differential cost analysis for operating decisions

CHAPTER 7

DIFFERENTIAL COST ANALYSIS FOR OPERATING DECISIONS

Questions, Exercises, and Problems: Answers and Solutions

7.1 See text or glossary at the end of the book.

7.2 Fixed costs are only fixed in the short-run so any long-run decision may have differential fixed costs. For instance, decisions affecting capacity would include differential fixed costs.

7.3 Short-term pricing decisions are based on differential costs, any price higher than differential costs will increase profits even if it is lower than full cost. However, in the long-term, prices must cover the full cost of producing the product.

7.4 No. Facility-sustaining costs are fixed in the short-term; they will be incurred regardless of production level. Therefore, they are not differential and should not be considered in a short-term pricing decision.

7.5 Full cost information is appropriate for long-term pricing decisions.

7.6 d. the differential costs of producing the order.

7.7 b. depreciation of buildings.

7-1 Solutions

7.8 "Setup" or "order" costs are costs incurred each time an order is placed or a production run is made. "Carrying" costs are the costs of keeping inventory, for example, maintaining warehouse facilities.

CostsTotal Costs

Carrying Costs

Order Costs

Order SizeOptimal Order

7.9 The costs that are relevant for make-or-buy decisions are the differential costs.

7.10 True. The objective of the theory of constraints is to increase throughput contribution.

7.11 Any differential costs should be considered in the decision, including overtime, and costs of additional shifts or other means of expanding capacity.

7.12 Answers will vary, but should all be short-term pricing decisions.

7.13 In the long-term full costs must be met so full-cost information is useful for decisions affecting the long-term.

7.14 The statement is true in general short-term decisions in which there is excess capacity. However, in any situation where the decision affects capacity, the statement would not be true.

7.15 In the short-run, sales revenues need only cover the differential costs of production and sale. So, from a short-run perspective so long as the sale does not affect other output prices or normal sales volume, a “below cost” sale may result in a net increase in income so long as the revenues cover the differential costs. However, in the long-run all costs must be covered or management would not reinvest in the same type of assets. If the company must continually sell below the full cost of production then it will most likely get out of that particular business when it comes time to replace those facilities.

7.16 Differential Costs

Solutions 7-2

Fuel

Wear and tear related to miles driven such as tires, mileage-related maintenance, lube and oil

Parking and tolls, if any

Car wash if needed due to the trip

Risk of casualties that vary with mileage

Other costs that vary with mileage

7.17 Differential Costs

Cost of the car

Foregone interest income on funds paid for the car

Interest on debt on the car

Insurance

Maintenance that is time-related

License and taxes

These costs are different from the costs in Question 7.16. The costs in Question 7.16 are those required to operate the car for an additional few miles. The costs that vary with the number of cars do not vary with mileage. The costs in this question vary with the number of cars and not with the mileage driven.

7.18 Activity-based costing may actually provide better cost information than costing systems that allocate indirect costs based on one volume-based cost driver. Activity-based costing provides more detailed cost data that might lead to more informed decision making regarding prices. Since market prices are typically not available for custom orders, many companies use cost-plus pricing. Since this company uses activity-based costing, it has the cost information necessary to use a cost-plus pricing approach.

7.19 In differential analysis, only alternative future cash flows are relevant for decision making. Past costs may provide useful information, but they are essentially sunk costs and not directly relevant to a decision.

7.20 The contribution margin per unit would be the most appropriate figure since it represents the price minus the product’s variable costs. The gross margin is based on full absorption unit costs that include allocated fixed costs, which can be misleading to the decision maker.

7-3 Solutions

7.21 Answers will vary but should include identification of differential costs. This question is directed to having students think about the many situations in which there are make or buy decisions.

7.22 (Special order.)

Alternative – Status Quo = Difference

Revenue............................... $ 41,280a $ 40,000b $ 1,280 Higher

Variable Costs...................... 31,200 c 30,000 d 1,200 HigherContribution Margin............. $ 10,080 $ 10,000 $ 80 HigherFixed Costs.......................... 7,000 7,000 -- Operating Profit.................... $ 3,080 $ 3,000 $ 80 Higher

Cisco’s should accept the order because it will increase profits by $80 for the period.

a$41,280 = (2,000 jerseys X $20) + (80 jerseys X $16).b$40,000 = 2,000 jerseys X $20.c$31,200 = (2,000 jerseys + 80 jerseys)($12 + $3).d$30,000 = 2,000 jerseys X ($12 + $3).

7.23 (Differential costs.)

Yes. Road-Runner should accept the special order. Operating profit will increase $5,400 as shown below.

Special-Order Sales (400 X $30).................................................... $ 12,000Less Variable Costs:

Manufacturing (400 X $15)....................................................... $ 6,000Sales Commissions (400 X $1.50)............................................. 600 6,600

Addition to Company Operating Profit........................................... $ 5,400

7.24 (Identify differential costs.)

The differential costs would probably include:

a. Product design work to design the boot.

c. Advertising the boot.

f. Sales commissions.

Solutions 7-4

7.25 (Target costing and pricing.)

Price – (20% X Price) = Highest acceptable costs

$50 – $10 = $40.

The highest acceptable manufacturing costs for which Donelan Products would be willing to produce the lines is $40 per foot.

7.26 (Target costing and pricing.)

Price – (20% X Price) = Highest acceptable costs

$6.00 – $1.20 = $4.80.

The highest acceptable manufacturing costs for which Irish Products would be willing to produce the wheels is $4.80.

7.27 (Customer profitability analysis.)

Note: Amounts are in thousands.

Alternative Status Quo DifferenceDrop

Super 6Motel Total

Revenues (Fees Charged)............. $ 350 $ 580 $ 230 LowerOperating Costs:

Cost of Services (Vari-able)..................................... 305 517 212 Lower

Salaries, Rent, and Gen-eral Administration (Fixed)................................. 55 55 0

Total OperatingCosts........................... 360 572 212 Lower

Operating Profit (Loss)................. $ (10 ) $ 8 $ 18 Lower

Squeaky should not drop the Super 6 Motel account in the short run as profits would drop by $18,000.

7.28 (Customer profitability analysis.)

7-5 Solutions

Note: Amounts are in thousands.

Alternative Status Quo DifferenceDrop

Hospital TotalRevenues (Fees Charged)............. $ 1,400 $ 2,320 $ 920 LowerOperating Costs:

Cost of Services (Vari-able)..................................... 1,220 2,068 848 Lower

Salaries, Rent, and Gen-eral Administration (Fixed)................................. 200 200 0

Total OperatingCosts........................... 1,420 2,268 848 Lower

Operating Profit (Loss)................. $ (20 ) $ 52 $ 72 Lower

H & B should not drop the Hospital account in the short run as profits would drop by $72,000.

