Problem 13. Problem 14
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1 Cost Accounting Acct 647 Professor authored homework problems Review of Matrix Operations Problem 13 Matrix addition 5 7 A = 3!3 B = 4! ! C = A + B Required: Solve for C Problem 14 Matrix multiplication 5 7 A = 3!3 B = 4! !5 12 C = A * B Required: Solve for C 153
2 Problem 15 Matrix multiplication 5 7!2 A =!2 3 4 A -1 = 4 10! ! ! ! ! C = A * A -1 Required: Solve for C 154
3 Cost Accounting Acct 647 Professor authored homework problems Department Cost Allocation Problem 16 Niagara Company has two service departments (designated below as S 1 and S 2 ) and three production departments (designated as P 1, P 2, and P 3 ). The schedule below shows overhead directly attributable to each department along with the percentages of service that each service department performs for other departments. Department S 1 S 2 P 1 P 2 P 3 S % 20% 40% 30% S 2 20% 0 50% 10% 20% Overhead before allocation $98,000 $117,600 $1,400,000 $2,100,000 $640, Reciprocal: First use the cyclical/interative approach. Then use matrices to solve for simultaneous equations (hint: use a spreadsheet program to get the inverse matrix). 155
4 Problem 17 During February Cronin Company experienced the following results. Department Maint(S 1 ) Engin(S 2 ) Admin(S 3 ) Milling(P 1 ) Machin(P 2 ) Maintenance 0 5% 5% 60% 30% Engineering 10% % 50% Administration 15% 10% 0 45% 30% Overhead before allocation $60,000 $90,000 $200,000 $0 $0 The service department direct costs were: maintenance, $60,000; engineering, $90,000; administration, $200, Reciprocal: Use matrices to solve for simultaneous equations (hint: use a spreadsheet program to get the inverse matrix). 156
5 Problem 18 The controller of PastItsPrime Manufacturing Company has prepared the following information related to operations for 19X6. Operating Departments Milling (P1) Refining (P2) Finishing (P3) Direct labor hours 141, , ,000 Direct labor cost $1,385,000 $2,416,000 $1,586,000 Direct overhead $2,740,000 $1,934,200 $1,017,000 Using various allocation bases, the controller developed the following estimates of percentages of service department effort devoted to other departments. Department (S1) (S2) (S3) (P1) (P2) (P3) S1 Personnel 0 10% 8% 17% 41% 24% S2 Admin 5% 0 11% 21% 35% 28% S3 Engineering 0 8% 0 38% 34% 20% OH to allocate $165,000 $486,000 $292,000 $0 $0 $0 1. Reciprocal: Use matrices to solve for simultaneous equations (hint: use a spreadsheet program to get the inverse matrix). 157
6 Problem 19 Niagara Company has four service departments (designated below as S 1, S 2, S 3, S 4 ) and four production departments (designated as P 1, P 2, P 3, P 4 ). The schedule below shows overhead directly attributable to each department along with the percentages of service that each service department performs for other departments. Dept S 1 S 2 S 3 S 4 P 1 P 2 P 3 P 4 S 1 0% 8% 22% 11% 31% 11% 7% 10% S 2 20% 0% 50% 10% 8% 0% 6% 6% S 3 13% 18% 0% 5% 3% 10% 21% 30% S 4 18% 21% 7% 0% 41% 3% 4% 6% Direct Overhead Cost $352,000 $273,000 $168,923 $823,945 $623,998 $289,534 $1,253,092 $423, Reciprocal: Use matrices to solve for simultaneous equations (hint: use a spreadsheet program to get the inverse matrix). 158
7 Problem 20 Niagara Company has six service departments (designated below as S 1, S 2, S 3, S 4, S 5, S 6 ) and three production departments (designated as P 1, P 2, P 3 ). The schedule below shows overhead directly attributable to each department along with the percentages of service that each service department performs for other departments. Dept S 1 S 2 S 3 S 4 S 5 S 6 P 1 P 2 P 3 S 1 0% 13% 22% 9% 15% 11% 5% 9% 16% S 2 30% 0% 11% 9% 6% 4% 10% 12% 18% S 3 13% 18% 0% 5% 4% 10% 35% 10% 5% S 4 5% 8% 7% 0% 18% 2% 21% 17% 22% S 5 4% 2% 4% 2% 0% 13% 40% 23% 12% S 6 14% 2% 4% 3% 2% 0% 20% 25% 30% Direct Overhead Cost $470,000 $821,000 $263,444 $1,316,555 $710,593 $153,598 $925,613 $1,389,411 $872, Reciprocal: Use matrices to solve for simultaneous equations (hint: use a spreadsheet program to get the inverse matrix). 159
8 Problem 21 Niagara Company has two service departments (designated below as S 1 and S 2 ) and three production departments (designated as P 1, P 2, and P 3 ). The schedule below shows overhead directly attributable to each department along with an allocation base for costs from each service department to all the rest. Department S 1 S 2 P 1 P 2 P 3 S 1 (sq ft) 0 1,800 2,700 3,100 2,400 S 2 (minutes) 24, ,000 18,000 42,000 Overhead before allocation $80,000 $140,000 $0 $0 $0 Required: Allocate the service department costs using each of the three methods (direct, step, and reciprocal). When using the step-down method, begin with the department that performs the largest percentage of service for For the reciprocal method, use matrices to solve for simultaneous equations. Solution hint: divide through to turn each raw item into percentages That means dividing by 10,000 sq. ft. and 120,000 minutes. 160
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