601 13,14 solutions

EXERCISE 13-33 (20 MINUTES)

The economic value added (EVA) is defined as follows:

For Golden Gate Construction Associates, we have the following calculations of each division’s EVA.

Division

After-Tax Operating Income

(in millions)

Total Assets

(in millions)

Current Liabilities

(in millions) WACC

Economic Value

Added (in millions)

Real Estate$30(1-.40) - $150 - $9 ´ .114 = $1.926

Construction $27(1-.40) - $ 90 - $6 ´ .114 = $6.624


1.Transfer price =

outlaycost +

opportunitycost

= $450* + $120† = $570

*Outlay cost = unit variable production cost†Opportunity cost = forgone contribution margin

= $570 – $450 = $120

2. If the Fabrication Division has excess capacity, there is no opportunity cost associated with a transfer. Therefore:

Transfer price =outlaycost +

opportunitycost

= $450 + 0 = $450

McGraw-Hill/Irwin 2005 The McGraw-Hill Companies, Inc.Managerial Accounting, 6/e 13-1


1. The Assembly Division's manager is likely to reject the special offer because the Assembly Division's incremental cost on the special order exceeds the division's incremental revenue:

Incremental revenue per unit in special order........................ $700Incremental cost to Assembly Division per unit

in special order:Transfer price....................................................................... $561Additional variable cost....................................................... 150

Total incremental cost............................................................... 711 Loss per unit in special order................................................... $ (11 )

2. The Assembly Division manager's likely decision to reject the special order is not in the best interests of the company as a whole, since the company's incremental revenue on the special order exceeds the company's incremental cost:

Incremental revenue per unit in special order..................... $700Incremental cost to company per unit in special order:

Unit variable cost incurred in Fabrication Division......... $450Unit variable cost incurred in Assembly Division........... 150

Total unit variable cost........................................................... 600 Profit per unit in special order............................................... $100

3. The transfer price could be set in accordance with the general rule, as follows:

Transfer price =outlaycost +

opportunitycost

= $450 + 0*

= $450

*Opportunity cost is zero, since the Fabrication Division has excess capacity.

Now the Assembly Division manager will have an incentive to accept the special order since the Assembly Division's incremental revenue on the special order exceeds the incremental cost. The incremental revenue is still $700 per unit, but the incremental cost drops to $600 per unit ($450 transfer price + $150 variable cost incurred in the Assembly Division).


PROBLEM 13-36 (25 MINUTES)

The answer to the question as to which division is the most successful depends on the firm's cost of capital. To see this, compute the residual income for each division using various imputed interest rates.

(a) Imputed interest rate of 10%:

Division I Division IIDivisional profit...................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 10%.............................................. 1,800,000II: $ 3,000,000 ´ 10%.............................................. ________ 300,000

Residual income.................................................................... $ 900,000 $300,000

(b) Imputed interest rate of 14%:

Division I Division IIDivisional profit...................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 14%.............................................. 2,520,000II: $ 3,000,000 ´ 14%.............................................. ________ 420,000

Residual income.................................................................... $ 180,000 $180,000

(c) Imputed interest rate of 15%:

Divisional profit...................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 15%.............................................. 2,700,000II: $ 3,000,000 ´ 15%.............................................. ________ 450,000

Residual income.................................................................... $ 0 $150,000

If the firm's cost of capital is 10 percent, then Division I has a higher residual income than Division II. With a cost of capital of 15 percent, Division II has a higher residual income. At a 14 percent cost of capital, both divisions have the same residual income. This scenario illustrates one of the advantages of residual income over ROI. Since the residual income calculation includes an imputed interest charge reflecting the firm's cost of capital, it gives a more complete picture of divisional performance.



Division I Division II Division IIISales revenue.......................................................... $40,000,000 $8,000,000e $3,200,000l

Income..................................................................... $ 8,000,000 $ 1,600,000 $ 800,000k

Average investment................................................ $10,000,000 $8,000,000f $4,000,000j

Sales margin ......................................................... 20%a 20% 25%Capital turnover...................................................... 4b 1 .8i

ROI........................................................................... 80%c 20%g 20%Residual income..................................................... $ 7,200,000d $ 960,000h $ 480,000

Explanatory notes:

c ROI = sales margin ´ capital turnover = 20% ´ 4 = 80%d Residual income = income – (imputed interest rate)(invested capital)

