chapter 24
24-13
E24-14
(1)
(2)
(3)
(4)
(5)
Periodic
Present
Standard
Value of
Deviation of
Present
Periodic
$1 at 12%
Independent Value of
Variance
Squared
Year
Cash Flow
$1@12%
(2) (2)
(3) (3)
0
0
1.000
0
1.000000
1
$1,000
.893
$1,000,000
.797449
2
1,000
.797
1,000,000
.635209
3
1,000
.712
1,000,000
.506944
4
1,000
.636
1,000,000
.404496
5
1,000
.567
1,000,000
.321489
6
1,000
.507
1,000,000
.257049
7
1,000
.452
1,000,000
.204304
Variance of NPV for independent cash flows..........................
(1)
(2)
(3)
Periodic
Present
Standard
Value of
Year
Deviation
$1 @ 10%
0
0
1.000
1
$1,500
.893
2
1,500
.797
3
1,500
.712
4
1,500
.636
5
1,500
.567
6
1,500
.507
7
1,500
.452
Standard Deviation of NPV for
dependent cash flows ......................
(6)
Present
Value of
Variance
(4) (5)
0.00
$797,449
635,209
506,944
404,496
321,489
257,049
204,304
$3,126,940
(4)
Present Value
of Standard
Deviation
(2) (3)
0.00
$1,339.50
1,195.50
1,068.00
954.00
850.50
760.50
678.00
$6,846.00
Variance of NPV for dependent cash flows = ($6,846)2 = $46,867,716
Variance of NPV for independent cash flows ............
Variance of NPV for dependent cash flows................
Variance of total NPV of investment ...........................
$ 3,126,940
46,867,716
$49,994,656
Standard deviation of total NPV of investment = $49, 994, 656 = $7, 070.69
.
24-14
Chapter 24
E24-15
(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 ( x) = ($30,000
expected NPV 0) $25,000 = 1.20).
Chapter 24
24-15
PROBLEMS
P24-1
(1)
Deterministic approach:
Sales (60,000 units most likely sales volume
$100) .................................................................
Variable costs:
Direct materials (60,000 units $25) .................
Direct labor (60,000 units $8.80 per
hour most likely rate 2 hours)................
Variable overhead (60,000 units
($.40 supplies + $.35 materials
handling + $1.25 heat, light, and power)
2 hours) ....................................................
Promotion fee (60,000 units $6) ......................
Contribution margin .....................................................
Additional fixed costs:
Supervisor salary ................................................
Equipment lease rentals .....................................
Annual pretax advantage of introducing new
product .................................................................
(2)
Expected value approach:
Sales in Units
50,000
60,000
70,000
80,000
Labor Hour Rate
$8.50
8.80
9.00
$6,000,000
$1,500,000
1,056,000
240,000
360,000
$
28,000
150,000
Probability
.25
.45
.20
.10
Expected Value
12,500
27,000
14,000
8,000
61,500
Probability
.30
.50
.20
Expected Value
$2.55
4.40
1.80
$8.75
3,156,000
$2,844,000
178,000
$2,666,000
24-16
Chapter 24
P24-1 (Concluded)
Sales (61,500 expected value $100).........................
Variable costs:
Direct materials (61,500 units $25) .................
Direct labor (61,500 units $8.75
expected value 2 hours) ........................
Variable overhead (61,500 $2 per labor
hour 2 hours) ...........................................
Promotion fee (61,500 units $6) ......................
Contribution margin .....................................................
Additional fixed costs:
Supervisor salary ................................................
Equipment lease rentals .....................................
Expected annual pretax advantage ............................
(3)
$6,150,000
$1,537,500
1,076,250
246,000
369,000
$
28,000
150,000
3,228,750
$2,921,250
178,000
$2,743,250
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 variables 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 mean calculated (which would be interpreted as the expected annual net pretax advantage) and a standard deviation (which could be interpreted as a measure of the
products risk).