7.29 (Product mix decision.)

Produce Product Y only, because its contribution per machine hour is greater.

Y Z Selling Price per Unit................................................................ $ 30 $ 55Variable Cost per Unit of Materials and Labor*......................... (5 ) (9 )Contribution per Unit to Overhead............................................. $ 25 $ 46 Machine Hours Required per Unit............................................. 1 2Contribution per Hour Required................................................ $ 25 $ 23

*Fixed costs are not differential and therefore excluded.

7.30 (Product choice.)

Solutions 7-6

Alternative 1: Warehouse.Alternative 2: Office space.Alternative 3: Restaurants and specialty shops.

Alternative 1 2 3

Revenue................................................ $ 960,000 $ 982,800 $ 1,101,100Variable Costs....................................... 40,000 70,000 95,000 Total Contribution Margin..................... $ 920,000 $ 912,800 $ 1,006,100Fixed Costs........................................... 600,000 600,000 600,000 Operating Profit..................................... $ 320,000 $ 312,800 $ 406,100

Renovation Enterprises should choose Alternative 3.

7.31 (Throughput contribution.)

With Option (a) the throughput contribution increases by $360 [= 24 units X ($25 selling price – $10 variable costs)] which is more than the additional cost of $100 per Saturday.

Option (b) would increase throughput contribution by $180 [= 12 units X ($25 selling price – $10 variable costs)] which is less than the additional costs of $200.

Victoria’s should go with Option (a) which has a positive impact on contribution while Option (b) has a negative effect on contribution.

7.32 (Throughput contribution.)

Increasing capacity to 15,000 is an increase of 1,560 units (=15,000 – 13,440 units with current capacity). The throughput contribution increases by $85,800 [= 1,560 units × ($120 selling price – $65 variable costs)]. This exceeds the additional cost of $60,000 per month by $25,800. Stay Warm should pursue this option to alleviate the bottleneck because it provides a positive contribution.

7.33 (Make or buy.)

a. Buy – Make = Difference

7-7 Solutions

Variable Costs................................. $ 300,000 – $ 250,000 = $ 50,000

Ol’ Salt should make the sails. The fixed costs are not relevant to this decision because they will be incurred regardless of the decision.

b. Buy – Make = DifferenceVariable Cost............. $ 300,000 – $ 250,000 = $ 50,000 HigherLess Revenue............ 80,000 – -0- = 80,000 HigherNet Effect on

Costs.................... $ 220,000 – $ 250,000 = $ 30,000 Lower

Yes, it would affect the recommendation in Part a. Ol’ Salt should buy in view of the rental opportunity.

7.34 (Make or buy.) VariableCost per 100 Units

Direct Material................................................................................................ $100Direct Labor.................................................................................................... 50Other Variable Costs....................................................................................... 25

Total............................................................................................................ $ 175

a. No, since the $200 price is greater than the incremental (variable) cost of $175. The fixed costs are not differential.

b. Yes. The $160 price is less than the incremental cost of $175.

7.35 (Sell or process further.) Process

Further – Sell = Difference

Revenue $1,560,000a – $900,000 = $660,000 higher

Solutions 7-8

Less Additional Fixed Costs 520,000 – 0 = 520,000 higher

Effect on Operating Profit $1,040,000– $900,000 = $140,000 higher

The company should process further.

a (0.3 x 75,000 x $32 for large grade) + (0.7 x 75,000 x $16 for medium grade) = $720,000 + $840,000 = $1,560,000

7.36 (Sell or process further.)

Cheese – Milk = Difference

Revenue $180,000 – $100,000 = $80,000 higher

Less Additional

Processing Costs 70,000 – 0 = 70,000 higher

Effect on Operating Profit $110,000 – $100,000 = $10,000 higher

The company should process further. The additional $20,000 mentioned in the exercise should either be ignored, as in the solution here, or included in both the “cheese” and “milk” alternatives.

7.37 (Dropping a product line.)

Manual Electric QuartzMachine Time per Unit...................... 0.4 hr. 2.5 hr. 5.0 hr.Contribution Margin........................... $10.00 $ 16.00 $ 22.00Contribution Margin per

Machine Hour............................. $25.00a $ 6 .40 b $ 4 .40 c

a$25 = $10/0.4 hours.b$6.40 = $16/2.5 hours.c$4.40 = $22/5 hours.

Timepiece Products should drop the Quartz line.

7.38 (Dropping a product line.)

Alternative

7-9 Solutions

DropProduct C – Status Quo = Difference

Revenue.................................. $ 50,000a $ 88,000 $ 38,000 Lower

Variable Costs......................... 37,000 a 71,000 34,000 LowerContribution Margin................ $ 13,000 $ 17,000 $ 4,000 Lower

Fixed Costs............................. 10,000 b 15,000 5,000 LowerOperating Profit....................... $ 3,000 $ 2,000 $ 1,000 Higher

Yes. Tiger Products should drop Product C because the loss of its contribution margin is lower than the reduction in fixed costs.

aSales and variable costs of Product C are eliminated.

bTotal fixed costs reduced by $5,000.

7.39 (Inventory management. )

Order Average Number InventoryAnnual Size of Units Carrying Order TotalOrders in Unitsa in Inventory Costsb Costsc Costs

40 1,250 625 $3,125 $4,000 $7,125

50 1,000 500 2,500 5,000 7,500

60 833.33 416.67 2,083 6,000 8,083

a 50,000 units/number of orders.bAverage units in inventory x $5c Number of orders x $100.

7.40 (Inventory management. )

Order Average Number InventoryAnnual Size of Units Carrying Order TotalOrders in Unitsa in Inventory Costsb Costsc Costs

40 2,000 1,000 $4,000 $2,000 $6,000

50 1,600 800 3,200 2,500 5,700

60 1,333 666.67 2,667 3,000 5,667

a80,000 units/number of orders.bAverage units in inventory x $4cNumber of orders x $50.

7.41 (Appendix 7.1) (Product choice using linear programming.)

Solutions 7-10

Maximize: 10A + 13B

Subject to: (1) 4A + 2B < 14,400 labor hours(2) 2A + 3B < 12,000 machine hours

4,000–

3,000–

1,000 2,000 3,000 4,0007,200

3,600–

Units of A

Machine Hours:

Units of B

a

b

c

Labor Hours: 4A + 2B = 14,400; 4A = 14,400 – 2B

14,400 – 2B 4

2A + 3B = 12,000 2A = 12,000 – 3B A = 6,000 – 1.5 B

1,000–

6,000–

0–

= 3,600 – .5BA =

At (a): B = 0, A = 6,000 – 1.5B = 6,000.