= $8,000,000 – (8%)($10,000,000) = $7,200,000

e Sales margin =

20% =

Therefore, sales revenue = $8,000,000

fCapital turnover =

1 =

Therefore, invested capital = $8,000,000gROI = sales margin ´ capital turnover ROI = 20% ´ 1 = 20%


PROBLEM 13-37 (CONTINUED)

hResidual income = income – (imputed interest rate)(invested capital)

= $1,600,000 – (8%)($8,000,000)

= $960,000iROI = sales margin ´ capital turnover

20% = 25% ´ capital trunover

Therefore, capital turnover = .8

jROI = = 20%

Therefore, income = (20%)(invested capital)

Residual income

= income – (imputed interest rate)(invested capital)

= $480,000

Substituting from above for income:

(20%)(invested capital) – (8%)(invested capital) = $480,000

Therefore, (12%)(invested capital) = $480,000

So, invested capital = $4,000,000

kROI =capital invested

income

20% =

Therefore, income = $800,000

lSales margin =revenue sales

income

25% =

Therefore, sales revenue = $3,200,000



1. Three ways to increase Division I's ROI:

(a) Increase income, while keeping invested capital the same. Suppose income increases to $9,000,000. The new ROI is:

(b) Decrease invested capital, while keeping income the same. Suppose invested capital decreases to $9,600,000. The new ROI is:

(c) Increase income and decrease invested capital. Suppose income increases to $8,400,000 and invested capital decreases to $9,600,000. The new ROI is:

2. ROI = sales margin ´ capital turnover

= 25% ´ 1

= 25%



This problem is similar to Problem 13-36, except that here students are given a hint in answering the question about which division is the most successful by requiring the calculation of residual income for three different imputed interest rates. If the firm's cost of capital is 12 percent, then Division I has a higher residual income than Division II. With a cost of capital of 15 percent or 18 percent, Division II has a higher residual income.

1. Imputed interest rate of 12%

Division I Division IIDivisional profit..................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 12%.............................................. 2,160,000 II: $ 3,000,000 ´ 12%.............................................. 360,000

Residual income.................................................................... $ 540,000 $240,000

2. Imputed interest rate of 15%

Division I Division IIDivisional profit....................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 15%................................................ 2,700,000 II: $ 3,000,000 ´ 15%................................................ 450,000

Residual income...................................................................... $ 0 $150,000



3. Imputed interest rate of 18%Division I Division II

Divisional profit....................................................................... $2,700,000 $600,000Less: Imputed interest charge:

I: $18,000,000 ´ 18%................................................. 3,240,000 II: $ 3,000,000 ´ 18%................................................. 540,000

Residual income...................................................................... $(540,000) $ 60,000

The imputed interest rate r, at which the two divisions’ residual income is the same, is 14 percent, computed as follows:

Division II’s residual income

= Division I's residual income

$600,000 – (r)($3,000,000) = $2,700,000 – (r)($18,000,000)

(r)($15,000,000) = $2,100,000

r = $2,100,000/$15,000,000

r = 14%

For any imputed interest rate less than 14 percent, Division I will have a higher residual income. For any rate over 14 percent, Division II's residual income will be higher.



1. Current ROI of the Western Division:

Sales revenue…………………………………… $4,200,000Less: Variable costs ($4,200,000 x 70%)…… $2,940,000

Fixed costs……………………………….. 1,075,000 4,015,000 Income…………………………………………….. $ 185,000

ROI = Income ÷ invested capital= $185,000 ÷ $925,000= 20%

Western Division’s ROI if competitor is acquired:

Sales revenue ($4,200,000 + $2,600,000)……. $6,800,000Less: Variable costs [$2,940,000 +

($2,600,000 x 65%)]………………… $4,630,000Fixed costs ($1,075,000 + $835,000)... 1,910,000 6,540,000

Income……………………………………………... $ 260,000

ROI = Income ÷ invested capital= $260,000 ÷ [$925,000 + ($312,500 +

$187,500)]= 18.25%

2. Divisional management will likely be against the acquisition because ROI will be lowered from 20% to 18.25%. Since bonuses are awarded on the basis of ROI, the acquisition will result in less compensation.

3. An examination of the competitor’s financial statistics reveals the following:

Sales revenue…………………………………….. $2,600,000Less: Variable costs ($2,600,000 x 65%)…….. $1,690,000

Fixed costs ……………………………….. 835,000 2,525,000 Income……………………………………………... $ 75,000

ROI = Income ÷ invested capital= $75,000 ÷ $312,500= 24%



Corporate management would probably favor the acquisition. Megatronics has been earning a 13% return, and the competitor’s ROI of 24% will help the organization as a whole. Even if the $187,500 upgrade is made, the competitor’s ROI would be 15% if past earnings trends continue [$75,000 ÷ ($312,500 + $187,500) = 15%].