Chapter 24
24-17
P24-2
Video Recreation Inc. should adopt Plan 3 because it results in the least cost of the
three alternatives as demonstrated below:
Number of
Service Calls
400
700
900
1,200
Parts Cost
Per Repair
$30
40
60
90
Probability
.1
.3
.4
.2
1.0
Frequency
.15
.15
.45
.25
1.00
Expected
Number
of Calls
40
210
360
240
850
=
=
Expected
Value of
Parts Cost
$ 4.50
6.00
27.00
22.50
$60.00
Plan 1
Vendor fees (6 vendors $15,000 fee per vendor)...........................
Service calls (850 calls $250 per call) ............................................
Parts ($60 expected value per call 850 calls (1 + 10% markup))
Estimated total cost of Plan 1 ............................................................
$ 90,000
212,500
56,100
$358,600
Urban service calls (850 calls 60% urban $450 per call) ..........
Rural service calls (850 calls 40% rural $350 per call) .............
Parts ($60 expected value per call 850 calls).................................
Estimated total cost of Plan 2 ............................................................
$229,500
119,000
51,000
$399,500
Employee salaries (9 employees $24,000 average salary) ...........
Employee fringe benefits ($216,000 employee wages 35%) ........
Preventive maintenance parts (200 calls per employee
9 employees $15 in parts per call) ........................................
Repair parts ((850 calls (1 30%))
($60 expected value per call (1 20%)))................................
Estimated total cost of Plan 3 ............................................................
$216,000
75,600
Plan 2
Plan 3
27,000
28,560
$347,160
24-18
Chapter 24
P24-3
Expected Value of Bearings
Rejected During Assembly
Expected
Quantity Probability
Value
100
.50
50.0
60
.25
15.0
30
.15
4.5
5
.10
0.5
70.0
(
Cost to
replace each
bearing
$20 per hour
$140
$300
(
((
1 hour
(
((
=
(
=
Cost of rejections
Cost of rejections
during assembly
+ during performance
per lot
testing per lot
($140 + $300) (1,000,000 units 1,000 units per lot)
=
$440,000
=
(
Cost to
replace each
bearing
$20 per hour
(Number
of lots
(
Expected value of
bearings rejected
during performance
testing
15
(
(
=
Maximum amount
for quality
control program
Replacement
time per
unit
(
Replacement
time per
unit
6 / 60 hour
(
Cost of rejections
during performance
=
testing per lot
(
=
(
(
=
Expected value of
bearings rejected
during assembly
70
(
(
(1.5)($8)
$20
=
overhead
(Variableper hour
cost
+
($8)
=
Cost of rejections
during assembly
per lot
+
(
Direct
( cost perlabor
hour
(
=
=
Hourly cost to
replace bearing
Expected Value of Bearings
Rejected During Performance Testing
Expected
Quantity
Probability
Value
20
.40
8.0
15
.30
4.5
10
.20
2.0
5
.10
0.5
15.0
Chapter 24
24-19
P24-4
(1)
The payoff table of expected contribution margins for Kenton Clothiers shirt
order sizes follows:
Possible Actions Contribution Margin (Conditional Value)
Contribution Margin
(Quantities to
for Possible Sales Quantities
(Expected Value of
be Ordered)
100
200
300
400
Each Strategy)
100
$ 700*
$ 700
$ 700
$ 700
$ 700
200
100**
1,600
1,600
1,600
1,420
300
(300)
1,200
2,700
2,700
1,620
400
(500)
1,000
2,500
4,000
1,480***
Probability 3/25 = .12
12/25 = .48
9/25 = .36 1/25 = .04
* 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 coefficient of variation for the best strategy (i.e., purchasing 300 shirts each year) is
.615 determined as follows:
(1)
xi
(2)
(3)
(4)
(5)
(xi E(x))
(xi E(x))2
P(xi)
P(xi)(xi E(x))2
Deviation from
Conditional
$1,620
Columns
2
Probability
(3) (4)
Value
Expected Value
Col. (2)
$ (300)
$1,920
$3,686,400
.12
$442,368
1,200
(420)
176,400
.48
84,672
2,700
1,080
1,166,400
.36
419,904
2,700
1,080
1,166,400
.04
46,656
2) .................................................................................