At (c): A = 0, 0 = 3,600 – .5B, B = 7,200.

At (b): Substitute the labor hours equation into the machine hours equation: A = 3,600 – .5B = 6,000 – 1.5B.

B = 2,400

A = 3,600 – .5(2,400) = 2,400.

Points (A, B) (6,000, 0)

(2,400, 2,400) (0, 7,200)

A $60,000 $24,000

$0

B $0

$31,200 $93,600

$60,000 $55,200 $93,600

Total

Contribution Margin

Optimal Point

The company should produce 0 units of Product A and 7,200 units of Product B.

7.42 (Appendix 7.1) (Product mix decisions [CPA adapted].)

7-11 Solutions

Problem Formulation:Maximize Total Contribution Margin = 4.25Z + 5.25BSubject to:

Process 1 Constraint: Z + 2B < 1,000Process 2 Constraint: Z + 3B < 1,275Technical Labor Constraint: B < 400

Critical Produce and Sell Total Contribution

Points Zeta Beta Marginc

a -0- -0- -0-b 1,000 -0- $ 4,250.00*

c 450 a 275 a $ 3,356.25

d 75 b 400 b $ 2,418.75e -0- 400 $ 2,100.00

*Optimal Solution.

aZ + 2B = 1,000 [Process 1 Constraint].

Z + 3B = 1,275 [Process 2 Constraint].

Solving simultaneously:(1,000 – 2B) + 3B = 1,275

B = 275.

Z + 2(275) = 1,000Z = 450.

bZ + 3B = 1,275B = 400.

Solving simultaneously:Z + 3(400) = 1,275

Z = 75.

cTotal Contribution Margin = ($4.25 X Zetas) + ($5.25 X Betas).

7.43 (Appendix 7.1) (Product mix decision.)

Each additional hour of Process 1 time yields an additional contribution of $4.25. Hence, the opportunity cost of additional Process 1 time is $4.25. Since Hanson already pays $1.75 for Process 1 time to produce one unit of Zeta, it would be willing to pay up to $6.00 for the additional time to produce one unit of Zeta.

7.44 (Appendix 7.2) (Economic order quantity.)

D = 10,000 axles

Solutions 7-12

Ko =$10

Kc = 0.20 X $100 = $20

N = = = 100

Annual ordering costs = $1,000 (= 100 X $10).

7.45 (Appendix 7.2) (Economic order quantity.)

a.

Ko = $15

Kc = $4

D = 30,000

b. Number of Orders per Year =

7.46 (Radios Inc.; Special order with lost sales.)

Assume that all radios are sold.

7-13 Solutions


Revenue....................................... $ 209,000a $ 300,000b $ 91,000 Lower

Variable Costs.............................. 60,000 c 69,000 d 9,000 LowerContribution Margin..................... $ 149,000 $ 231,000 $ 82,000 Lower

Fixed Costs.................................. 61,000 e 61,000 e -- Operating Profit........................... $ 88,000 $ 170,000 $ 82,000 Lower

Radios Inc. should turn down the contract unless there are non-pecuniary benefits that will offset the $82,000 reduction in profits.

a$209,000 = (10,000 units X $15) + (10,000 units X $3.40) + $25,000.b$300,000 = 20,000 units X $15.c$60,000 = (10,000 units X $3.45) + (10,000 units X $2.55).d$69,000 = 20,000 units X $3.45.e$61,000 = 20,000 units X ($0.85 + $2.20).


The company should have accepted the special order. Profits would increase by $400,000.

Alternative Status Quo DifferenceOrder Order Not Incremental

Accepted Accepted Cash Flows

Revenues........................... $ 66,500,000a $ 64,000,000b $ 2,500,000 Higher

Variable Costs................... 40,500,000c 38,400,000d 2,100,000 Higher

Fixed Costs....................... 9,600,000 e 9,600,000 e -0 - Operating Profit................. $ 16,400,000 $ 16,000,000 $ 400,000 Higher

a$66,500,000 = ($400 × 160,000 regular sales units) + ($250 × 10,000 special order units).

b$64,000,000 = $400 × 160,000 units.

c$40,500,000 = [($160 + $80) × 160,000 regular sales units] + [($160 + $50) × 10,000 special order units].

d$38,400,000 = ($160 + $80) × 160,000 regular sales units.

e$9,600,000 = $60 × 160,000 units = total fixed costs under both the alternative and the status quo.

Solutions 7-14

7.48 (Pricing decisions.)

a. Alternative Status Quo Difference20,400 20,000Quarts Quarts

Sales Revenue................... $ 61,000 a $ 60,000 b $ 1,000 HigherLess Variable Costs:

Materials...................... 20,400 20,000 400 HigherLabor............................ 10,200 10,000 200 HigherVariable Over-

head........................... 5,100 5,000 100 HigherTotal Variable

Cost..................... 35,700 35,000 700 HigherContribution Margin.......... 25,300 25,000 300 HigherLess Fixed Costs............... 20,000 20,000 0 Operating Profit................. $ 5,300 $ 5,000 $ 300 Higher

a$61,000 = (20,000 quarts × $3.00 per quart) + (400 quarts × $2.50 per quart).

b$60,000 = 20,000 quarts × $3.00 per quart.

b. The lowest price for which the ice cream could be sold without reducing profits is $1.75 per quart, which would just cover the variable costs of the ice cream.

7-15 Solutions


On the basis of the data in the question, it would not pay Nancy to accept the order.

New Sales (10,000 Units × $6).................................................. $ 60,000Less Standard Sales................................................................... 12,500 Differential Revenue................................................................. $ 47,500

Differential Costsa.................................................................... 49,050 Net Advantage to Special Units................................................. $ (1,550 )

Other factors must be considered such as the reliability of the cost estimates and the importance of this valued customer.

aDifferential cost of the order is:

Costs Incurred to Fill Order*Material (10,000 Units × $2)................................................................... $ 20,000Labor (10,000 Units × $3.60).................................................................. 36,000Special Overhead.................................................................................... 2,000

$ 58,000

Costs Reduced for Standard ProductsMaterial.................................................................................................. $ 4,000Labor...................................................................................................... 4,500Other....................................................................................................... 450

$ 8,950 Total Differential Costs...................................................................... $ 49,050

*Depreciation, rent, heat, and light are not affected by the order. Power might be dependent upon the particular requirements of the special units. It is assumed here that the same amount of power will be used in each case.

7.50 (Multiple choice—special order.)

