CHAPTER 3 ACTIVITY COST BEHAVIOR QUESTIONS FOR WRITING AND DISCUSSION 1. Knowledge of cost behavior allows a manager to assess changes in costs that result from changes in activity. This allows a manager to assess the effects of choices that change activity. For example, if excess capacity exists, bids that at least cover variable costs may be totally appropriate. Knowing what costs are variable and what costs are fixed can help a manager make better bids. 2. The longer the time period, the more likely that a cost will be variable. The short run is a period of time for which at least one cost is fixed. In the long run, all costs are variable. 3. Resource spending is the cost of acquiring the capacity to perform an activity, whereas resource usage is the amount of activity actually used. It is possible to use less of the activity than what is supplied. Only the cost of the activity actually used should be assigned to products. 4. Flexible resources are those acquired from outside sources and do not involve any longterm commitment for any given amount of resource. Thus, the cost of these resources increases as the demand for them increases, and they are variable costs (varying in proportion to the associated activity driver). 5. Committed resources are acquired by the use of either explicit or implicit contracts to obtain a given quantity of resources, regardless of whether the quantity of resource available is fully used or not. For multiperiod commitments, the cost of these resources essentially corresponds to committed fixed costs. Other resources acquired in advance are short term in nature and essentially correspond to discretionary fixed costs. 6. Committed fixed costs are those incurred for the acquisition of long-term activity capacity and are not subject to change in the short run. Annual resource expenditure is independent of actual usage. For example, the cost of a factory building is a committed fixed cost. Discretionary fixed costs are those incurred for the acquisition of shortterm activity capacity, the levels of which can be altered quickly. In the short run, re-
41
source expenditure is also independent of actual activity usage. An engineer’s salary is an example of such an expenditure. 7. A variable cost increases in direct proportion to changes in activity usage. A one-unit increase in activity usage produces an increase in cost. A step cost, however, increases only as activity usage changes in small blocks or chunks. An increase in cost requires an increase in several units of activity. When a step cost changes over relatively narrow ranges of activity, it may be more convenient to treat it as a variable cost. 8. A step cost with narrow steps can be treated as variable, while one with wide steps is typically treated as fixed. 9. An activity rate is the resource expenditure for an activity divided by the activity’s practical capacity. 10.
Mixed costs are usually reported in total in the accounting records. How much of the cost is fixed and how much is variable is unknown and must be estimated.
11.
A scattergraph allows a visual portrayal of the relationship between cost and activity. It reveals to the investigator whether a relationship may exist and, if so, whether a linear function can be used to approximate the relationship. A scattergraph also can assist in identifying any outliers.
12.
Managers can use their knowledge of cost relationships to estimate fixed and variable components. A scattergraph can be used as an aid in this process. From a scattergraph, a manager can select two points that best represent the relationship. These two points can then be used to derive a linear cost formula. The high-low method tells the manager which two points to select to compute the linear cost formula. The selection of these two points is not left to judgment.
13.
Because the scatterplot method is not restricted to the high and low points, it is possible to select two points that better represent the relationship between activity and costs,
producing a better estimate of fixed and variable costs. A scattergraph also identifies outliers that could represent a high or low point that is an aberration. The main advantage of the high-low method is that it removes subjectivity from the choice process. The same line will be produced by two different people. 14.
Assuming that the scattergraph reveals that a linear cost function is suitable, then the method of least squares selects a line that best fits the data points. The method also provides a measure of goodness of fit so that the strength of the relationship between cost and activity can be assessed.
15.
The best-fitting line is the one that is “closest” to the data points. This is usually measured by the line that has the smallest sum of squared deviations.
16.
No. The best-fitting line may not explain much of the total cost variability. There must be a strong relationship as well.
17.
The coefficient of determination is the percentage of total variability in costs explained
42
by the activity. As such, it is a measure of the goodness of fit, the strength of the relationship between cost and activity. 18.