$993,600
Variance (
Standard deviation ( ) = Variance ( )2 = $993, 600 = $996.795
Standard Deviation ( ) $996.795
Coefficient
= .615
=
=
of variation Expected Value (E( ))
$1, 620
24-20
Chapter 24
P24-4 (Concluded)
(3)
The expected value of perfect information is $364 determined as follows:
Average contribution if Kenton Clothiers knew sales in advance and ordered just
enough to meet sales demand:
CM Per
Quantity
Unit Sold
Total CM
Probability
100
$7
$ 700
.12
200
8
1,600
.48
300
9
2,700
.36
400
10
4,000
.04
Expected value with perfect information ..............................
Less expected value of best strategy under uncertainty
(ordering 300 shirts from requirement (1) above)..........
Expected value of perfect information...................................
Expected
Value
$
84
768
972
160
$ 1,984
1,620
$ 364
P24-5
(1)
Events
1,600
2,000
2,400
2,800
(1)
Prior
Probability
.20
.50
.20
.10
1.00
(2)
Conditional
Probability
.25
.25
.75
.75
(3)
(1) (2)
.050
.125
.150
.075
.400
(4)
Posterior
Probability
.1250
.3125
.3750
.1875
1.0000
(2)
Actions
Events (House Size Most in Demand)
Size To
Build
1,600
2,000
2,400
2,800
1,600
$200,000
$180,000
$160,000
$140,000
2,000
160,000
400,000
360,000
320,000
2,400
120,000
320,000
600,000
540,000
2,800
80,000
240,000
480,000
800,000
Posterior
probability .1250
.3125
.3750
.1875
Expected
Value
$167,500
340,000
441,250
415,000
Gant should be advised to build the 2,400 square-foot houses on the tract of
land because that course of action has the highest expected value.
Chapter 24
24-21
P24-6
(1)
Expected value of outside printers offer:
Enrollments
25,000
26,000
27,000
28,000
29,000
Probability
.05
.15
.40
.25
.15
1.00
Fees to be paid to the outside printer:
Fixed fee..........................................................
Variable fee ((27,300 25,000) $15) ...........
Savings available from closing Printing Department:
Lease income from renting equipment............
Avoidable fixed costs:
Salaries and benefits ($160,000
110%)................................
$176,000
Less cost of part-time
clerk ($16,000 110%
3/5 week) .............................
(10,560)
Less employee severance pay
(($160,000 $16,000)
12 months) ..........................
(12,000)
Telephone
($4,000 ($80 12 months))..................
Occupancy and administration
($10,800 + $7,300) ...................................
Avoidable variable costs:
Materials, supplies, and postage
((($165,100 26,000) $1) 27,300)
Increase in total costs from acceptance of
printers offer......................................................
Expected
Value
1,250
3,900
10,800
7,000
4,350
27,300
$325,000
34,500
$359,500
$ 33,000
153,440
3,040
18,100
146,055
353,635
$
5,865
In this case, the outside printers offer should not be accepted because the total
costs would increase by $5,865.
24-22
Chapter 24
P24-6 (Concluded)
(2)
Revised expected value of outside printers offer:
(1)
(2)
(3)
Enrollments
25,000
26,000
27,000
28,000
29,000
Prior
Probability
.05
.15
.40
.25
.15
1.00
Conditional
Probability
.90
.90
.10
.10
.10
(1) (2)
.045
.135
.040
.025
.015
.260
(4)
(5)
Revised
Posterior
Expected
Probability
Value
.045 .260 = .173
4,325
.135 .260 = .519 13,494
.040 .260 = .154
4,158
.025 .260 = .096
2,688
.015 .260 = .058
1,682
1.000 26,347
Fees to be paid to the outside printer:
Fixed fee ..............................................................................