Solutions 7-16

a. (4) $8,000 = $8 per unit × 1,000 units.

b. (2) $6,000 = ($4 + $2) × 1,000 units.

c. (1) $0. Total fixed costs do not change as a result of the special order.

d. (4) Decrease $0.25: Fixed Costs per Unit Without theSpecial Order ($10,000 + $8,000) ÷ 8,000 Units..................................................... $ 2.25

Fixed Costs per Unit with the SpecialOrder ($10,000 + $8,000) ÷ 9,000 Units............................................................... 2.00

Decrease as a Result of Special Order................. $ 0.25

e. (1) Increase it.

7.51 (Customer profitability analysis)

Differential revenue from new accounts = $170 × 7,000 = $1,190,000.

Differential costs of new accounts: Acquisition costs = $180,000 - $20,000 costs that are not differential = $160,000Transaction processing costs = ($150 - $10 non-differential costs) × 7,000 = $980,000

Differential operating income = $1,190,000 - $160,000 - $980,000 = $50,000.

The effect of offering these accounts has a small positive impact on operating income. Management should consider the likely positive effect of attracting these students as long term customers of the bank, which makes the offer to students even more attractive.

7.52 (Customer profitability analysis)

7-17 Solutions

a. First compute cost driver rates.Transportation costs = $.80 per mile = $800,000/1,000,000 miles.Processing an order = $1 per minute = $100,000/100,000 minutes.Marketing management = 10% of sales = $700,000/$7,000,000 in sales.Special requirements—foreign = $500 per car = $100,000/200 cars.

Next apply costs driver rates to customers. For each customer and each cost driver, multiply the cost driver rate by the cost driver volume given in the problem.

Customer X: ($.80 × 400 miles) + ($1 × 30 minutes) + ($10% × $600 sales) = $320 + $30 + $60 = $410.

Customer Y: ($.80 × 2,200 miles) + ($1 × 35 minutes) + ($10% × $2,000 sales) = $1,760 + $35 + $200 = $1,995.

Customer Z: ($.80 × 1,300 miles) + ($1 × 80 minutes) + ($10% × $1,500 sales) + $500 = $1,040 + $80 + $150 + $500 = $1,770.

b. Using the sales dollars given in the problem, compute the profitability as follows: X: $600 – $410 = $190.

Y: $2,000 - $1,995 = $5.Z: $1,500 -$1,770 = $(270).

If these customers are representative of all customers (and that is questionable), then the company has a big problem with its shipments to foreign locations and a small problem with domestic national shipments. Management should consider ways to manage costs (e.g., outsource shipments to Mexico or Canada), or raise prices on unprofitable shipments or drop unprofitable product lines or some combination of these suggestions.

Solutions 7-18

7.53 (Throughput contribution)

Note: The status quo gives a contribution of $24,000 per hour [= ($200 - $120) × 300 units].

Option a. Adding capacity adds $400 per hour to contribution but costs only $200 per hour [$400 = ($200 - $120) × 5 units], adding $200 per hour to increase contribution to $24,200 per hour. This is a good option.

Option b. Outsourcing some of the food preparation would increase the contribution per hour by $180. This is also a good option. Here are the calculations:

Alternative Status Quo Difference

Output 310 units 300 units 10 units

Revenue ($200 per unit) $62,000 $60,000 $2,000 higher

Variable costs ($122 for alternativeand $120 for the status quo) $37,820 $36,000 $1,820 higher

Contribution margin $24,180 $24,000 $180 higher

If both options are taken, then the company would still get the contribution margin for Option b + the contribution from Option a for the five additional units, less the $200 cost for additional capacity. Here are the calculations, starting with Option b:

Option b Option a

[310 units × ($200 - $122)] + {[5 units × ($200 - $120)] - $200} = $24,380.

Compare this contribution to the $24,000 status quo or the $24,180 for Option b alone or the $24,200 for Option a alone. Consequently, we recommend that the company take both Options a and b.

7-19 Solutions

7.54 (Throughput contribution)

Note: The status quo gives a contribution of $104,000 per day [= ($240 - $110) × 800 units].

Option a. Outsourcing 80 units of packaging increases output to 880 units per day. This adds $10,400 contribution per day but costs only $8,000 for a net gain of $2,400 per day. [$10,400 = ($240 - $110) × 80 units.] This is a good option that increases contribution from $104,000 per day to $106,400 per day.

Option b. Renting equipment increases output by 50 units per day. This adds $6,500 contribution per day but costs only $4,000 for a net gain of $2,500 per day. [$6,500 = ($240 - $110) × 50 units.] This is a good option that increases contribution from $104,000 per day to $106,500 per day.

If the company tries both options, it encounters a capacity constraint in cooking. Cooking is limited to 900 units per day. Therefore the company can increase output by only 100 units per day. Assuming that the company takes both options, then its contribution increases by 100 units for an increase in contribution of $13,000 [= ($240 - $110) × 100 units.] The cost of taking both options is $12,000 (= $8,000 for option a + $4,000 for option b). The net gain in contribution is only $1,000 which is less than the net gain for either options a or b. Therefore we recommend that the company take Option b, although both a and b give similar improvements in contribution.

7.55 Spectra, Inc.; make or buy.)

VariableCost per 500 Units

Direct Material................................................................................................ $ 80Direct Labor.................................................................................................... 90Other Variable Costs....................................................................................... 25

Total............................................................................................................ $ 195

a. No, since the $200 price is greater than the incremental (variable) cost of $195.

b. Yes. The $180 price is less than the incremental cost of $195.

c. $195 plus the incremental cash inflow which can be generated from the alternative use of the facilities.

7.56 (Sell or process further.)

Solutions 7-20

a. Like many sell or process further problems in the real world, this problem is easier than it appears if one just cuts to the chase. The costs of producing product X up to the split-off point are sunk. The costs of producing y and z are not differential to this decision and are therefore not relevant to the decision to sell X or process it further. If processed further, product X would generate a contribution after split-off of $322,000 [= ($4.30 - $2.00) × 140,000 pounds]. At present, product X has sales at split-off of $280,000. Processing further increases contribution by $42,000 =($322,000 - $280,000).

b. The memo would make the points in part a above. Management should not attempt to incorporate sunk costs into this decision or be concerned about the costs of products Y and Z. Our recommendation to process further does assume that product X will not cannibalize (i.e., reduce) sales of products Y and Z.

7.57 (Hayley and Associates; dropping a product line.)

Status quo: Keep all three services, audit, tax, and consulting.Alternative: Drop consulting, increase tax.