The correlation coefficient is the square root of the coefficient of determination. The correlation coefficient reveals the direction of the relationship in addition to the strength of the relationship.
19.
If the variation in cost is not well explained by activity usage (the coefficient of determination is low) as measured by a single driver, then other explanatory variables may be needed to build a good cost formula.
20.
If the mixed costs are immaterial, then the method of decomposition is unimportant. Furthermore, sometimes managerial judgment may be more useful for assigning costs than the use of formal statistical methodology.
EXERCISES 3–1 1.
Number of Units 0 50,000 100,000 150,000 200,000 250,000
Total Cost $120,000 120,000 120,000 120,000 120,000 120,000
2.
Supervision cost is strictly fixed.
Cost per Unit NA $2.40 1.20 0 .80 0 .60 0 .48
3–2 1.
Miles Traveled 0 $ 2,000 600 4,000 1,200 6,000 1,800 8,000 2,400 10,000 3,000
Total Cost 0 $0.00 0.30* 0.30 0.30 0.30 0.30
*$1,200/4,000 or $3,000/10,000 = $.30 2.
The cost of fuel for the delivery activity is strictly variable.
43
Cost per Mile
3–3 1.
Depreciation Cost
Graph of Truck Depreciation $250,000 $200,000 $150,000 $100,000 $50,000 $0 0
10 20 30 40 50 60 70 80 90 100
Cubic Yards of Concrete (in thousands)
2.
Cost of raw materials
Graph of Raw Materials Cost 3,000,000 2,000,000
Series2
1,000,000 0 1
2
3 4
5
Cubic yards of concrete
3. Truck depreciation: Fixed cost Raw materials cost: Variable cost 3-4 1.
Number of Units 0 10,000 20,000 30,000 40,000 50,000
Total Cost $10,000 10,000 10,000 20,000 20,000 30,000
44
Cost per Unit NA $1.00 0.50 0.67 0.50 0.60
2.
Forming machines rental cost is a step cost.
3-5 1. Graph of Machining Direct Labor Cost
Cost of Direct Labor
350000 300000 250000 200000 150000 100000 50000 0 0
1000
2000
3000
4000
5000
Number of units
The direct labor cost in the machining department is a step cost (with narrow steps). 2.
Cost of Supervision
Graph of Machining Department Supervision Cost 150000 100000 50000 0 0
1000
2000
3000
4000
5000
Number of units
The cost of supervision for the machining department is a step cost (with wide steps).
45
3. Direct labor cost increase = $144,000 – $108,000 = $36,000 Supervision increase = $80,000 – $40,000 = $40,000
3-6 Cost Category
Variable Cost
Technician salaries Laboratory facility Laboratory equipment Chemicals and other supplies
Discretionary Fixed Cost X
Committed Fixed Cost X X
X
3–7 Resource Jet rental Hotel rooms Buffet Favor package Buses
Flexible/Committed Committed Committed Flexible Flexible Committed
Cost Behavior Fixed Fixed Variable Variable Step
3–8 1.
Resource Plastic1 Direct labor and variable overhead2 Mold sets3 Other facility costs4 Total
Total Cost $ 10,800 8,000 20,000 10,000 $48,800
Unit Cost $0.027 0.020 0.050 0.025 $0.122
1
0.90 × $0.03 × 400,000 = $10,800; $10,800/400,000 = $0.027 $0.02 × 400,000 = $8,000; $8,000/400,000 = $0.02 3 $5,000 × 4 quarters = $20,000; $20,000/400,000 = $0.05 4 $10,000; $10,000/400,000 = $0.025 2
2.
Plastic, direct labor, and variable overhead are flexible resources; molds and other facility costs are committed resources. The cost of plastic, direct labor, and variable overhead are strictly variable. The cost of the molds is fixed for 46
the particular action figure being produced; it is a step cost for the production of action figures in general. Other facility costs are strictly fixed.
