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skelet666 [1.2K]
1 year ago
7

Recher Corporation uses part Q89 in one of its products. The company's Accounting Department reports the following costs of prod

ucing the 6,200 units of the part that are needed every year. Per Unit Direct materials$7.60 Direct labor$4.20 Variable overhead$8.30 Supervisor's salary$3.20 Depreciation of special equipment$2.70 Allocated general overhead$1.40 An outside supplier has offered to make the part and sell it to the company for $27.00 each. If this offer is accepted, the supervisor's salary and all of the variable costs, including direct labor, can be avoided. The special equipment used to make the part was purchased many years ago and has no salvage value or other use. The allocated general overhead represents fixed costs of the entire company. If the outside supplier's offer were accepted, only $5,000 of these allocated general overhead costs would be avoided. In addition, the space used to produce part Q89 could be used to make more of one of the company's other products, generating an additional segment margin of $15,600 per year for that product. Required: a. Prepare a report that shows the financial impact of buying part Q89 from the supplier rather than continuing to make it inside the company. b. Which alternative should the company choose
Business
1 answer:
DedPeter [7]1 year ago
5 0

Answer:

Recher Corporation:

a) Financial impact of buying part Q89:

i) Relevant costs for In-house production of part Q89 are the avoidable costs:

Direct materials - $7.60

Direct labour - $4.20

Variable overhead - $8.30

Supervisor's salary $3.20

Avoidable general overhead - $0.81

Avoidable cost = $24.11 per unit

Total = $24.11 x 6,200 = $149,482

ii) Relevant cost of buying outside equals outside price minus additional segment savings = (6,200 x $27) - $15,600 = $151,800

When i) is compared with ii), it shows that it would cost more to buy outside ($151,800) than to produce the part in-house ($149,482).

b) The alternative the company should choose is to produce in-house.

Explanation:

a) The avoidable general overhead of $0.81 was obtained by dividing $5,000 of general overhead by 6,200 units, i.e. $5,000 / 6,200.

b) The depreciation for the special equipment is not included as it is not relevant.  It must be incurred no matter the option chosen.

c) The relevant cost of buying the part outside was reduced by $15,600 since this amount would be realized as additional margin with the choice.

d) |n making cost decisions, relevant and avoidable costs are considered.  Any cost that will be incurred notwithstanding the choice made is not relevant.  Such costs are unavoidable.  For example, the depreciation on the equipment.

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Instructions are below.

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Answer:

Under this cartel arrangement, they will maximize joint profits if each of the firms produces 257.14 units and sells at $1,542.88 per unit.

Explanation:

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MC_i = dC(q_i)/dq = 2q_i ……………………. (3)

Since q = q_1 + q_2, we have:

p = 3,600 - 4(q_1 + q_2)

p = 3,600 - 4q_1 - 4q_2 .................................... (4)

For Firm 1:

TR_1 = p * q_1 = (3,600 - 4q_1 - 4q_2)q_1

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MR_1 = dTR_1/dq_1 = 3,600 - 8q_1 - 4q_2

From equation (3), MC_1 = 2q_1

Since at the optimum MC_1 = MR_1, we have:

2q_1 = 3,600 - 8q_1 - 4q_2

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q_1 = (3,600 - 4q_2)/10

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For Firm 2:

TR_2 = p * q_2 = (3,600 - 4q_1 - 4q_2)q_2

TR_2 = 3,600q_2 - 4q_2q_1 - 4q_2^2

MR_2 = dTR_2/dq_2 = 3,600 - 4q_1 - 8q_2

From equation (3), MC_2 = 2q_2

Since at the optimum MC_2 = MR_2, we have:

2q_2 = 3,600 - 4q_1 - 8q_2

10q_2 = 3,600 - 4q_1

q_2 = (3,600 - 4q_1)/10

q_2 = 360 - 0.4q_1 .......... (6)

a. Calculation of Cournot equilibrium quantities

Substituting equation (6) for q_2 into equation (5), we have:

q_1 = 360 - 0.4(360 - 0.4q_1)

q_1 = 360 – 144 + 0.16q_1

q_1(1 – 0.16) = 216

q_1 = 216 / 0.84

q_1 = 257.14 <------------- Cournot equilibrium quantity for firm 1

Substitute for q_1 in equation (6), we have:

q_2 = 360 - 0.4(257.14)

q_2 = 360 – 102.86

q_2 = 257.14 <------------- Cournot equilibrium quantity for firm 2

b. Calculation of Cournot equilibrium price

Substitute for q_1 and q_2 into equation (4), we have:

p = 3,600 – 4(257.14) – 4(257.14)

p = 1,542.88

Therefore, under this cartel arrangement, they will maximize joint profits if each of the firm produces 25.14 and sells at $1,542.88 per unit.

8 0
1 year ago
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