Variable fee ((26,347 25,000) $15)................................
Savings available from closing Printing Department:
Lease income from renting equipment ............................
Avoidable fixed costs:
Salaries and benefits ($160,000
110%) ...............................................
$176,000
Less cost of part-time clerk
($16,000 110%
3/5 week) .....................................
(10,560)
Less employee severance pay
(($160,000 $16,000)
12 months) ...............................
(12,000)
Telephone and telegraph
($4,000 ($80 12 months))..................................
Occupancy and administration
($10,800 + $7,300) ..................................................
Avoidable variable costs:
Materials, supplies, and postage
((($165,100 26,000) $1) 26,347) .....................
Decrease in total costs from acceptance of
printers offer.......................................................................
$325,000
20,205
$345,205
$ 33,000
153,440
3,040
18,100
140,956
348,536
$ (3,331)
Considering the new information, the outside printers offer should be accepted
because the total costs would decrease by $3,331.
Chapter 24
24-23
P24-7
The tests should be administered because the expected value is $115 per applicant greater than the case where no test is administered ($1,015 $900).
Payoffs
Satisfactory (.7)
$ 2,500
1
Expected
Value
$ 1,750
$1,600
Abbreviated Training (.9)
$1,420 4
Unsatisfactory (.3)
Acceptable
Score
150
200
Not hired (.1)
500
$ 1,600
(.75)
$1,015 5
Test
(.75)
Unacceptable
Score
Satisfactory (.2)
Full training (.1)
Full training
$ 900
440
800
640
$ 200
$ 2,400
3
$ 1,200
$ 900
Unsatisfactory (.5)
Not hired
$
200
Not hired (.9)
Satisfactory (.5)
No
Test
2
$ 200
Unsatisfactory (.8)
$ 200
$ 2,200
600
0
300
$
900
24-24
Chapter 24
P24-7 (Concluded)
1Successful
hire salary savings ................
Less costs:
Testing....................................................
Abbreviated training ............................
Payoff .........................................................
2Successful
$200
300
hire salary savings .................
Less costs:
Testing ...................................................
Full training............................................
Payoff .........................................................
3Successful
$3,000
hire salary savings .................
Less full training cost.................................
Payoff .........................................................
500
$2,500
$3,000
$200
600
800
$2,200
$3,000
600
$2,400
4Expected
$1,440
20
$1,420
5Expected
$1,065
50
$1,015
value of abbreviated training ................................ $1,600 .9 =
Expected value of not hiring ...................................................
200 .1 =
Expected value when test score acceptable ...................................................
value of acceptable test score ............................... $1,420 .75 =
Expected value of unacceptable test score...........................
200 .25=
Expected value of administering test ..............................................................
Chapter 24
24-25
P24-8
Sales
Price
$5.25
5.25
5.25
5.25
5.00
5.00
5.00
5.00
Material
Lot Size
200,000
200,000
240,000
240,000
200,000
200,000
240,000
240,000
State of
Economy
Weak
Strong
Weak
Strong
Weak
Strong
Weak
Strong
Sales
Demand
180,000
200,000
180,000
200,000
200,000
240,000
200,000
240,000
Expected Payoff
($5.25 180,000) ($3 200,000) = $345,000
($5.25 200,000) ($3 200,000) = $450,000
($5.25 180,000) ($2.90 240,000) = $249,000
($5.25 200,000) ($2.90 240,000) = $354,000
($5 200,000) ($3 200,000) = $400,000
($5 200,000) ($3 200,000) = $400,000
($5 200,000) ($2.90 240,000) = $304,000
($5 240,000) ($2.90 240,000) = $504,000
Payoffs
Weak economy (.6)
$345,000
$ 207,000
Strong economy (.4)
450,000
180,000
$ 387,000
Weak economy (.6)
249,000
$ 149,400
Strong economy (.4)
354,000
141,600
$ 291,000
Weak economy (.6)
400,000
$ 240,000
Strong economy (.4)
400,000
160,000
$ 400,000
Weak economy (.6)
304,000
$ 182,400
Strong economy (.4)
Order 200,000
Expected
Value
504,000
201,600
$ 384,000
$387,000
$387,000
Select
$5.25
Sales
Price
Select
$5.00
Sales
Price
Order 240,000
Order 200,000
$291,000
$400,000
$400,000
Order 240,000
$384,000
Slick Inc. should set the sales price at $5.00 per unit and order 200,000 units of material, because this course of action will result in the greatest expected value ($400,000
contribution margin).