3–9 1. Total maintenance cost = $24,000 + $0.30(200,000) = $84,000 2. Total fixed maintenance cost = $24,000 3. Total variable maintenance cost = $0.30(200,000) = $60,000 4. Total maintenance cost per unit = [$24,000 + $0.30(200,000)]/200,000 = $84,000/200,000 = $0.42 5. Fixed maintenance cost per unit = $24,000/200,000 = $0.12 6. Variable maintenance cost per unit = $0.30 7. Requirements1-6 repeated: 1. Total maintenance cost = $24,000 + $0.30(100,000) = $54,000 2. Total fixed maintenance cost = $24,000 3. Total variable maintenance cost = $0.30(100,000) = $30,000 4. Total maintenance cost per unit = [$24,000 + $0.30(100,000)]/100,000 = $54,000/100,000 = $0.54 5. Fixed maintenance cost per unit = $24,000/100,000 = $0.24 6. Variable maintenance cost per unit = $0.30
47
3–10 1.
Committed resources: trucks and technicians’ salaries Flexible resources: supplies, small tools, and fuel
2.
Variable activity rate = $420,000/35,000 = $12 per call Fixed activity rate = $600,000*/40,000** = $15 per call Total cost of one call = $12 + $15 = $27 per call *($24,000 × 20) + ($10,000 × 12); **8 × 250 × 20
3.
Activity availability = Calls available = 40,000 calls =
4.
Total cost of committed resources $600,000 $600,000
Activity usage Calls made 35,000 calls
+ Unused capacity + Unmade calls + 5,000 calls
Cost of = activity used + = ($15 × 35,000) + = $525,000 +
Cost of unused capacity ($15 × 5,000) $75,000
Note: The analysis is restricted to committed resources, since only these resources will ever have any unused capacity.
48
3–11 1.
Committed resource charges: monthly fee, activation fee, cancellation fee (if triggered by contract cancellation prior to one year) Flexible resource charges: all additional charges for airtime, long distance and roaming
2.
Plan 1: Minutes available 60 minutes
= =
Minutes used 45 minutes
+ +
Unused minutes 15 minutes
Plan 2: Minutes available 120 minutes
= =
Minutes used 45 minutes
+ +
Unused minutes 75 minutes
Plan 1 is more cost effective. Jana will have some unused capacity (on average, 15 minutes a month), and the overall cost will be lower by $10 per month. 3.
Plan 1*: Minutes available 60 minutes
= =
Minutes used 90 minutes
+ +
Unused minutes (− 30) minutes
Plan 1*: Minutes available = 60 minutes = Additional minutes =
Minutes used 60 minutes 30 minutes
+ +
Unused minutes 0 minutes
*There are a number of ways to illustrate the use of minutes with Plan 1. Here are two possibilities. The problem, of course, is that all included monthly minutes are used, and Jana must purchase additional minutes. Plan 2: Minutes available 120 minutes
= =
Minutes used 90 minutes
+ +
Unused minutes 30 minutes
Plan 2 is now more cost effective, as the monthly cost is $30. Under Plan 1, Jana will pay $20 plus $30 (30 minutes × $1.00) or $50 per month. (The $1.00 additional charge includes the airtime and regional roaming charge.)
49
3-12 1. Graph of Cost of Giving Opening Shows 8000 7000
Cost
6000 5000 4000 3000 2000 1000 0 0
5
10
15
Number of opening shows
This is a strictly variable cost. 2. Graph of Cost of Running the Gallery 100000
Cost
80000 60000 40000 20000 0 0
5
10
15
20
Number of opening shows
This is a strictly fixed cost.