Sales Revenue........................ $ 1,100,000a $ 1,200,000d $ 100,000 Lower

Variable Costs....................... 800,000 b 900,000 e 100,000 LowerContribution Margin.............. $ 300,000 $ 300,000 $ -0-

Fixed Costs............................ 182,000 c 190,000 f 8,000 LowerOperating Profit..................... $ 118,000 $ 110,000 $ 8,000 Higher

a$1,100,000 = (1.50 X $400,000) + $500,000.b$800,000 = (1.50 X $300,000) + $350,000.c$182,000 = (1.2 X $60,000) + $80,000 + (.6 X $50,000).d$1,200,000 = $300,000 + $400,000 + $500,000.e$900,000 = $250,000 + $300,000 + $350,000.f$190,000 = $50,000 + $60,000 + $80,000.

The report should show the above analysis and state that dropping consulting and increasing tax work would increase profits by $8,000.

7.58 (Dropping a machine from service.)

7-21 Solutions

Disagree. Assuming all expenses except depreciation are variable, the number 2 machine should be dropped. Depreciation expense will be incurred whether or not a machine is operating, it is a sunk cost, and so should not be considered when deciding which machines to operate. (We ignore tax consequences in this solution.) Only variable costs requiring future cash outlays are relevant in this decision.

CASH OUTFLOWS—20X5

No. 1 No. 2 No. 3 No. 4Labor............................................. $ 15,000 $ 19,000 $ 18,000 $ 21,000Materials........................................ 4,000 4,500 5,000 2,500Maintenance.................................. 500 500 500 400

Total........................................... $ 19,500 $ 24,000 $ 23,500 $ 23,900

7.59 Cost estimate for bidding.

a. One Four Eight

Solutions 7-22

Seminar Seminars Seminars25 80 144

Participants Participants ParticipantsStartup costs................................. $ 600 $ 600 $ 600Materials...................................... 2,500 8,000 14,400Direct labor.................................. 1,200 5,000 8,800Fixed costs (75% of direct

labor)....................................... 900 3,750 6,600 Total costs.......................... $ 5,200 $ 17,350 $ 30,400

Profit margin (20% abovecost)........................................ 1,040 3,470 6,080

Bid price...................................... $ 6,240 $ 20,820 $ 36,480

b. One Four EightSeminar Seminars Seminars

25 80 144Participants Participants Participants

Revenues....................................... $ 6,240 $ 20,820 $ 36,480Less:

Startup costs............................. 600 600 600Materials................................... 2,500 8,000 14,400Direct labor............................... 1,200 5,000 8,800

Contribution Margin...................... $ 1,940 $ 7,220 $ 12,680

c. One Four EightSeminar Seminars Seminars

25 80 144Participants Participants Participants

Revenues....................................... $ 6,240 $ 20,820 $ 32,102a

Less:Startup costs............................. 600 600 600Materials................................... 2,500 8,000 14,400Direct labor............................... 1,200 5,000 8,800

Contribution Margin...................... $ 1,940 $ 7,220 $ 8,302

Disagree. Eight seminars provide a greater contribution to fixed costs and profits even with the lower price.

a $32,102 = .88 x $36,480

7.60 (LLP; differential cost analysis in a service organization.)

a. Variable Costs = $200 + $40 = $240 per Hour.Total Fixed Costs = ($160 + $100) X 5,000 Hours = $1,300,000.

7-23 Solutions

To break even, set profit to zero, and solve for X.

$0 = ($600 – $240)X – $1,300,000

X = $1,300,000/$360 = 3,611 Hours.

b. Alternative – Status Quo = Differential

Revenue................. $ 3,000,000a $ 3,000,000b $ --Variable

Costs................. 960,000 c 1,200,000 d 240,000 LowerContribution

Margin............... $ 2,040,000 $ 1,800,000 $ 240,000 HigherFixed

Costs................. 1,000,000 1,300,000 300,000 LowerOperating

Profit................. $ 1,040,000 $ 500,000 $ 540,000 Higher

a$3,000,000 = $750 X 4,000 hours.

b$3,000,000 = $600 X 5,000 hours.

c$960,000 = $240 X 4,000 hours.

d$1,200,000 = $240 X 5,000 hours.

Profits would increase by $540,000.

c. Since the additional 1,000 hours are within the firm’s capacity of 6,000 hours, Columbo Connections would want to cover its variable costs of $240 at a minimum. Therefore, the minimum price would be slightly higher than $240.

Solutions 7-24

7.61 (Troy Manufacturing; comprehensive differential costing problem.)

This problem gives students a good understanding of the fixed/variable cost dichotomy. It is worthwhile to emphasize to students that fixed costs may be “unitized” (i.e., allocated to individual units of product) for certain purposes, and that this allocation procedure may make such costs appear to be variable. Indeed, many students treat the per unit fixed costs as though they were variable costs, despite the fact that they are clearly labeled “fixed.”

This problem can be used to introduce the concept of opportunity cost. Part b. can be used in this way, as can Part d. if you suggest a scrap value for the obsolete hoists.

a. Recommendation: Lowering prices reduces operating profit. Other factors, such as the reduction of available capacity and the impact on market share, could also affect the decision.

(Alternative) (Status Quo)After Price Before PriceReduction Reduction

Price............................. $ 900 $ 1,000Quantity....................... 3,500 3,000

Revenue....................... $ 3,150,000 $ 3,000,000 $ 150,000 IncreaseVariable Maufac-

turing Costs............. 1,050,000 900,000 150,000 IncreaseVariable Nonman-

ufacturing Costs....................... 350,000 300,000 50,000 Increase

Contribution Mar-gin........................... $ 1,750,000 $ 1,800,000 $50,000 Decrease

Fixed Manufactur-ing Costs.................. 600,000 600,000 -- Note

Fixed Nonmanu- Equalityfacturing Costs......... 300,000 300,000 --

Income......................... $ 850,000 $ 900,000 $ 50,000 Decrease

7-25 Solutions

7.61 continued.

b. Recommendation: Don’t accept contract.

Income without the government contract for 4,000 units = $1,500,000.

$1,500,000 = ($600 per unit contribution margin × 4,000 units) – ($600,000 + $300,000 fixed costs). The $600 contribution margin = sales price – variable mfg. cost – variable nonmfg cost.

Income with the government contract = $1,325,000 as shown below.

With Government Contract Regular Government Total

Revenue............................................ $ 3,500,000 $ 275,000a $ 3,775,000Variable Manufacturing

Costs............................................. 1,050,000 150,000 1,200,000Variable Nonmanufacturing

Costs............................................. 350,000 -- 350,000 Contribution Margin......................... $ 2,100,000 $ 125,000 $ 2,225,000Fixed Manufacturing Costs............... 600,000 Fixed Nonmanufacturing

Costs............................................. 300,000 Income.............................................. $ 1,325,000

aGovernment revenue (500 X $300) + (1/8 X $600,000) + $50,000 = $275,000, assuming the government’s “share” of March fixed manufacturing costs is 12.5% (= 500 units /4,000 units). Alternatives are to get 1/6 X $600,000 fixed manufacturing costs, which would increase revenue from $275,000 to $300,000; or get no reimbursement for fixed manufacturing costs, which would reduce revenue to $200,000.