24-26
Chapter 24
P24-9
(1)
Expected
Payoff
Do Not Introduce
Expected
Value
$ 500,000
$ 500,000
$2,300,000
$900,000 1
y1
teg
ra
St
ign
pa
am
2
$ 2,800,000
$ 2,500,000
3
500,000
$ 2,300,000
$2,300,000
)
(.5
ful
ss
ce
uc
tS
No
st
Te
Unsuccessful (.2)
Do Not Introduce
$ 500,000
Te
s
tC
$ 3,500,000
t
uc
Te
st
od
Pr
Su
cc
es
s
ew
eN
ful
uc
(.5
)
rod
Int
Successful (.8)
$ 500,000
$1,000,000
ew
eN
uc
rod
Int
$
3,500,000
700,000
t
e
id
uc
nw
od
tio
Pr
Na
Successful (.2)
Pr
ot
om
$ 1,300,000
n
io
Unsuccessful (.8)
2,000,000
$ 1,300,000
2,500,000
No
n
ig
pa
am
tC
s
Te
gy
te
ra
St
2
$ 1,000,000
Successful (.5)
Unsuccessful (.5)
1 $2,300,000
500,000
2Successful
$ 4,000,000
4
$ 2,000,000
2,000,000
5
1,000,000
$ 1,000,000
.5 = $1,150,000
.5 =
250,000
$ 900,000
with test = ($40 $30 $6 $.5) million = $3.5 million
with test = ($16 $12 $6 $.5) million = $ 2.5 million
4Successful without test = ($40 $30 $6) million = $4 million
5Unsuccessful without test = ($16 $12 $6) million = $ 2 million
3Unsuccessful
Chapter 24
24-27
P24-9 (Concluded)
(2)
If the probability estimates can be relied upon, management should conduct the
nationwide promotion and distribution without first performing a test campaign
because the expected value of Strategy 2 is $100,000 greater than the expected
value of Strategy 1.
(3)
Criticism of the expected value decision criterion would include:
(a) Selection of the probabilities associated with the possible outcomes for the
alternative strategies is a subjective process. If the probability estimates are
biased, the expected values will be biased.
(b) The values for the alternative courses of action are estimates that could be
inaccurate.
(c) The decision model does not incorporate psychological factors. For
instance, people are often risk averse, and personal evaluations will not necessarily coincide with monetary evaluations.
(d) A model is often overly simplified to make it manageable and may consequently leave out important considerations or assumptions.