50
20
3. Graph of Ben's Total Costs 88000
Total Cost
87000 86000 85000 84000 83000 82000 81000 80000 79000 0
5
10
15
20
Number of opening shows
This is a mixed cost. 4. Total cost = $80,000 + $500(Number of opening shows) 5. Total cost = $80,000 + $500(12) = $86,000 Total cost = $80,000 + $500(14) = $87,000
3-13 1. The high point is March with 3,100 appointments. The low point is January with 700 appointments. 2. Variable rate = ($2,790 – $1,758)/(3,100 – 700) = $1,032/2,400 = $0.43 per tanning appointment Using the high point: Fixed cost = $2,790 – $0.43(3,100) = $1,457 OR
Using the low point: Fixed cost = $1,758 – $0.43(700) = $1,457 3. Total tanning service cost = $1,457 + $0.43 × Number of appointments 4. Total predicted cost for September = $1,457 + $0.43(2,500) = $2,532
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Total fixed cost for September = $1,457 Total predicted variable cost = $0.43(2,500) = $1,075
3-14 1. Scattergraph of Tanning Services 3000
Monthly Cost
2500 2000 1500 1000 500 0 0
1000
2000
3000
4000
Number of appointments
Yes, it appears that there is a linear relationship between tanning cost and number of appointments. 2. Total cost of tanning services = $1,290 + $0.45 × Number of appointments 3. Total predicted cost for September = $1,290 + $0.45(2,500) = $2,415
52
3–15 1.
Cost of Oil Changes $9,000 $8,000 $7,000
Cost
$6,000 $5,000 $4,000 $3,000 $2,000 $1,000 $0 0
500
1,000
Number of Oil Changes The scattergraph provides evidence for a linear relationship. 2.
High (1,400, $7,950); Low (700, $5,150) V = ($7,950 – $5,150)/(1,400 – 700) = $2,800/700 = $4 per oil change F = $5,150 – $4(700) = $5,150 – $2,800 = $2,350 Cost = $2,350 + $4 (oil changes) Predicted cost for January = $2,350 + $4(1,000) = $6,350
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1,500
3–15 3.
Concluded
Output of the regression routine calculated by a spreadsheet: Constant
1697.097
Std. Err. of Y Est.
243.6784
R Squared
0.967026
No. of Observations
8
Degrees of Freedom
6
X Coefficient(s)
4.64678
Std. Err. of Coef.
0.350304
Rounding the coefficients: Variable rate = $4.65 per oil change Fixed cost = $1,697 Predicted cost for January = $1,697 + $4.65 (oil changes) = $1,697 + $4.65(1,000) = $6,347 R2 = 0.97 (rounded) This says that 97 percent of the variability in the cost of providing oil changes is explained by the number of oil changes performed. 4.
The least-squares method is better because it uses all eight data points instead of just two.
54
3–16 1.
Cost of Moving Materials $16,000 $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0 0
500
1,000
Number of Moves
The scattergraph provides evidence for a linear relationship, but the observation for 300 moves may be an outlier. 2.
High (800, $14,560); Low (100, $3,000) V = ($14,560 – $3,000)/(800 – 100) = $11,560/700 = $16.51 per move (rounded) F = $3,000 – $16.51(100) = $3,000 – $1,651 = $1,349 Cost = $1,349 + $16.51 (moves) Predicted cost = $1,349 + $16.51(550) = $10,430 (rounded)
55
3–16 3.
Concluded
Output of the regression routine calculated by a spreadsheet: Constant
497.50
Std. Err. of Y Est.
987.0073
R Squared
0.926208
No. of Observations
8
Degrees of Freedom
6
X Coefficient(s)
18.425
Std. Err. of Coef.
1.954566
Rounding the coefficients: Variable rate = $18.43 per move Fixed cost = $498 Cost = $498 + $18.43 (moves) = $498 + $18.43(550) = $10,635 (rounded) R2 = 0.93 (rounded) This says that 93 percent of the variability in the cost of moving materials is explained by the number of moves. 4.
Normally, we would prefer the least-squares method since the data appear to be linear. However, the third observation may be an outlier. If the third obser2 vation (300 moves and $3,400 of cost) is dropped, the R rises to 99 percent. The new cost formula would be Cost = $1,411 + $17.28 (moves) The higher fixed cost is much more in keeping with what we observed with the scatterplot in requirement 1.