The deal would be a good one if the company had no opportunity costs. The $50,000 fee and reimbursement for (nondifferential) fixed costs would normally flow to the bottom line. But in this case, the company gives up the contribution from 500 units to regular customers making the deal a bad one.

Solutions 7-26

7.61 continued.

c. Minimum Price = (Variable Manufacturing Costs + Shipping Costs + Marketing Costs)/Units = ($300,000 + $75,000 + $4,000)/1,000 = $379 per unit.

At this price per unit, the $379,000 of differential costs caused by the 1,000 unit order will just be recovered.

Some students solve for this price using the breakeven formula:

= X

= 1,000 Units

$4,000 = 1,000P – $375,000

$379,000 = 1,000P

$379 = P

d. The manufacturing costs are sunk; therefore, any price in excess of the differential costs of selling the hoists will add to income. In this case, those differential costs are apparently the $100 per unit variable marketing costs, since the hoists are to be sold through regular channels; thus, the minimum price is $100. (If the instructor wishes to reinforce the concept of opportunity cost, the general answer to this question is that the price should exceed the sum of 1) the differential marketing costs and 2) the potential scrap proceeds, which are an opportunity cost of selling the hoists rather than scrapping them.)

7-27 Solutions

7.61 continued.

e. Alternative Status Quo1,000 Units All ProductionContracted In-house

Total Revenue.......................................... $ 3,000,000 $ 3,000,000Total Variable Manufacturing

Costs.................................................... 600,000 900,000Total Variable Nonmanufactur-

ing Costs.............................................. 280,000 300,000 Total Contribution Margin........................ $ 2,120,000 $ 1,800,000Total Fixed Manufacturing

Costs.................................................... 420,000 600,000Total Fixed Nonmanufacturing

Costs.................................................... 300,000 300,000Payment to Contractor..................... X --

Profit.......................................... $ 1,400,000 – X $ 900,000

$1,400,000 – X = $900,000X = $500,000 or $500 per unit maximum purchase price.

Therefore, a $600 purchase price is not acceptable; it would decrease income by $100,000 [= ($600 – $500) X 1,000].

A shorter (but more difficult) approach uses the concept of opportunity costs:

Variable Manufacturing Cost................................................................... $ 300Variable Nonmanufacturing Opportunity Cost

($100 – $80)....................................................................................... 20Fixed Manufacturing Opportunity Cost................................................... 180 *Equivalent In-house Cost......................................................................... $ 500

*($600,000 – $420,000) ÷ 1,000 units.

f. Alternative Status QuoContract 1,000 Regular Bicycles and 3,000

Regular Produce 800 Low Impact Bicycles Bicycles

Regular Regular Low Impact Produced (In) (Out) Bicycles Total In-house

Revenue........................... $2,000,000 $1,000,000 $960,000 $3,960,000 $3,000,000Var. Mfg. Costs............... 600,000 -- 560,000 1,160,000 900,000Var. Nonmfg. Costs......... 200,000 80,000 80,000 360,000 300,000

Contrib. Margin............ $1,200,000 $ 920,000 $320,000 $2,440,000 $1,800,000Fixed Mfg. Costs............. 600,000 600,000Fixed Nonmfg. Costs....... 300,000 300,000Payment to Contractor..... -- X -- X --

Profit............................ $1,540,000 – X $ 900,000

Maximum payment = $640,000 (= $1,540,000 – $900,000). Now the proposal should be accepted at a price of $600.

Solutions 7-28

7.62 (KM; alternative concepts of cost [CMA adapted].)

a. (1) Costs incurred to fill order:Material...................................................................................... $ 3,000Labor.......................................................................................... 2,000Special Machine......................................................................... 1,000Power......................................................................................... 250 Total........................................................................................... $ 6,250

Costs reduced for regular products:Material...................................................................................... $ 1,500Labor.......................................................................................... 2,000Other.......................................................................................... 200Power......................................................................................... 150 Total........................................................................................... $ 3,850

Net differential costs...................................................................... $ 2,400

(2) Sales of regular product.................................................. $ 10,000Less:

Material...................................................................... $ 1,500Labor.......................................................................... 2,000Power.......................................................................... 150Other........................................................................... 200 3,850

Opportunity cost of special order............................ $ 6,150

b. SpecialOrder Standard Differential

Sales................................ $ 7,000 $ 10,000 $ 3,000 LowerLess differential

costs............................ 6,250 3,850 2,400 HigherDecrease in contri-

bution margin.............. $ 5,400 Lower

The special order should not be accepted because the contribution margin decreases.

7-29 Solutions

7.63 (Leastan Company; department closing.)

We recommend that the dry goods department be continued. If the department is abandoned, the following costs will be saved for sure:

Commissions............................................... $ 15,000State Taxes.................................................. 1,500Insurance on Inventory................................. 2,000Interest on Inventory.................................... 2,500 Total Operating Costs Saved........................ $ 21,000

Presumably, the payroll and direct labor costs will also be saved, but we cannot be so sure about supervision costs. Closing down the department may not save all supervisory costs, because we may not be able to release a supervisor.

Clearly, the rent will not decline and most of the administrative and general office costs will continue as before. Depreciation on the equipment will not necessarily continue because the company can dispose of the equipment. There may be some cash receipts from equipment disposal. At any rate, the depreciation is not a cash outlay. The fact that rent payments for the company will continue unreduced is sufficient for us to recommend continuation.

To summarize, the Dry Goods Department contributes $25,000 to overhead:

Gross Margin ................................................................................…….. $ 62,500Total Differential Operating Costs (see above)................................................ (21,000)Payroll (Assumed Variable) Cost Saved.......................................................... (16,500 )Contribution to Overhead................................................................................ $ 25,000

Solutions 7-30

7.64 (Biggs Company; sell or process further [CMA adapted].)

Revenue Increase Arising from Producing Product DSale of Product D 100,000 pounds @ $30.00.................. $ 3,000,000Less: Sales of B Lost 100,000 pounds @ $20.25.................. 2,025,000

$ 975,000Cost Increase Arising from Producing Product D

Direct Labor $ 5.50Variable Overhead 2.00 Fixed Overhead 1.75

$ 9.25 Cost per Unit, $9.25 × 100,000 pounds.......................................... 925,000 Differential Profit from Producing Product D................................. $ 50,000

Relying on the economic information given in the problem, the company should produce Product D. Note that the fixed costs attributable to Product D are differential because they did not appear in the

7.65 (Liquid Chemical Co.; make or buy.)