24-28
Chapter 24
P24-10
(1)
Expected value of periodic cash flows:
(1)
(2)
(3)
Expected
Expected
Value of
Value of
Annual cash
Annual
Contribution
Inflow
Sales
Margin
From Sales
in Units
Per Unit
(1) (2)
4,000
$14
$56,000
(1)
(2)
Year
1
2
3
4
5
6
7
8
9
10
Tax Basis
(Cost)
$200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
(1)
(2)
(3)
Year
0
1
2
3
4
5
6
7
8
9
10
Expected
Value of
Pretax Net
Cash Flow
$(200,000)
47,900
47,900
47,900
47,900
47,900
47,900
47,900
47,900
47,900
47,900
Tax
Depreciation
0
$28,600
49,000
35,000
25,000
17,800
17,800
17,800
9,000
0
0
(3)
Tax
Depreciation
Rate
.143
.245
.175
.125
.089
.089
.089
.045
.000
.000
(4)
Expected
Value of
Taxable
Income
(2) (3)
0
$19,300
(1,100)
12,900
22,900
30,100
30,100
30,100
38,900
47,900
47,900
(4)
Annual
Fixed
Cash
Outflow
$8,100
(5)
Expected
Value of
Annual
Pretax Net
Cash Inflow
(3) (4)
$47,900
(4)
Annual
Tax
Depreciation
$ 28,600
49,000
35,000
25,000
17,800
17,800
17,800
9,000
0
0
$200,000
(5)
Expected
Value
of Tax
Liability
(4) 40%
0
$ 7,720
(440)
5,160
9,160
12,040
12,040
12,040
15,560
19,160
19,160
(6)
Expected
Value of
After-Tax Net
Cash Flow
(2) (5)
$(200,000)
40,180
48,340
42,740
38,740
35,860
35,860
35,860
32,340
28,740
28,740
$ 167,400
Chapter 24
24-29
P24-10 (Continued)
Expected value of the periodic standard deviation:
(1)
Standard
Deviation
in Units
of Sales
1,750
(2)
(2)
Pretax
Cash Flow
per Unit
$14
(3)
Pretax
Cash Flow
Value of
Standard
Deviation
(1) (2)
$24,500
(4)
After-Tax
Portion
(1 40%)
60%
Expected net present value of investment:
(1)
(2)
(3)
(4)
Expected
Present
Value of
Present
Value of
After-Tax Net
Value of
After-Tax Net
Year
Cash Flow
$1 at 12%
Cash Flow
0
$(200,000)
1.000
$ (200,000)
1
40,180
.893
35,881
2
48,340
.797
38,527
3
42,740
.712
30,431
4
38,740
.636
24,639
5
35,860
.567
20,333
6
35,860
.507
18,181
7
35,860
.452
16,209
8
32,340
.404
13,065
9
28,740
.361
10,375
10
28,740
.322
9,254
Expected net present value ................................... $ 16,895
(5)
After-Tax
Cash Flow
Value of
Standard
Deviation
(3) (4)
$14,700
24-30
Chapter 24
P24-10 (Concluded)
(3)
Variance and standard deviation of expected net present value:
(1)
(2)
(3)
(4)
(5)
(6)
Present
Value of
Present
Periodic
Periodic
Present
$1 at 12%
Value of
Standard
Variance
Value of
Squared
Variance
$1 at 12%
Col. (4)2
(3) (5)
Year
Deviation
Col. (2)2
0
0
0
1.000
1.000000
0
1
$14,700
$216,090,000
.893
.797449 $172,320,754
2
14,700
216,090,000
.797
.635209
137,262,313
3
14,700
216,090,000
.712
.506944
109,545,529
4
14,700
216,090,000
.636
.404496
87,407,541
5
14,700
216,090,000
.567
.321489
69,470,558
6
14,700
216,090,000
.507
.257049
55,545,718
7
14,700
216,090,000
.452
.204304
44,148,051
8
14,700
216,090,000
.404
.163216
35,269,345
9
14,700
216,090,000
.361
.130321
28,161,065
10
14,700
216,090,000
.322
.103684
22,405,076
Variance of net present value.............................................
$761,535,950
Standard deviation
Variance of net
= present value = $761, 535, 950 = $27, 596
of net present value
(4)
$27, 596
Standard deviation
Coefficient =
=
= 1.633
of variation
Expected net present value $16, 895
(5)
The probability that the net present value will exceed zero is approximately 73%,
i.e., the 50% area under the curve that is above the mean plus the approximately
23% area under the curve that is below the mean but above zero (determined
from the table of Z values in Exhibit 24-8 of the text for ( X) = ($16,895 0)
$27,596 = .61, which is about 23% of the total area under the normal curve).
