10GP.1 Service Department Cost Allocations
10GP.1.E1 Direct Method
A firm has two service departments (A and B) and two production departments (X and Y). The various departments consume service department services as follows. Department A has incurred costs of $900,000 this period. Department B has incurred costs of $750,000 this period.
Dept. A (driver is labor hours):
- Dept. B consumes 200 labor hours.
- Dept. X consumes 2,000 labor hours.
- Dept. Y consumes 1,000 labor hours.
Dept. B (driver is work orders):
- Dept. A consumes 300 work orders.
- Dept. X consumes 350 work orders.
- Dept. Y consumes 350 work orders.
Required
If the firm uses the direct method to allocate service department costs to production departments, how much with the allocations be to Departments X and Y?
Answer
First we must convert the raw consumption/driver data into percentages. Because the direct method ignores all interdependency (i.e. any work that Departments A and B do for each other), we need to use the total driver consumption from the production departments as the denominator.
Dept. A -> Dept. X
2,000 Dept. X labor hours / (2,000 Dept. X labor hours + 1,000 Dept. Y labor hours) = 0.667
(I won’t round this percentage in the below A -> X calculation)
Dept. A -> Dept. Y
1,000 Dept. Y labor hours / (2,000 Dept. X labor hours + 1,000 Dept. Y labor hours) = 0.333
(I won’t round this percentage in the below A -> Y calculation)
Dept. B -> Dept. X
350 Dept. X work orders / (350 Dept. X work orders + 350 Dept. Y work orders) = 0.5
Dept. B -> Dept. Y
350 Dept. Y work orders / (350 Dept. X work orders + 350 Dept. Y work orders) = 0.5
Now we can simply multiply each service department’s cost by it’s calculated percentage to get the allocation.
Dept. A -> Dept. X = 900,000 * 0.667 = 600,000
Dept. A -> Dept. Y = 900,000 * 0.333 = 300,000
Dept. B -> Dept. X = 750,000 * 0.5 = 375,000
Dept. B -> Dept. Y = 750,000 * 0.5 = 375,000
Total allocations to Department X are 600,000 + 375,000 = 975,000
Total allocations to Department Y are 300,000 + 375,000 = 675,000
10GP.1.M2 Step-Down Method
A firm has two service departments (A and B) and two production departments (X and Y). The various departments consume service department services as follows. Department A has incurred costs of $900,000 this period. Department B has incurred costs of $750,000 this period.
Dept. A (driver is labor hours):
- Dept. B consumes 200 labor hours.
- Dept. X consumes 2,000 labor hours.
- Dept. Y consumes 1,000 labor hours.
Dept. B (driver is work orders):
- Dept. A consumes 300 work orders.
- Dept. X consumes 350 work orders.
- Dept. Y consumes 350 work orders.
Required
If the firm uses the step-down method to allocate service department costs to production departments, how much with the allocations be to Departments X and Y? Assume that Department B’s costs are allocated first and then Department A’s costs are allocated.
Answer
Like with the direct method, we must convert the raw consumption/driver data into percentages. However, we include all down-step consumption in the denominator (i.e. any production department consumption or down-step service department consumption).
Dept. B -> Dept. A
300 Dept. A work orders / (300 Dept. A work orders + 350 Dept. X work orders + 350 Dept. Y work orders) = 0.3
Dept. B -> Dept. X
350 Dept. X work orders / (300 Dept. A work orders + 350 Dept. X work orders + 350 Dept. Y work orders) = 0.35
Dept. B -> Dept. Y
350 Dept. Y work orders / (300 Dept. A work order + 350 Dept. X work orders + 350 Dept. Y work orders) = 0.35
(Notice that, because Dept. A is the bottom-step in the step-down, Dept. A’s percentages below are the same as they were in the direct method.)