7-31 Solutions

Working this case requires knowledge of how to calculate discounted cash flows.

a. The four alternatives are:

• Alternative A: It is the “status quo,” i.e., Liquid Chemical Co. will continue making the containers and performing maintenance.

• Alternative B: Liquid Chemical Co. will continue making the containers, but will outsource the maintenance contracting Packages, Inc.

• Alternative C: Liquid Chemical Co. will buy containers from Packages, Inc., but will perform the maintenance.

• Alternative D: It is the completely outsourcing alternative. Packages, Inc. will make the containers and provide the necessary maintenance.

b. The incremental cash flow analyses were conducted assuming a five-year time horizon. Appendices I, II, III, and IV present the cash flow analyses for Alternatives A, B, C, and D respectively, as well as more detailed information on the calculations. General considerations for the incremental cash flows are provided below.

• All cash flows occur at the end of the year.

• The last day of Year 0 is when the decision on the alternatives is made. It can also be considered the first day of Year 1.

• The company has an after-tax cost of capital of 10% per year and uses an income tax rate of 40% for decisions like this.

• Cash flows were not adjusted for inflation.

• 200 tons of GHL were purchased at the beginning of Year 0 (= $1,000,000/$5,000). 40 tons were consumed during Year 0 (expense of $200,000 = 40 tons X $5,000/ton), leaving 160 tons in stock at the beginning of Year 1.

• Rent on the container department and the proportion of general administrative overhead allocated to the container department are the same independent of the alternative. Therefore, they are not considered in the cash flow analyses.

Solutions 7-32

7.65 continued.

The table below presents the net present values for the four alternatives. Note that all net present values are negative, so the more attractive alternative for Liquid Chemical Co. is the one with the smallest negative value, i.e., Alternative C. It means that, considering our assumptions and the available information regarding costs, Liquid Chemical Co. should buy containers from Packages, Inc., and keep performing the maintenance.

Alternative A Alternative B Alternative C Alternative DMake Make Buy Buy

Containers; Containers; Containers; Containers;Perform Buy Perform Buy

Maintenance Maintenance Maintenance Maintenance

NPV ($) –2,735,502 –3,082,945 –2,619,684 –2,712,251

c. Although Alternative C seems to be the more attractive, its net present value is not significantly different from the net present values of Alternatives A and D. This situation requires a careful examination of facts and assumptions made. A brief discussion of some points that should be reevaluated, as well as additional information that should be taken into account, is presented below.

Administrative Overhead: A proportion of general administrative overhead is allocated to the container department. Is this cost proportional to the number of employees in the container department? Apparently the answer is yes, and in this case it is not the best estimate because it is not considering the real administrative resources consumed by the container department.

Quality of Outsource Services: Quality issues are always important when a company is considering outsourcing some services. In this case, it is assumed that Packages, Inc. will perform maintenance and/or make containers with a quality at least as good as Liquid Chemical’s quality. Due to the importance of quality, Liquid Chemical Co. should carefully evaluate Package Inc.’s ability to meet quality requirements imposed by Liquid Chemical.

Container Contract Terms: Does Packages Inc. have the ability to meet Liquid Chemical’s future container needs?

Time Horizon and Inflation: Is the price locked in for five years regardless of inflation?

Employees: The effect of eliminating some employees may have a detrimental effect on the morale of remaining employees.

7-33 Solutions

7.65 continued

Incremental Cash Flow—Alternative A: Make Containers and Perform Maintenance

Year of Operation0 1 2 3 4 5

Buy GHL $ (240,000)Tax Savings on

Purchase 96,000 Cash Flow on

Purchase $ (144,000)Other Materials $ (500,000) $ (500,000) $ (500,000) $ (500,000) $ (500,000)Labor: Super-

visor (50,000) (50,000) (50,000) (50,000) (50,000)Labor: Workers (450,000) (450,000) (450,000) (450,000) (450,000)Rent: Ware-

house (85,000) (85,000) (85,000) (85,000) (85,000)Maintenance (36,000) (36,000) (36,000) (36,000) (36,000)Other Expenses (157,500) (157,500) (157,500) (157,500) (157,500)Manager’s Sal-

ary (80,000 ) (80,000 ) (80,000 ) (80,000 ) (80,000 )Total Costs $(1,358,500) $(1,358,500) $(1,358,500) $(1,358,500) $(1,358,500)Tax Savings 543,400 543,400 543,400 543,400 543,400Cash Flow due

to Costs $ (815,100) $ (815,100) $ (815,100) $ (815,100) $ (815,100)

Tax Effects ofDepreciation $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ --

Tax Effects of GHL Costs $ 80,000 $ 80,000 $ 80,000 $ 80,000 $ --

Total Cash Flow $ (675,100) $ (675,100) $ (675,100) $ (675,100) $ (959,100)

Discount Rate 10%Factor 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209PV $ -- $ (613,727) $ (557,934) $ (507,213) $ (461,102) $ (595,526)NPV $(2,735,502)

Considerations:

• Under this alternative, GHL consumption is 40 tons per year. At the end of Year 4 the GHL stock is zero, and a purchase of 40 tons is necessary. At that time, the price will be $6,000 per ton.

• There is no cash outflow due to GHL consumption from Year 1 to Year 4, just “accounting” expenses because the product is in stock. Due to these GHL expenses, there is tax savings of $80,000 per year (= 40 tons X $5,000/ton X 40%) from Year 1 to Year 4.

• It uses straight-line depreciation, resulting in depreciation expense of $150,000 per year (= $1,200,000/8 years). It generates a cash inflow of $60,000 per year (= $150,000 X 40%) from Year 1 to Year 4 because the book value of the machinery at the beginning of Year 1 is $600,000.