4. Yes, the divisional ROI would increase to 21.01%. However, the absence of the upgrade could lead to long-run problems, with customers being confused (and perhaps turned-off) by two different retail environments—the retail environment they have come to expect with other Megatronics outlets and that of the newly acquired, non-upgraded competitor.

Sales revenue ($4,200,000 + $2,600,000)……. $6,800,000Less: Variable costs [$2,940,000 +

($2,600,000 x 65%)]………………… $4,630,000Fixed costs ($1,075,000 + $835,000)... 1,910,000 6,540,000

Income……………………………………………... $ 260,000

ROI = Income ÷ invested capital= $260,000 ÷ ($925,000 + $312,500)= 21.01%

5. Current residual income of the Western Division:

Divisional profit……………………………………………… $185,000Less: Imputed interest charge ($925,000 x 12%)…… 111,000 Residual income…………………………………………….. $ 74,000

Residual income if competitor is acquired:

Divisional profit ($185,000 + $75,000)……………... $260,000Less: Imputed interest charge [($925,000 +

($312,500 + $187,500)) x 12%]…………... 171,000 Residual income………………………………………... $ 89,000

Yes, management most likely will change its attitude. Residual income will increase by $15,000 ($89,000 - $74,000) as a result of the acquisition.



Year

IncomeBefore

DepreciationAnnual

Depreciation

IncomeNet of

Depreciation

AverageNet Book

Value*

ROIBased

onNet Book

Value†

AverageGrossBookValue

ROIBased

onGross Book Value

1 $150,000 $200,000 $(50,000) $400,000 — $500,000 —2 150,000 120,000 30,000 240,000 12.5% 500,000 6.0%3 150,000 72,000 78,000 144,000 54.2% 500,000 15.6%4 150,000 54,000 96,000 81,000 118.5% 500,000 19.2%5 150,000 54,000 96,000 27,000 355.6% 500,000 19.2%

*Average net book value is the average of the beginning and ending balances for the year in net book value. In Year 1, for example, the average net book value is:

†ROI rounded to the nearest tenth of 1 percent.

1. This table differs from Exhibit 13-3 in that ROI rises even more steeply across time than it does in Exhibit 13-3. With straight-line depreciation, ROI rises from 11.1 percent in Year 1 to 100 percent in Year 5. Under the accelerated depreciation schedule used here, we have a loss in Year 1 and then ROI rises from 12.5 percent in Year 2 to 355.6 percent in Year 5.

2. One potential implication of such an ROI pattern is a disincentive for new investment. If a proposed capital project shows a loss or very low ROI in its early years, a manager may worry about the effect on his or her performance evaluation in the early years of the project. In an extreme case, a manager may worry that he or she will no longer have the job when the project begins to show a higher return in its later years.



Based on Net Book Value Based on Gross Book Value

Year

IncomeBefore

DepreciationAnnual

Depreciation

IncomeNet of

Depreciation

AverageNet Book

Value*

ImputedInterestCharge†

ResidualIncome

AverageGrossBookValue

ImputedInterestCharge†

ResidualIncome

1 $150,000 $100,000 $50,000 $450,000 $45,000 $ 5,000 $500,000 $50,000 02 150,000 100,000 50,000 350,000 35,000 15,000 500,000 50,000 03 150,000 100,000 50,000 250,000 25,000 25,000 500,000 50,000 04 150,000 100,000 50,000 150,000 15,000 35,000 500,000 50,000 05 150,000 100,000 50,000 50,000 5,000 45,000 500,000 50,000 0

*Average net book value is the average of the beginning and ending balances for the year in net book value.†Imputed interest charge is 10 percent of the average book value, either net or gross.

Notice in the table that residual income, computed on the basis of net book value, increases over the life of the asset. This effect is similar to the one demonstrated for ROI.

It is not very meaningful to compute residual income on the basis of gross book value. Notice that this asset shows a zero residual income for all five years when the calculation is based on gross book value.



1. Sales margin: income divided by sales revenue.

Capital turnover: sales revenue divided by invested capital

Return on investment: income divided by invested capital (or sales margin x capital turnover).