56
3–17 1.
Maintenance cost = $5,750 + $16X
2.
Maintenance cost = $5,750 + $16(650) = $5,750 + $10,400 = $16,150
3.
To obtain the percentage explained, r needs to be squared: 0.89 × 0.89 = 79.21 percent. The relationship appears strong but perhaps could be improved by searching for another explanatory variable. Leaving about 20 percent of the variability unexplained may produce less than satisfactory predictions.
4.
Maintenance cost = 12($5,750) + $16(8,400) = $69,000 + $134,400 = $203,400
Note: The fixed cost from the regression results is the fixed cost for the month (since monthly data were used to estimate the equation). However, the question asks for the cost for the year. Therefore, the fixed cost from the regression equation must be multiplied by 12.
3–18 1.
Overhead = $2,130 + $17(DLH) + $810(setups) + $26(purchase orders)
2.
Overhead = $2,130 + $17(600) + $810(50) + $26(120) = $2,130 + $10,200 + $40,500 + $3,120 = $55,950
3.
Since total setup cost is $40,500 for the following month, a 50 percent decrease would reduce setup cost to $20,250, saving $20,250 for the month.
57
3–19 1.
Warranty repair cost = $2,000 + $60(number of defects) - $10(inspection hours)
2.
Warranty repair cost = $2,000 + $60(100) – $10(150) = $6,500
3.
The number of defects is positively correlated with warranty repair costs. Inspection hours are negatively correlated with warranty repair costs.
4.
In this equation, the independent variables—number of defects and inspection hours—account for 88 percent of the variability in warranty repair costs. It seems that analysts have identified some very good drivers for warranty repair costs.
58
PROBLEMS 3-20 a. Variable cost b. Committed fixed cost c. Discretionary fixed cost d. Discretionary fixed cost e. Discretionary fixed cost f. Variable cost g. Variable cost h. Discretionary fixed cost i. Discretionary fixed cost j. Committed fixed cost
3-21 1.
Receiving Cost
Scattergraph of Receiving Activity 35000 30000 25000 20000 15000 10000 5000 0 0
500
1000
1500
2000
Number of receiving orders
Yes, the relationship appears to be reasonably linear. 2. Using the high-low method: Variable receiving cost = ($27,000 – $15,000)/(1,700 – 700) = $12 Fixed receiving cost = $15,000 – $12(700) = $6,600 Predicted cost for 1,475 receiving orders: Receiving cost = $6,600 + $12(1,475) = $24,300 3. Receiving cost for the quarter = 3($6,600) + $12(4,650)
59
= $19,800 + $55,800 = $75,600 Receiving cost for the year = 12($6,600) + $12(18,000) = $79,200 + $216,000 = $295,200 4. Receiving cost = $3,212 + $15.15 × Number of receiving orders Receiving cost = $3,212 + $15.15(1,475) = $25,558 Receiving cost for the quarter = 3($3,212) + $15.15(4,650) = $9,636 + $70,448 = $80,084 Receiving cost for the year = 12($3,212) + $15.15(18,000) = $38,544 + $272,700 = $311,244 3-22 1. Results of regressions:
10 Months Data 12 Months Data Intercept 3,212.121 3,820 Slope 15.15152 15.10 0.8485 0.7451 R2
60
2.
Receiving cost
Scattergraph of Receiving Activity 12 Months Data 35000 30000 25000 20000 15000 10000 5000 0 0
500
1000
1500
2000
Number of receiving orders
The point for the 11th month (1,200 receiving orders and $28,000 total receiving cost) appears to be an outlier. Since the cost was so much higher in this month due to an event that is not expected to happen again, this data point could easily be dropped. Then, data from the 11 remaining months could be used to develop a cost formula for receiving cost.