Dept. A -> Dept. X
2,000 Dept. X labor hours / (2,000 Dept. X labor hours + 1,000 Dept. Y labor hours) = 0.667
Dept. A -> Dept. Y
1,000 Dept. Y labor hours / (2,000 Dept. X labor hours + 1,000 Dept. Y labor hours) = 0.333
Now we can simply multiply each service department’s cost by it’s calculated percentage to get the allocation. We must do this in the order that service departments are stepped down because this will affect what the “service department’s cost” is for down-step service departments (i.e. Dept. A will be credited with more than $900,000 in cost because some of Dept. B’s costs will be debited to it).
First Step:
Dept. B -> Dept. A = 750,000 * 0.3 = 225,000
Dept. B -> Dept. X = 750,000 * 0.35 = 262,500
Dept. B -> Dept. Y = 750,000 * 0.35 = 262,500
Second Step:
Dept. A -> Dept. X = (900,000 + 225,000) * 0.667 = 750,375
Dept. A -> Dept. Y = (900,000 + 225,000) * 0.333 = 374,625
Total allocations to Department X are 750,375 + 262,500 = 1,012,875
Total allocations to Department Y are 374,625 + 262,500 = 637,125
Notice that we allocated more cost to Department X than we did with the direct method. That is because less of the cost is moving through the 50-50 consumption of Department B’s services by production departments and more of the cost is moving through the 67-33 split for Department A’s services.
10GP.2 Transfer Pricing
10GP.2.E1 Negotiated Price: Ceiling and Floor
A firm has two departments, C and D. Department D uses an important gasket produced by Department C. Department D can obtain a comparable gasket on the external market for the price of $25 per unit.
Department C produces 200,000 gaskets each period. It incurs fixed costs of $2,000,000 per period. It also incurs, per gasket, $5 of direct material cost and $3 of direct labor cost. Department C does not sell these gaskets in an external market.
Required
If the firm has a policy of negotiating transfer prices, what would be the ceiling and floor for this gasket’s negotiated transfer price?
Answer
The buying department (Department D) sets the ceiling and the selling department (Department C) sets the floor. The buying department would not want to buy the gasket from Department C for more than it can purchase the gasket in the external market (i.e. $25). That is the ceiling.
The selling department will determine the floor by determining the relevant cost of each unit. It would not want to sell the gasket for less than it cost.
Ignore fixed costs, since these are almost always not relevant to the transfer pricing decision.
$5 DM per gasket + $3 DL per gasket = $8. That is the floor.
10GP.2.M1 Negotiated Price: Floor (Complex)
The same firm described in 10GP.2.E1 has two departments, C and D. Department D uses an important gasket produced by Department C. Department D can obtain a comparable gasket on the external market for the price of $25 per unit.
Per gasket, Department C incurs $5 of fixed overhead cost, $5 of variable overhead cost, $5 of direct material cost, and $3 of direct labor cost. Department C sells gaskets externally for $27 each. Department C incurs $4 per gasket in shipping and transportation costs on external sales only (Department D is housed in an adjacent building and there would be negligible shipping and handling costs).
Department C only has 10,000 of excess capacity, wheras Department D requires 15,000 gaskets per period. (Thus Department C would lose 5,000 gaskets’ worth of external sales by supplying Department D with gaskets.)
Required
If the firm has a policy of negotiating transfer prices, what would be the ceiling and floor for this gasket’s negotiated transfer price?
Answer
The ceiling remains the same: the buying department’s external market price of $25. Solving for the floor in this problem is slightly more complex because we have to factor in lost sales. Again ignore fixed costs.
$5 DM per gasket + $3 DL per gasket + per unit cost of lost sales = $8 + per unit cost of lost sales.
For each unit of lost sales, we lost the contribution margin of that sale. $27 external sales price – 5 DM – 3 DL – 5 VOH – 4 S&H = 10 CM per unit. Given the 5,000 gaskets’ worth of customers Department C’s giving up, that’s $50,000 of lost CM overall. Divide that by the number of units being supplied to Department D (to get a per gasket charge we would apply to each gasket). 50,000 / 15,000 =
$3.33 (rounded). That is the per unit cost of lost sales.
