Exercise 13-29

Insert your answers in the gray-shaded cells. Insert amounts to be subtracted as negatives.

If an answer is incorrect, the word “wrong” will appear.

Type equation to show how much cost is allocated to each department

S1 =

$170,000 + .40S2 + .20S3

S2 =

$360,000 + .10S1 + .30S3

S3 =

$600,000 + .20S1 + .30S2

Substitute S3 into the equations for S1 and S2:
   (1) S1 = $170,000 + .40S2 + .20($600,000 + .20S1 + .30S2)
   (2) S2 = $360,000 + .10S1 + .30($600,000 + .20S1 + .30S2)

  Simplifying:
   (1)        S1 = $170,000 + .40S2 + $120,000 + .04S1 + .06S2
    .96S1 = $290,000 + .46S2
    S1 = $302,083 + .48S2
   (2) S2 = $360,000 + .10S1 + $180,000 + .06S1 + .09S2
    .91S2 = $540,000 + .16S1
    S2 = $593,407 + .18S1
  Substitute S2 into the equation for S1:
S1 = $302,083 + .48($593,407 + .18S1)
S1 = $302,083 + $284,835 + .09S1
.91 S1 = $586,918
S1 = $644,965

a. Substitute S3 equation ino equations for S1 and S2:       
(1) S1 = $170,000 + .40S2 + .20($600,000 + .20S1 + .30S2)     
(2) S2 = $360,000 + .10S1 + .30($600,000 + .20S1 + .30S2)      
Simplifying:                                                                                   
(1) .96S1 = $290,000 + .46S2                                                      
(2) .91S2 = $540,000 + .16S1                                                      
S2 = $593,407 + .18S1                                                   
Substitute in S2 equation for S1:                                                
.96S1 = $290,000 + .46($382,418 + .1758S1)                     
S1 $409,409.7235                                                                         
b. Substitue S1 ($409,409.7235) into the S2 and S3 equations:                                                                                        (1)S2 = $240,000 + .10($409,410 + .30S3                         
(2)S3 = $360,000 + .20($409,410 + .30S2                         
Simplifying:                                                                                 

Substitute S1 ($644,965) into the original S2 and S3 equations:
   (1) S2 = $360,000 + .10($644,965) + .30S3
   (2) S3 = $600,000 + .20($644,965) + .30S2

  Simplifying:
   (1) S2 = $360,000 + $64,497 + .30S3
    S2 = $424,497 + .30S3
   (2) S3 = $600,000 + $128,993 + .30S2
    S3 = $728,993 + .30S2
  Substitute S3 into the equation for S2:
   S2 = $424,497 + .30($728,993 + .30S2)
   S2 = $424,497 + $218,698 + .09S2
  .91S2 = $643,195
   S2 = $706,808

  Substitute S1 and S2 into the original equations and solve for S3:

  S3 = $600,000 + .20($644,965) + .3($706,808)
  S3 = $600,000 + $128,993 + $212,042
  S3 = $941,035

S1

S2

S3

RP1

RP2

Direct Costs

$1,70,000

$   3,60,000

$6,00,000

S1

(6,44,965)

         64,497

   1,28,993

$   1,93,490

$   2,57,986

S2

   2,82,723

    (7,06,808)

   2,12,042

      1,41,362

         70,681

S3

   1,88,207

      2,82,311

(9,41,035)

      3,76,414

         94,104

To RP

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