61
3. Results for the method of least squares after dropping month 11. SUMMARY OUTPUT Regression Statistics Multiple R 0.926737 R Square 0.858841 Adjusted R Square 0.843157 2051.781 Standard Error Observations 11 ANOVA df Regression Residual Total
1 9 10
SS 2.31E+08 37888233 2.68E+08
Intercept X Variable 1
Coefficients 3168.56 15.17946
Standard Error 2565.262 2.051314
MS 2.31E+08 4209804
F 54.7581
t Stat 1.23518 7.399872
P-value 0.248035 4.1E-05
Significance F
4.1E-05
Lower 95% -2634.47 10.53906
Upper 95% 8971.589 19.81986
Lower 95.0% -2634.47 10.53906
Upper 95.0% 8971.589 19.81986
Receiving cost = $3,168.56 + $15.18 × Number of receiving orders Predicted receiving cost for a month = $3,168.56 + $15.18(1,475) = $25,559.06 The regression run on the 11 months of data from “typical” months appears to be better than the one for all 12 months. R2 is higher for the regression without the outlier (85.88 percent versus 74.512 percent), and the scattergraph gives Joseph confidence that the data without the outlier describe a relatively linear relationship. Since the storm damage is not expected to recur, month 11 can safely be dropped from a regression meant to help predict future receiving cost.
62
3–23 1.
Salaries: Senior accountant—fixed Office assistant—fixed Internet and software subscriptions—mixed Consulting by senior partner—variable Depreciation (equipment)—fixed Supplies—mixed Administration—fixed Rent (offices)—fixed Utilities—mixed
2.
Internet and software subscriptions: V = (Y2 – Y1)/(X2 – X1) = ($850 – $700)/(150 – 120) = $5 per hour F = Y2 – VX2 = $850 – ($5)(150) = $100 Consulting by senior partner: V = (Y2 – Y1)/(X2 – X1) = ($1,500 – $1,200)/(150 – 120) = $10 per hour F = Y2 – VX2 = $1,500 – ($10)(150) = $0 Supplies: V = (Y2 – Y1)/(X2 – X1) = ($1,100 – $905)/(150 – 120) = $6.50 per hour F = Y2 – VX2 = $1,100 – ($6.50)(150) = $125 Utilities: V = (Y2 – Y1)/(X2 – X1) = ($365 – $332)/(150 – 120) = $1.10 per hour F = Y2 – VX2 = $365 – ($1.10)(150) = $200
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3–23
Concluded
3.
Unit Variable Cost
Fixed Salaries: Senior accountant Office assistant Internet and subscriptions Consulting Depreciation (equipment) Supplies Administration Rent (offices) Utilities Total cost
$2,500 1,200 100 — 2,400 125 500 2,000 200 $9,025
$ — — 5.00 10.00 — 6.50 — — 1.10 $22.60
Thus, total clinic cost = $9,025 + $22.60/professional hour For 140 professional hours: Clinic cost = $9,025 + $22.60(140) = $12,189 Charge per hour = $12,189/140 = $87.06 Fixed charge per hour = $9,025/140 = $64.46 Variable charge per hour = $22.60 4.
For 170 professional hours: Charge/day = $9,025/170 + $22.60 = $53.09 + $22.60 = $75.69 The charge drops because the fixed costs are spread over more professional hours.
64
3–24 1.
High (1,700, $21,000); Low (700, $15,000) V = (Y2 – Y1)/(X2 – X1) = ($21,000 – $15,000)/(1,700 – 700) = $6 per setup F = Y2 – VX2 = $21,000 – ($6)(1,700) = $10,800 Y = $10,800 + $6X
2.
Output of spreadsheet regression routine with number of setups as the independent variable: Constant
4512.98701298698
Std. Err. of Y Est.
3456.24317476605
R Squared
0.633710482694768
No. of Observations
10
Degrees of Freedom
8
X Coefficient(s)
13.3766233766234
Std. Err. of Coef.