Sales margin: $540,000 ÷ $7,200,000 = 7.5%Capital turnover: $7,200,000 ÷ $9,000,000 = 80%Return on investment: $540,000 ÷ $9,000,000 = 6%, or

7.5% x 80% = 6%

2. Strategy (a): Income will be reduced to $450,000 because of the loss, and invested capital will fall to $8,910,000 from the disposal. ROI = $450,000 ÷ $8,910,000, or 5.05%. This strategy should be rejected, since it further hurts Washburn’s performance.

Strategy (b): In terms of ROI, this strategy neither hurts nor helps. The acceleration of overdue receivables increases cash and decreases accounts receivable, producing no effect on invested capital. Of course, it is possible that the newly acquired cash could be invested in something that would provide a positive return for the firm.

3. Yes. A drastic cutback in advertising could lead to a loss of customers and a reduced market share. This could translate into reduced profits over the long term. With respect to repairs and maintenance, reduced outlays could prove costly by unintentional shortening of the useful lives of plant and equipment. Such action would likely result in an accelerated asset replacement program.



4. Anderson Manufacturing ROI: ($4,500,000 - $3,600,000) ÷ $7,500,000 = 12%Palm Beach Enterprises ROI: ($6,750,000 - $6,180,000) ÷ $7,125,000 = 8%

From the preceding calculations, both investments appear attractive given the current state of affairs (i.e., the Hardware Division’s current ROI of 6%). However, if Washburn desires to maximize ROI, he would be advised to acquire only Anderson Manufacturing.

CurrentCurrent + Anderson

Current + Anderson + Palm Beach

Income………………. $ 540,000 $ 1,440,000* $ 2,010,000**Invested capital…… 9,000,000 16,500,000 23,625,000ROI…………………… 6% 8.73% 8.51%

* $540,000 + ($4,500,000 - $3,600,000)** $540,000 + ($4,500,000 - $3,600,000) + ($6,750,000 - $6,180,000)


1. The weighted-average cost of capital (WACC) is defined as follows:

The following calculation shows that the company’s WACC is 9.72 percent.



2. The three divisions’ economic-value-added measures are calculated as follows:

Division

After-TaxOperating

Income(in millions)

-

TotalAssets

(inmillions)

-

CurrentLiabilities

(inmillions)

´ WACC =

EconomicValueAdded

(in millions)

Pacific...... $14 ´ (1-.30) - [($ 70 - $6) ´ .0972] = $ 3,579,200Plains....... $45 ´ (1-.30) - [($300 - $5) ´ .0972] = $ 2,826,000Atlantic..... $48 ´ (1-.30) - [($480 - $9) ´ .0972] = $(12,181,200)

3. The EVA analysis reveals that the Atlantic Division is in trouble. Its substantial negative EVA merits the immediate attention of the management team.



1. a. Transfer price = outlay cost + opportunity cost

= $130 + $30 = $160

b. Transfer price = standard variable cost + (10%)(standard variable cost)

= $130 + (10%) ($130) = $143

Note that the Frame Division manager would refuse to transfer at this price.

2. a. Transfer price = outlay cost + opportunity cost

= $130 + 0 = $130

b. When there is no excess capacity, the opportunity cost is the forgone contribution margin on an external sale when a frame is transferred to the Glass Division. The contribution margin equals $30 ($160 – $130). When there is excess capacity in the Frame Division, there is no opportunity cost associated with a transfer.

c. Fixed overhead per frame (125%)($40) = $50

Transfer price = variable cost + fixed overhead per frame

+ (10%)(variable cost + fixed overhead per frame)

= $130 + $50 + [(10%)($130 + $50)]

= $198

d. Incremental revenue per window................................... $310Incremental cost per window, for Weathermaster Window Company:

Direct material (Frame Division)................................ $30Direct labor (Frame Division)..................................... 40Variable overhead (Frame Division).......................... 60Direct material (Glass Division)................................. 60Direct labor (Glass Division)...................................... 30Variable overhead (Glass Division)........................... 60Total variable (incremental) cost............................... 280

Incremental contribution per window in special orderfor Weathermaster Window Company........................ $ 30

The special order should be accepted because the incremental revenue exceeds the incremental cost, for Weathermaster Window Company as a whole.


e. Incremental revenue per window................................... $ 310McGraw-Hill/Irwin 2005 The McGraw-Hill Companies, Inc.Managerial Accounting, 6/e 13-16

Incremental cost per window, for the Glass Division:Transfer price for frame [from requirement 2(c)]..... $198Direct material (Glass Division)................................. 60Direct labor (Glass Division)...................................... 30Variable overhead (Glass Division)........................... 60Total incremental cost................................................ 348

Incremental loss per window in special orderfor Glass Division......................................................... $ (38)

The Glass Division manager has an incentive to reject the special order because the Glass Division's reported net income would be reduced by $38 for every window in the order.

f. One can raise an ethical issue here to the effect that a division manager should always strive to act in the best interests of the whole company, even if that action seemingly conflicts with the division’s best interests. In complex transfer pricing situations, however, it is not always as clear what the company’s optimal action is as it is in this rather simple scenario.