Solutions 7-34

7.65 continued

Incremental Cash Flow—Alternative B: Make Containers and Buy Maintenance


Buy GHL $ (120,000)Tax Savings on

Purchase 48,000 Cash Flow on

Purchase $ (72,000)Other Materials $ (450,000) $ (450,000) $ (450,000) $ (450,000) $ (450,000)Labor: Super-


house (85,000) (85,000) (85,000) (85,000) (85,000)Maintenance (36,000) (36,000) (36,000) (36,000) (36,000)Other Expenses (92,500) (92,500) (92,500) (92,500) (92,500)Manager’s Sal-

ary (80,000) (80,000) (80,000) (80,000) (80,000)Maintenance

Contract (375,000 ) (375,000 ) (375,000 ) (375,000 ) (375,000 )Total Costs $(1,528,500) $(1,528,500) $(1,528,500) $(1,528,500) $(1,528,500)Tax Savings 611,400 611,400 611,400 611,400 611,400Cash Flow due

to Costs $ (917,100) $ (917,100) $ (917,100) $ (917,100) $ (917,100)

Tax Effects ofDepreciation $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ --

Tax Effects of GHL Costs $ 72,000 $ 72,000 $ 72,000 $ 72,000 $ 32,000

Total Cash Flow $ (785,100) $ (785,100) $ (785,100) $ (785,100) $ (957,100)

Discount Rate 10%Factor 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209PV $ -- $ (713,727) $ (648,843) $ (589,857) $ (536,234) $ (594,284)NPV $(3,082,945)

• Under this alternative, GHL consumption is 36 tons per year (= 40 X 90%). At the end of Year 4 the GHL stock is 16 tons, and a purchase of 20 tons is necessary. At that time, the price will be $6,000 per ton.

• Due to lower GHL consumption, during Year 5 there is still an “accounting” expense of $80,000 (= 16 tons X $5,000/ton). It will generate tax savings of $32,000 (= $80,000 X 40%) at Year 5.

• When the department contracts external maintenance, it decreases materials costs by 10%, and reduces employee expenses by 20%. Other expenses total $92,500.

• There is no severance pay or pension under this alternative.

7-35 Solutions

7.65 continuedIncremental Cash Flow—Alternative C:

Buy Containers and Perform Maintenance


Sell Machinery $ 200,000Tax Savings on

Sale 160,000 Cash Flow on

Sale $ 360,000Sell GHL $ 560,000Tax Savings on

on Sale 56,000Cash Flow on

Sale $ 616,000Other Materials $ (50,000) $ (50,000) $ (50,000) $ (50,000) $ (50,000)Labor: Super-


house (85,000) (85,000) (85,000) (85,000) (85,000)Severance Pay $ (16,000) -- -- -- -- --Other Expenses (65,000) (65,000) (65,000) (65,000) (65,000)Manager’s Sal-

ary -- -- -- -- --Container Con-

tract (1,250,000 ) (1,250,000 ) (1,250,000 ) (1,250,000 ) (1,250,000 )Total Costs $ (16,000) $(1,590,000) $(1,590,000) $(1,590,000) $(1,590,000) $(1,590,000)Tax Savings 6,400 636,000 636,000 636,000 636,000 636,000Cash Flow due

to Costs $ (9,600) $ (954,000) $ (954,000) $ (954,000) $ (954,000) $ (954,000)

Tax Effects ofDepreciation $ -- $ -- $ -- $ -- $ --

Tax Effects of GHL Costs $ 8,000 $ 8,000 $ 8,000 $ 8,000 $ 8,000

Total Cash Flow $ 966,400 $ (946,000) $ (946,000) $ (946,000) $ (946,000) $ (946,000)

Discount Rate 10%Factor 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209PV $ 966,400 $ (860,000) $ (781,818) $ (710,744) $ (646,131) $ (587,392)NPV $(2,619,684)

(See Following Page for Considerations)

Solutions 7-36

7.65 continued

Considerations:

• Under this alternative, GHL consumption is 4 tons per year (40 X 10%), or 20 tons over five years. Therefore, Liquid Chemical can sell 140 tons (= 160 – 20) at the end of Year 0 at $4,000 per ton.

Market Price = $560,000 Loss on Sale = $ 140,000Book Value = $700,000 Tax Savings on Sale = $ 56,000

• Machinery is not necessary for maintenance, and can also be sold at the end of Year 0.Market Price = $200,000 Loss on Sale = $ 400,000Book Value = $600,000 Tax Savings on Sale = $ 160,000

• When the department performs maintenance and buys containers, it decreased materials costs by 90%, and reduces employees by 80%. Other expenses total $65,000.

• In this case, there is a severance pay of $16,000 (= $20,000 X 0.8). The supervisor is still necessary, but Mr. Duffy can be transferred to another department.

• Tax effects on GHL consumption are computed based on an expense of $20,000 per year (= 4 tons X $5,000/ton). It results in savings of $8,000 per year (= $20,000 X 40%).

7-37 Solutions

7.65 continuedIncremental Cash Flow—Alternative D: Buy Containers and Buy Maintenance


Sell Machinery $ 200,000Tax Savings on

Sale 160,000 Cash Flow on

Sale $ 360,000Sell GHL $ 640,000Tax Savings on

on Sale 64,000Cash Flow on

Sale $ 704,000Other Materials $ -- $ -- $ -- $ -- $ --Labor: Super-

visor -- -- -- -- --Labor: Workers -- -- -- -- --Rent: Ware-

house -- -- -- -- --Severance Pay $ (20,000) -- -- -- -- --Pension (30,000) (30,000) (30,000) (30,000) (30,000)Other Expenses -- -- -- -- --Manager’s Sal-

ary -- -- -- -- --Container Con-

tract (1,250,000) (1,250,000) (1,250,000) (1,250,000) (1,250,000)Maintenance

Contract (375,000 ) (375,000 ) (375,000 ) (375,000 ) (375,000 )Total Costs $ (20,000) $(1,655,000) $(1,655,000) $(1,655,000) $(1,655,000) $(1,655,000)Tax Savings 8,000 662,000 662,000 662,000 662,000 662,000Cash Flow due

to Costs $ (12,000) $ (993,000) $ (993,000) $ (993,000) $ (993,000) $ (993,000)

Tax Effects ofDepreciation $ -- $ -- $ -- $ -- $ --

Tax Effects of GHL Costs $ -- $ -- $ -- $ -- $ --

Total Cash Flow $ 1,052,000 $ (993,000) $ (993,000) $ (993,000) $ (993,000) $ (993,000)

Discount Rate 10%Factor 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209PV $ 1,052,000 $ (902,727) $ (820,661) $ (746,056) $ (678,232) $ (616,575)NPV $(2,712,251)

See following page for considerations.Considerations:

Solutions 7-38

• Under this alternative, there is no GHL consumption. Therefore, Liquid Chemical can sell 160 tons at the end of Year 0 at $4,000 per ton.

Market Price = $640,000 Loss on Sale = $160,000Book Value = $800,000 Tax Savings on Sale = $ 64,000

• Machinery is not necessary for maintenance, and can also be sold at the end of Year 0.Market Price = $200,000 Loss on Sale = $400,000Book Value = $600,000 Tax Savings on Sale = $160,000

• There is a severance pay of $20,000 at Year 0, and a pension payment of $30,000 per year from Year 1 to Year 5.

7-39 Solutions

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