3.59557461331427
V = $13.38 per receiving order (rounded) F = $4,513 (rounded) Y = $4,513 + $13.38X R2 = 0.634, or 63.4% Setups explain about 63.4 percent of the variability in order filling cost, providing evidence that Brett’s choice of a cost driver is reasonable. However, other drivers may need to be considered because 63.4 percent may not be strong enough to justify the use of only receiving orders.
65
3–24 3.
Continued
Regression with setup hours as the independent variable: Constant
5632.28109733183
Std. Err. of Y Est.
2390.10628259277
R Squared
0.824833789433823
No. of Observations
10
Degrees of Freedom
8
X Coefficient(s)
4.49642991356633
Std. Err. of Coef.
7.32596
V = $4.50 per setup hour F = $5,632 (rounded) Y = $5,632 + $4.50X R2 = 0.825, or 82.5% Setup hours explain about 82.5 percent of the variability in order filling cost. This is a better result than that of setups and should convince Brett to try multiple regression.
66
3–24 4.
Concluded
Regression routine with pounds of material and number of receiving orders as the independent variables: Constant
752.104072925631
Std. Err. of Y Est.
1350.46286973443
R Squared
0.951068418023306
No. of Observations
10
Degrees of Freedom
7
X Coefficient(s)
3.33883151096915
7.14702865269395
Std. Err. of Coef.
0.495524841198368
1.68182916088492
V1 V2 F Y
= $3.34 per pound of material delivered (rounded) = $7.147 per receiving order (rounded) = $752 (rounded) = $752 + $3.34a + $7.147b
R2 = 0.95, or 95% Multiple regression with both variables explains 95 percent of the variability in receiving cost. This is the best result.
3–25 1.
The order should cover the variable costs described in the cost formulas. These variable costs represent flexible resources. Materials ($94 × 20,000) Labor ($16 × 20,000) Variable overhead ($80 × 20,000) Variable selling ($7 × 20,000) Total additional resource spending Divided by units produced Total unit variable cost
$1,880,000 320,000 1,600,000 140,000 $3,940,000 ÷ 20,000 $ 197
Garner should accept the order because it would cover total variable costs and increase income by $15 per unit ($212 – $197), for a total increase of $300,000.
67
3–25
Concluded
2.
The correlation coefficients indicate the reliability of the cost formulas. Of the four formulas, overhead activity may be a problem. A correlation coefficient of 0.75 means that only about 75 percent of the variability on overhead cost is explained by direct labor hours. This should have a bearing on the answer to Requirement 1 because if the percentage is low, there are activity drivers other than direct labor hours that are affecting variability in overhead cost. What these drivers are and how resource spending would change need to be known before a sound decision can be made.
3.
Resource spending attributable to order: Material ($94 × 20,000) Labor ($16 × 20,000) Variable overhead: ($85 × 20,000) ($5,000 × 12) ($300 × 600) Variable selling ($7 × 20,000) Total additional resource spending Divided by units produced Total unit variable cost
$ 1,880,000 320,000 1,700,000 60,000 180,000 140,000 $ 4,280,000 ÷ 20,000 $ 214
The order would not be accepted now because it does not cover the variable activity costs. Each unit would lose $2 ($212 – $214). It would also be useful to know the step-cost functions for any activities that have resources acquired in advance of usage on a short-term basis. It is possible that there may not be enough unused activity capacity to handle the special order, and resource spending may also be affected by a need (which, in this case, would be unexpected) to expand activity capacity.
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3–26 1.
High (2,000; $120,000); Low (1,200; $52,000) V = ($120,000 – $52,000)/(2,000 – 1,200) = $85/nursing hour F = $52,000 – ($85 × 1,200) = –$50,000 This problem illustrates how the high-low method can be misleading when cost behavior patterns have changed. Fortunately, in this case, the negative value of fixed cost tells us that something is wrong.
2.
a. Output of spreadsheet multiple regression routine: Constant
236.211171346831
Std. Err. of Y Est.