3. The use of a transfer price based on the Frame Division's full cost has caused a cost that is a fixed cost for the entire company to be viewed as a variable cost in the Glass Division. This distortion of the firm's true cost behavior has resulted in an incentive for a dysfunctional decision by the Glass Division manager.



The owner’s analysis incorrectly includes the following allocated costs that will be incurred regardless of whether the ice cream counter is operated:

Utilities ........................................................................................................................ $ 4,350Depreciation of building ........................................................................................... 6,000Deli manager’s salary ................................................................................................ 4,500 Total ............................................................................................................................ $14,850

It is possible that closing the ice cream counter might save a portion of the utility cost, but that is doubtful.

A better analysis follows:

Sales ...................................................................................................... $67,500Less: Cost of food ............................................................................... 30,000 Gross profit .......................................................................................... 37,500Less: Operating expenses

Wages of counter personnel ................................................ $18,000Paper products ....................................................................... 6,000Depreciation of counter equipment and furnishings* ........ 3,750 Total ......................................................................................... 27,750

Profit on ice cream counter $ 9,750

*Depreciation on the counter equipment and furnishings is included because it is traceable to the ice cream operation and is an expense in the determination of income. If a cash-flow analysis is desired, this noncash expense should be excluded.


1. (a) $11,100 allocation of rent on factory building: Irrelevant, since Toon Town Toy Company will rent the entire factory building regardless of whether it continues to operate the Packaging Department. If the department is eliminated, the space will be converted to storage space.

(b) $13,000 rental of storage space in warehouse: Relevant, since this cost will be incurred only if the Packaging Department is kept in operation. If the department is eliminated, this $13,000 rental cost will be avoided.

2. The $13,000 warehouse rental cost is the opportunity cost associated with using space in the company’s factory building for the Packaging Department.



(a) $51,000 salary of Packaging Department manager: Irrelevant, since this manager will be employed by the company at $51,000 per year regardless of whether the Packaging Department is kept in operation.

(b) $66,000 salary of Cutting Department manager if a new person must be hired: Relevant, since this cost will be incurred only if the Packaging Department is kept in operation. If the Packaging Department is eliminated, then that department’s current manager will move to the Cutting Department at $51,000 per year.

The following comparison may help to clarify the analysis:

ANNUAL SALARY COST INCURRED BY TOON TOWN TOY COMPANY

If Packaging Department

is Kept

If Packaging Department

is EliminatedSalary of the person currently managing the Packaging Department ..................................... $ 51,000* $51,000†

Salary of newly hired person to manage the Cutting Department ............................................. 66,000 ____ Total ........................................................................ $117,000 $51,000 Difference ............................................................... $66,000

*Continues to manage Packaging Department.†Moves to Cutting Department position.

Additional comment:

There are many possible reasons why it might cost Toon Town Toy Company more to hire a new Cutting Department manager than to transfer a current employee to the position. One possible scenario is that the current Packaging Department manager is a relatively young and inexperienced manager, to whom top management is willing to give the Cutting Department opportunity if the Packaging Department is eliminated. However, if a new person must be hired, Toon Town Toy Company will be forced to go into the job market for more senior and experienced managers. Other possible reasons include existing contractual agreements, union contracts, and so forth.



1. The owner’s reasoning probably reflects the following calculation:

Savings in annual operating expenses if old pizza oven is replaced .................. $3,000Write-off of old oven’s remaining book value ($10,500 ÷ 3) ................................. (3,500)“Loss” associated with replacement ...................................................................... $ (500)

2. The owner’s analysis is flawed, because the book value of the old pizza oven is a sunk cost. It should not enter into the equipment replacement decision.

