Part 2 Section C.3. Marginal Analysis 限界分析

Marginal Revenue and Marginal Cost

Relevant Information

  • Differential: differ between two alternatives
    • 例)既存設備が壊れてしまい、同型機種を買うか、上位機種を買うか2つの購入プランの差
  • Incremental: incurred additionally as a result of an activity
    • 例)既存設備はまだ使えるが、追加で上位機種を購入した差額のこと
  • Relevant:
    • on the future
    • differ among possible alternatives
      • 変動費でも、発生額が不変の場合は、irrelevant cost になる
  • Irrelevant:
    • in the past ( sunk cost)
    • cannot be changed
    • the same for all options under consideration
  • An avoidable cost:
    • is an existing cost that can be avoided
    • is relevant to the decision-making process
  • An unavoidable cost:
    • cannot be avoided and will not go away
    • is not relevant (is irrelevant)
  • Sunk cost:
    • is a cost that the money has already been spent and cannot be recovered
    • is not relevant (is irrelevant)
  • An explicit cost: accounting concept
    • is a cost that can be identified and accounted for
    • represents obvious cash outflows from a business (= cash outlay cost)
  • An implicit cost: economic concept
    • does not appear in the income statement
    • but affects the company’s net income just as if it were in the income statement (= opportunity cost)
  • An opportunity cost:
    • the potential earnings from a forgone alternative
    • 次善の策(諦めた策)から得られたはずの利益

Economic vs Accounting Concepts of Costs & Opportunity Costs

 

 AccountingEconomic
ExplicitImplicit
売上100100
費用7080
会計的利益3020
経済的利益10
  • Explicit cost は 70 だが、Implicit cost が追加で 20 あるので、Economic profit は 10 になる
  • 次善の策の会計的利益:20opportunity cost となるから

例題

フル操業での受注可否 特注オーダーの引合いと提供がある場合

前提条件

schedule
Direct materials$4.00
Direct labor$1.30
Variable OH$2.50
Fixed OH$3.40
Sales commission$0.90
Sum$12.10
Sales units10,000
The firm has found it can sell all it can produce at the market price o $16.50

The firm is considering two separate proposals:

C company has offered to buy 1,000 units at $14.35 each. Sales commission would be $0.35 on this special order.

S company has offered to produce 1,000 units at a delivered cost to the firm of $14.50 each.

問い

What would be the effect on the firm’s operating income of each of the following actions?

The cost to produce the units is irrelevant, because the firm can sell all that it produces at a market price of $16.50. The net realizable value per unit is $15.60($16.50 – $0.90 sales commission).

1. Acceptance of the proposal from C company, but rejection of the proposal from S company.

The first option would decrease net income by $1,600.
The net realizable value per unit sold to C company is $14.00 ($14.35 – $0.35 sales commission).
In order to supply C company, the firm would be displacing sales in the regular market having a NRV of $15.60.
That reduction of $1.60 per unit multiplied by 1,000 units would decrease net income by $1,600.

Alternate solution:
Normal profit per unit is $4.40 ($16.50 – $12.10).
The profit per unit sold to C company is $2.80 ($14.35 – $ 11.55).
C company cost is $11.55 ($4.00 + $1.30 + $2.50 + $3.40 + $0.35).
The difference of $1.60 per unit ($4.40 – $2.80) × 1,000 units would decrease net income by $1,600.

2. Acceptance of the proposal from S company, but rejection of the proposal from C company.

The second option would increase net income by $1,100.
The extra units could be sold in the regular market at a NRV of $15.60 ($16.50 – $0.90 commission).
The cost is $14.50.
Thus, profits would increase by $1.10 per unit, or $1,100 in total.
($16.50 – $0.90 commission).

Alternate solution:
Selling price $16.50 – cost to purchase from S company $14.50 – sales commission $0.90
= profit per unit $1.10
Increase in net income $1.10 × 1,000 = $1,100 in total.

3. Acceptance of both proposals.

The third option would decrease net income by $500.
Regular business is unaffected. As explained above, the 1,000 units bought cost $14.50 each, and the NPV of the produced units sold to C company is $14.00.
The net difference is $0.50 per unit.
$0.50 × 1,000 units = $500.

Alternate solution:
Action 1 decrease in net income of $(1,600) + Action 2 increase in net income of $1,100
= net decrease in net income of $(500).

C company has offered a second proposal to purchase 2,000 units at the market price of $16.50, but has required product modifications that would increase direct materials cost by $0.30 per unit and increase direct labor and variable OH by 15%. The sales commission would be $0.35 per unit.

Direct material $4.00 + $0.30 = $4.30.
Direct labor $1.30 × 1.15 = $1.495.
Variable OH $2.50 × 1.15 = $2.875.
Total cost $12.42 ($4.30 + $1.495 + $2.875 + $3.40 + $0.35).
Profit per unit $4.08 ($16.50 – $12.42).
Market profit $4.40 ($16.50 – $12.10)
Decrease in net income ($4.08 – $4.40) = $(0.32) × 2,000 = $(640) decrease.
Do not accept proposal.

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