1788.59942408259
R Squared
0.993939842186014
No. of Observations
14
Degrees of Freedom
11
X Coefficient(s)
40.8752113255057
35307.5122042085
Std. Err. of Coef.
2.2207348945557
970.201096681915
b. Output of spreadsheet regression routine on 2008 data: Constant
10081.3333333337
Std. Err. of Y Est.
94.8068211329403
R Squared
0.999887905585866
No. of Observations
8
Degrees of Freedom
6
X Coefficient(s)
34.9533333333331
Std. Err. of Coef.
0.151087766637518
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3–26
Concluded
c. Output of spreadsheet regression routine on 2009 data: Constant
19964.2403242688
Std. Err. of Y Est.
12.0521931978647
R Squared
0.999999089146329
No. of Observations
6
Degrees of Freedom
4
X Coefficient(s) Std. Err. of Coef.
50.0216788702923 0.0238700194326353
While each regression has a high R2, the multiple regression gives unacceptable results. Notice the $35,308 coefficient on the independent variable “changes.” Yet, the increased fixed cost was only $10,000 per month. Regression (c) gives more reasonable results. The intercept term, $19,964, is roughly $10,000 higher than the intercept term for Regression (b), as expected. So, the hospital should use Regression (c) to budget for the rest of the year.
3–27 1.
Output of spreadsheet regression with pounds as independent variable: Constant
4,997.2877
Std. Err. of Y Est.
571.36
R Squared
0.9315
No. of Observations
9
Degrees of Freedom
7
X Coefficient(s)
2.5069
Std. Err. of Coef.
0.257
Budgeted setup cost at 5,200 pounds: Y = $4,997.29 + $2.51(5,200) = $18,033.24
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3–27 2.
Continued
Output of spreadsheet regression with number of orders as the independent variable: Constant
17,485.8088
Std. Err. of Y Est.
2168.03
R Squared
0.01327
No. of Observations
9
Degrees of Freedom
7
X Coefficient(s)
6.0507
Std. Err. of Coef.
19.718
Budgeted setup cost for 160 orders: Y = $17,485.81 + $6.05(160) = $18,453.81 3.
The regression equation based on pounds is better because the coefficient of determination is much higher. Pounds explain about 93 percent of the variation in receiving costs, while number of orders explains only 1.3 percent of the variation in receiving costs.
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3–27 4.
Concluded
Output of spreadsheet for multiple regression: Constant
2986.529
Std. Err. of Y Est.
99.67
R Squared
0.9982
No. of Observations
9
Degrees of Freedom
6
X Coefficient(s)
2.6056
13.7142
Std. Err. of Coef.
0.0453
0.9163
Y = $2,986.53 + $2.61(5,200) + $13.71(160) = $18,729.81 The explanatory power of both variables is very high. Yet, pounds seems to explain most of the variation, and the use of one driver would vastly simplify budgeting and product costing. The increased complexity is probably not worth adding the second driver.
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MANAGERIAL DECISION CASE 3–28 1.
Jackie violated the standard of confidentiality. Management accountants should not disclose confidential information acquired in the course of their work unless legally obligated to do so. Her motives for disclosing the confidential information apparently were intended to further her personal interests. Management accountants are prohibited from using confidential information for unethical advantages. In addition, some could argue that Jackie also violated the standard of integrity. Conflict of interest, receipt of favors or gifts, and subversion of an organization’s pursuit of its legitimate objectives all could be in violation.
2.
Assuming that the data were acquired illicitly, Brindon’s instincts were on target. To analyze the data and be party to its use would most certainly violate the standard of integrity. Management accountants should not engage in or support any activity that would discredit the profession. In addition, Brindon would violate the standard of confidentiality if he chose to analyze the data. Management accountants should refrain from using confidential information acquired in the course of their work for unethical advantage, either personally or through a third party (II-3).
RESEARCH ASSIGNMENT 3–29 Answers will vary.
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