3. Correct analysis:

Savings in annual operating expenses if old pizza oven is replaced .................. $3,000Acquisition cost of new oven, which will be operable for one year ..................... (2,200)Net benefit from replacing old pizza oven .............................................................. $ 800



1. The relevant cost of the theolite to be used in producing the special order is the 21,750p sales value that the company will forgo if it uses the chemical. This is an example of an opportunity cost.

p denotes Argentina’s peso.

2. (a) 21,750p sales value: Discussed in requirement (1).

(b) 24,000p book value (8,000 kilograms ´ 3p per kilogram): Irrelevant, since thebook value is a sunk cost.

(c) 28,800p current purchase cost (8,000 kilograms ´ 3.60p per kilogram): Irrelevant, since the company will not be buying any theolite.



1. The relevant cost of genatope is calculated as follows:

Cost of replacing the 1,000 kilograms to be used in the special order (1,000 kilograms ´ 13.05p) .................................................................................. 13,050 P*Additional cost incurred on the next order of genatope as a result of having to place the order early [4,000 kilograms ´ (13.05p – 12.45p)] ........... 2,400 PTotal relevant cost ..................................................................................................... 15,450 p

p denotes Argentina’s peso.

*This cost would not be incurred if the special order were not accepted.

2. (a) 97,200p book value (8,000 kilograms ´ 12.15p per kilogram): Irrelevant, since it is a sunk cost.

(b) 1,000 kilograms to be used in the special order: Relevant, as shown in requirement (1).

(c) 13.05p price if next order is placed early: Relevant, since this is the cost of replacing the used genatope.

(d) 12.45p price if next order is placed on time: Relevant, because an additional 4,000 kilograms in the next order will be purchased at a .60p per kilogram premium. This .60p premium is the difference between the 13.05p price and the 12.45p price.



The most profitable product is the one that yields the highest contribution margin per unit of the scarce resource, which is direct labor. We do not know the amount of direct-labor time required per unit of either product, but we do know that Beta requires six times as much direct labor per unit as Alpha. Define an arbitrary time period for which direct laborers earn $1.00, and call this a “time unit.” The two products’ contribution margins per “time unit” are calculated as follows:

Alpha BetaUnit contribution margin ...................................................... $9.00 $36.00“Time units” required per unit of product .......................... 3 18Contribution margin per “time unit” Alpha: ($9.00 ÷ 3) .............................................................. $3.00 Beta: ($36.00 ÷ 18) ............................................................ $ 2.00

Therefore, Alpha is a more profitable product. Any arbitrary amount of direct labor time expended on Alpha production will result in a greater contribution margin than an equivalent amount of labor time spent on Beta production.



1. Decision variables:

X = number of units of Alpha to be produced

Y = number of units of Beta to be produced

2. Objective function:

Maximize 9X + 36Y

The coefficients of X and Y are the unit contribution margins for Alpha and Beta, respectively. Maximizing this objective function will result in the highest possible total contribution margin.

3. Constraints:

(a) Direct-labor time constraint: .25X + 1.5Y 11,000

The coefficients of X and Y are the number of hours of direct labor required to produce one unit of Alpha and one unit of Beta, respectively. For example, the direct-labor cost per unit of Beta is $18.00, so it must require 1.5 direct-labor hours per unit of Beta.

(b) Machine time constraint: 1X + 2Y 9,000

The coefficients of X and Y are the number of hours of machine time required to produce one unit of Alpha and one unit of Beta, respectively.

(c) Nonnegative production quantities: X, Y 0

The complete linear program is the following

Maximize 9X + 36Y

Subject to: .25X + 1.5Y 11,000

1X + 2Y 9,000

X, Y 0



1. (a) Notation: X denotes the quantity of zanide produced per day

Y denotes the quantity of kreolite produced per day

(b) Contribution margin:

Zanide KreolitePrice .......................................................................................$108 $126Unit variable cost .................................................................. 84 84 Unit contribution margin ......................................................$ 24 $ 42

(c) Linear program:

Maximize 24X + 42Y

Subject to: 2X + 2Y 24

1X + 3Y 24

X, Y 0

2. Graphical solution: See next page.

Corner points in feasible region: Objective function value:

X = 0 Y = 0 $ 0

X = 0 Y = 8 336

X = 6 Y = 6 396

X = 12 Y = 0 288

The maximum objective function value is achieved when X = 6 and Y = 6. Thus, the company should produce 6 drums of zanide per day and 6 drums of kreolite per day.