Chapter 24
24-31
P24-11
(1)
Expected value of periodic cash flows:
(1)
(2)
(3)
Contribution
Expected
Expected
Margin per
Value of
Value of
Unit (Cash
Annual Cash
Annual
Inflow Net
Inflow
Sales
of Outflow
From Sales
in Units
per Unit)
(1) (2)
5,000
$18
$90,000
(1)
(2)
Year
1
2
3
4
5
6
7
8
Tax Basis
(Cost)
$180,000
180,000
180,000
180,000
180,000
180,000
180,000
180,000
(3)
Tax
Depreciation
Rate
.143
.245
.175
.125
.089
.089
.089
.045
(1)
(2)
(3)
Year
0
1
2
3
4
5
6
7
8
Expected
Value of
Pretax Net
Cash Flow
$(180,000)
80,000
80,000
80,000
80,000
80,000
80,000
80,000
80,000
Tax
Depreciation
0
$25,740
44,100
31,500
22,500
16,020
16,020
16,020
8,100
(4)
Expected
Value of
Taxable
Income
(2) (3)
0
$54,260
35,900
48,500
57,500
63,980
63,980
63,980
71,900
(4)
Annual
Fixed
Cash
Outflow
$10,000
(5)
Expected
Value of
Annual
Pretax Net
Cash Inflow
(3) (4)
$80,000
(4)
Tax
Depreciation
$ 25,740
44,100
31,500
22,500
16,020
16,020
16,020
8,100
$180,000
(5)
Expected
Value of
Tax
Liability
(4) 40%
0
$21,704
14,360
19,400
23,000
25,592
25,592
25,592
28,760
(6)
Expected
Value of
After-Tax Net
Cash Flow
(2) (5)
$ (180,000)
58,296
65,640
60,600
57,000
54,408
54,408
54,408
51,240
$ 276,000
24-32
Chapter 24
P24-11 (Continued)
Expected value of the periodic standard deviation:
(1)
Standard
Deviation
in Units
of Sales
2,000
(2)
(2)
Pretax
Cash Flow
per Unit
$18
(3)
Pretax
Cash Flow
Value of
Standard
Deviation
(1) (2)
$36,000
(4)
After-Tax
Portion
(1 40%)
.6
Expected net present value of investment:
(1)
(2)
(3)
Expected
Value of
Present
After-Tax Net
Value of
Year
Cash Flow
$1 at 12%
0
$(180,000)
1.000
1
58,296
.893
2
65,640
.797
3
60,600
.712
4
57,000
.636
5
54,408
.567
6
54,408
.507
7
54,408
.452
8
51,240
.404
Expected net present value.................................
(4)
Present
Value of
After-Tax Net
Cash Flow
$ (180,000)
52,058
52,315
43,147
36,252
30,849
27,585
24,592
20,701
$ 107,499
(5)
After-Tax
Cash Flow
Value of
Standard
Deviation
(3) (4)
$21,600
Chapter 24
24-33
P24-11 (Concluded)
(3)
Standard deviation of expected net present value:
(1)
(2)
(3)
Periodic
Present
Standard
Value of
Year
Deviation
$1 at 12%
0
0
1.000
1
$21,600
.893
2
21,600
.797
3
21,600
.712
4
21,600
.636
5
21,600
.567
6
21,600
.507
7
21,600
.452
8
21,600
.404
Standard deviation of net
present value .....................................................
(4)
Present
Value of
Standard
Deviation
(2) (3)
0
$ 19,289
17,215
15,379
13,738
12,247
10,951
9,763
8,726
$107,308
(4)
Standard deviation
$107, 308
Coefficient =
=
= .998
of variation Expected net present value $107, 499
(5)
The probability that the net present value will exceed zero is approximately 84%,
i.e., the 50% area under the curve that is above the mean plus the 34% area under
the curve that is below the mean but above zero (determined from the table of Z
values in Exhibit 24-8 of the text for ( X) = ($107,499 0) $107,308 = 1.0,
which is about 34% of the total area under the normal curve.)