$8 + $3.33 = $11.33. That is the floor for this problem.
10GP.3 ROI and Residual Income
10GP.3.E1
Three department managers at a firm–Able, Baker, and Charlie–are compensated using ROI (i.e. when department ROI is at or above the firm’s hurdle rate, 12%, the manager earns a bonus). They are each considering whether to upgrade their departments’ information technology systems. The three departments and upgrades have the following fact patterns.
Able’s department:
- $11,000,000 in assets
- $1,650,000 in profit annually
- Upgrade expected to cost $500,000.
- Upgrade expected to save $100,000 in costs annually.
Baker’s department:
- $1,000,000 in assets
- $250,000 in profit annually
- Upgrade expected to cost $750,000.
- Upgrade expected to save $70,000 in costs annually.
Charlie’s department:
- $2,750,000 in assets
- $350,000 in profit annually
- Upgrade expected to cost $1,300,000.
- Upgrade expected to save $162,500 in costs annually.
Required
(A) What are the three departments’ ROI (without the upgrade)?
(B) What is the ROI for each of department’s upgrade?
(C) Which department managers are likely to be motivated by their ROI-based contract to accept the upgrade project?
Answer (A)
Able’s department: 1,650,000 / 11,000,000 = 0.15
Baker’s department: 250,000 / 1,000,000 = 0.25
Charlie’s department: 350,000 / 2,750,000 = 0.127 (rounded)
Answer (B)
Able: 100,000 / 500,000 = 0.20
Baker: 70,000 / 750,000 = 0.093 (rounded)
Charlie: 162,500 / 1,300,000 = 0.125
Answer (C)
Managers are likely to choose projects that raise their ROI.
For Able, the upgrade has an ROI of 20%, which is greater than the current ROI of 15%. Able is likely motivated to accept the upgrade project.
Baker has an ROI of 25%. The upgrade has an ROI of 9.3%, which means Baker is likely motivated to reject the upgrade.
Charlie has an ROI of 12.7% and the upgrade has an ROI of 12.5%. This means that Charlie is likely motivated to reject the upgrade project.
10GP.3.M1
Three department managers at a firm–Able, Baker, and Charlie–are compensated using both ROI and residual income (i.e. manager earns a bonus equal to a percentage of residual income). The firm’s hurdle rate is 12%. Each manager is considering whether to upgrade their departments’ information technology systems. The three departments and upgrades have the following fact patterns.
Able’s department:
- $11,000,000 in assets
- $1,650,000 in profit annually
- Upgrade expected to cost $500,000.
- Upgrade expected to save $100,000 in costs annually.
Baker’s department:
- $1,000,000 in assets
- $250,000 in profit annually
- Upgrade expected to cost $750,000.
- Upgrade expected to save $70,000 in costs annually.
Charlie’s department:
- $2,750,000 in assets
- $350,000 in profit annually
- Upgrade expected to cost $1,300,000.
- Upgrade expected to save $162,500 in costs annually.
Required
(A) What is the residual income for each of department’s upgrade?
(B) Which department managers are likely to be motivated by their residual income-based contract to accept the upgrade project?
Answer (A)
Able: 100,000 – 500,000 * 0.12 = 40,000
Baker: 70,000 – 750,000 * 0.12 = (20,000)
Charlie: 162,500 – 1,300,000 * 0.12 = 6,500
Answer (B)
Managers are likely to choose projects’ residual income (since positive residaul income).
For Able, the upgrade has a large positive residual income, so Able is likely motivated to accept the upgrade project.
Baker’s upgrade has a negative residual income ()i.e. a residual loss). This means Baker is likely motivated to reject the upgrade.
If Charlie upgrades, residual income is $6,500. This most likely means Charlie is motivated to accept the upgrade project.