3. The objective function value at the optimal solution is a $396 total contribution margin as shown in requirement (2).


EXERCISE 14-43 (CONTINUED)

Graphical solution:


Y

25

15

10

5

5 10 15 20 25X

Machine I constraint

Optimal solution (X = 6, Y = 6)

Objective functionMachine II constraint

20

Feasible region

SOLUTIONS TO PROBLEMS


1. Contemporary Trends will be worse off by $6,400 if it discontinues wallpaper sales.

Paint andSupplies Carpeting Wallpaper

Sales…………………….. $190,000 $230,000 $ 70,000Less: Variable costs…. 114,000 161,000 56,000 Contribution margin…. $ 76,000 $ 69,000 $ 14,000

If wallpaper is closed, then:

Loss of wallpaper contribution margin…... $(14,000)Remodeling……………………………………. (6,200)Added profitability from carpet sales*…… 32,500Fixed cost savings ($22,500 x 40%)………. 9,000Decreased contribution margin from paint and supplies ($76,000 x 20%)…………….. (15,200)Increased advertising……………………….. (12,500 )Income (loss) from closure………………… $ (6,400)

* The current contribution margin ratio for carpeting is 30% ($69,000 ÷ $230,000). This ratio will increase to 35%, producing a new contribution for the line of $101,500 [($230,000 + $60,000) x 35%]. The end result is that carpeting’s contribution margin will rise by $32,500 ($101,500 - $69,000), boosting firm profitability by the same amount.

2. This cost should be ignored. The inventory cost is sunk (i.e., a past cost that is not relevant to the decision). Regardless of whether the department is closed, Contemporary Trends will have a wallpaper inventory of $11,850.

3. The Internet- and magazine-based firms likely have several advantages:

These companies probably carry little or no inventory. When a customer places an order, the firm simply calls its supplier and acquires the goods. The result may be lower expenditures for storage and warehousing.

These firms do not need retail space for walk-in customers. Internet- and magazine-based firms can conduct business globally.

Contemporary Trends, on the other hand, is confined to a single store in Baltimore.



1. Sets result in a 20% increase, or 1,500 dresses (1,250 ´ 1.20 = 1,500).

Total Number ofPercentof Total Dresses

Accessory Capes Handbags Total

Complete sets................................... 70% 1,050 1,050 1,050Dress and accessory cape.............. 6% 90 90Dress and handbag.......................... 15% 225 225Dress only......................................... 9 % 135 Total units if additional items are introduced...................................... 100 % 1,500 1,140 1,275Less: Unit sales if additional items are not introduced.......................... 1,250 -- -- Incremental sales............................. 250 1,140 1,275Incremental contribution margin per unit (excluding material and cutting costs)................................. ́ $192 .00 ́ $12 .80 ́ $4 .80 Total incremental contribution margin............................................. $48,000 $14,592 $6,120 $68,712

Additional costs: Additional cutting cost (1,500 ´ $14.40)........................... $21,600 Additional material cost (250 ´ $80.00).............................. 20,000 Lost remnant sales (1,250 ´ $8.00)............................. 10,000 Incremental cutting for extra dresses (250 ´ $32.00)...... 8,000

59,600

Incremental profit............................. $ 9,112

2. Qualitative factors that could influence the company’s management team in its decision to manufacture matching accessory capes and handbags include:

accuracy of forecasted increase in dress sales.

accuracy of forecasted product mix.



company image of a dress manufacturer versus a more extensive supplier of women’s apparel.

competition from other manufacturers of women’s apparel.

whether there is adequate capacity (labor, facilities, storage, etc.).


1.

BlenderFood

ProcessorUnit cost if purchased from an outside supplier .......................................$60 $114 Incremental unit cost if manufactured: Direct material ...........................................................................................$18 $ 33 Direct labor ................................................................................................ 12 27 Variable overhead $48 – $30 per hour fixed ....................................................................... 18 $96 – (2)($30 per hour fixed) ................................................................ 36 Total .......................................................................................................$48 $ 96 Unit cost savings if manufactured ..............................................................$12 $ 18 Machine hours required per unit ................................................................. 1 2Cost savings per machine hour if manufactured $12 ÷ 1 hour ...............................................................................................$12 $18 ÷ 2 hours ............................................................................................. $ 9

Therefore, each machine hour devoted to the production of blenders saves the company more than a machine hour devoted to food processor production.