24-34
Chapter 24
P24-12
(1) Expected net present value of mixed cash flows:
(1)
(2)
(3)
(4)
(5)
(6)
Present
Expected
Expected
Total
Value of
Independent Dependent
Expected
Expected
After-Tax
After-Tax After-Tax Net
After-Tax Net
Net Cash
Net Cash
Cash Inflow
Present
Cash Inflow
Inflow
Inflow
(Outflow)
Value of
(Outflow)
Year
70%
30%
(2) + (3)
$1 at 10%
(4) (5)
0
$(30,000)
1.000
$ (30,000)
1
$5,600
$2,400
8,000
.909
7,272
2
7,700
3,300
11,000
.826
9,086
3
7,000
3,000
10,000
.751
7,510
4
6,300
2,700
9,000
.683
6,147
5
4,900
2,100
7,000
.621
4,347
Expected net present value ...............................................................
$ 4,362
(2) Variance and standard deviation of expected net present value:
(1)
(2)
(3)
(4)
(5)
Independent Independent
Present
Cash Flow
Cash Flow
Value of
Periodic
Periodic
Present
$1 at 10%
Standard
Variance
Value of
Squared
2
$1 at 10%
Col. (4)2
Year
Deviation
Col. (2)
0
0
0
1.000
1.000000
1
$1,000
$1,000,000
.909
.826281
2
1,000
1,000,000
.826
.682276
3
1,000
1,000,000
.751
.564001
4
1,000
1,000,000
.683
.466489
5
1,000
1,000,000
.621
.385641
Variance of expected NPV for independent cash flows...................
(6)
Present
Value of
Variance
(3) (5)
0
$ 826,281
682,276
564,001
466,489
385,641
$2,924,688
Chapter 24
24-35
P24-12 (Concluded)
(2)
(3)
Dependent
Cash Flow
Periodic
Present
Standard
Value of
Year
Deviation
$1 at 10%
0
0
1.000
1
$500
.909
2
500
.826
3
500
.751
4
500
.683
5
500
.621
Standard deviation of NPV ..................................
Variance of net
present value for
dependent cash flows
=
(
(4)
Present
Value of
Standard
Deviation
(2) (3)
0
$ 455
413
376
342
311
$1,897
Standard deviation of
net present value for
dependent cash flows
=
($1,897)2
(
(1)
2
=
Variance of NPV for dependent cash flows ..................................
Variance of NPV for independent cash flows ...............................
Variance of total NPV of investment..............................................
Standard deviation of
total net present value
$3,598,609
$3,598,609
2,924,688
$6,523,297
Variance of total
= net present value
= $6, 523, 297
= $2, 554
(3)
Standard deviation
$2, 554
Coefficient =
=
= 0.586
of variation
Expected net present value $4, 362
(4)
The probability that the net present value will exceed zero is approximately 96%,
i.e., the 50% area under the curve that is above the mean plus the approximately
46% area under the curve that is below the mean but above zero (determined
from the table of Z values in Exhibit 24-8 of the text for ( X) = ($4,362 0)
$2,554 = 1.71, which is about 46% of the total area under the normal curve.)
Factors
Net present value ....................................
Reduce setup time...................................
Reduce throughput time .........................
Improve product quality ..........................
Reduce inventory levels .........................
Improve image to outsiders ....................
Total...........................................................
Relative
Importance
Weighting
30
20
15
15
10
10
100
Modernize With Existing Technology
Performance Likelihood Weighted
Rating
Estimate
Score
2
.8
48.0
0
.5
0
1
.5
7.5
1
.9
13.5
0
.9
0
1
.5
5.0
74.0
GLOTYNE CORPORATION
Capital Expenditure Proposal
MADM Worksheet
Modernize With New Technology
Performance Likelihood Weighted
Rating
Estimate
Score
0
.5
0
2
.9
36.0
2
.9
27.0
2
.5
15.0
1
.6
6.0
1
.6
6.0
90.0
Based on the results of the MADM worksheet below, Glotyne management should choose the CIM system because
its composite weighted score is higher than the alternative. Based on this analysis, the CIM system is expected to
more adequately satisfy managements modernization goals.
P24-13
24-36
Chapter 24