Machine hours available ...................................................................................... 50,000Machine hours needed to manufacture 20,000 blenders ................................. 20,000

Remaining machine hours ................................................................................... 30,000

Number of food processors to be produced (30,000 ÷ 2) ................................ 15,000Conclusion: Manufacture 20,000 blenders

Manufacture 15,000 food processorsPurchase 13,000 food processors


2. If the company’s management team is able to reduce the direct material cost per food processor to $18 ($15 less than previously assumed), then the cost


savings from manufacturing a food processor are $33 per unit ($18 savings computed in requirement (1) plus $15 reduction in material cost):

BlenderFood

ProcessorNew unit cost savings if manufactured .......................................... $12.00 $33.00Machine hours required per unit ..................................................... 1 MH 2 MH Cost savings per machine hour if manufactured $12 ÷ 1 hour .................................................................................. $12.00 $33 ÷ 2 hours ................................................................................ $16.50

Therefore, devote all 50,000 hours to the production of 25,000 food processors.

Conclusion: Manufacture: 25,000 food processorsPurchase: 3,000 food processorsPurchase: 20,000 blenders


1. Incremental unit cost if purchased: Purchase price .......................................................................................... $ 45,000 Material handling ...................................................................................... 9,000 Total ........................................................................................................... $ 54,000

Incremental unit cost if manufactured: Direct material ........................................................................................... $ 3,000 Material handling ...................................................................................... 600 Direct labor ................................................................................................ 24,000 Variable manufacturing overhead ($36,000 ´ 1/3) ................................ 12,000 Total ........................................................................................................... $ 39,600Increase in unit cost if purchased ($54,000 – $39,600) .............................. $ 14,400

2. Increase in monthly cost of acquiring part RM67 if purchased (10 ´ $14,400, as computed above) .......................................................... $144,000Less: rental revenue from idle space .......................................................... 75,000Increase in monthly cost .............................................................................. $ 69,000


Problem 14-47 (continued)

3. Contribution forgone by not manufacturing alternative product ............. $156,000Savings in the cost of acquiring RM67 (10 ´ $14,400 as computed in requirement 1) ......................................... 144,000Net cost of using limited capacity to produce part RM67 ......................... $ 12,000


The analysis prepared by the engineering, manufacturing, and accounting departments of Cincinnati Flow Technology (CFT) was not correct. However, their recommendation was correct, provided that potential labor-cost improvements are ignored. An incremental cost analysis similar to the following table should have been prepared to determine whether the pump should be purchased or manufactured. In the following analysis, fixed factory overhead costs and general and administrative overhead costs have not been included because they are not relevant; these costs would not increase, because no additional equipment, space, or supervision would be required if the pumps were manufactured. Therefore, if potential labor cost improvements are ignored, CFT should purchase the pumps because the purchase price of $102 is less than the $108 relevant cost to manufacture.

Incremental cost analysis:

Cost of10,000 Unit

Assembly Run Per UnitPurchased components ................................................................... $ 180,000 $ 18Assembly labor ................................................................................. 450,000 45Variable manufacturing overhead ................................................... 450,000 45 Total relevant cost......................................................................... $1,080,000 $108



1. Per-unit contribution margins:Standard Enhanced

Selling price………………………………….. $375.00 $495.00Less: Variable costs:

Direct material………………………… $42.00 $67.50Direct labor…………………………….. 22.50 30.00Variable manufacturing overhead … 36.00 48.00Sales commission $375 x 10%; $495 x 10%………….Total unit variable cost……………….

37 .50 138 .00

49 .50 195 .00

Unit contribution margin…………………… $237 .00 $300 .00

2. The following costs are not relevant to the decision: Development costs—sunk Fixed manufacturing overhead—will be incurred regardless of which

product is selected Sales salaries—identical for both products Market study—sunk

3. Martinez, Inc. expects to sell 10,000 Standard units (40,000 units x 25%) or 8,000 Enhanced units (40,000 units x 20%). On the basis of this sales forecast, the company would be advised to select the Standard model.

Standard EnhancedTotal contribution margin:

10,000 units x $237; 8,000 units x $300…. $2,370,000 $2,400,000Less: Marketing and advertising……………… 195,000 300,000 Income……………………………………………... $2,175,000 $2,100,000

4. The quantitative difference between the profitability of Standard and Enhanced is relatively small, which may prompt the firm to look at other factors before a final decision is made. These factors include:

- Competitive products in the marketplace - Data validity - Growth potential of the Standard and Enhanced models - Production feasibility - Effects, if any, on existing product sales - Break-even points


601 13,14 solutions

Documents

outlay cost opportunity

total incremental cost

companys incremental

incremental cost drops

special order

total unit variable

additional variable

fabrication division