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Large versus Small Decisions: Short-Run

• The accounting library – Provides information for decision making (framing)– Records consequences of choices made

• Small decisions here means variations on the status quo– Our LLAs are assumed to be reasonably accurate– Interactions with other decisions and strategic interaction play a minor

role

• Separating small and large decisions is a matter of judgment

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Break-Even Analysis

• Assumptions:– Demand q ranges between– Total revenue TR = 600q– Total cost TC = 150,000+100q– Combining the two LLAs we estimate profit as

TR-TC= [600-100]q-150,000

• Example 1:– Assume cost of closing down for the period is F0

– The firm knows that demand will fall in the relevant range specified– What determines the choice?

– Extension 1: How does the choice change if the firm can lease out the production facility if it closes down for F0+10,000?

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• Example 2: – No leasing opportunity present– Cost of shutdown F0

– Firm knows that q>qBE

• Example 3:– Firm produces several products– Adding another one for a single period will lead to incremental cost and

revenues of TR = 600q and TC = 100q + 150,000– What determines the choice?

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Inventory valuation

• A firm manufactures and sells a product in each of two periods• Production and sale are contemporaneous, the finished product

cannot be stored• The only production factor of interest is direct material• Net cash flow per unit produced is 100 in the first and 110 in the

second period• Capacity is limited to 100 units per period• Direct material market is imperfect

– First period: firm acquires material at a price of 10 and sells at 8– Second period: estimated acquisition price is P+ and estimated selling

price is P-

– Interest rate is 10%– All transactions occur in cash

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• With the previous setting in place the firm now has the option to produce and sell one unit of a second product in the first period– If the firm decides not to it remains at– If it decides to produce this requires one unit of material and leads to

additional cash inflow of – The additional product does not affect the demand of q1 = 100 but

requires additional material• The optimization problem changes as follows

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• Whether the firm should produce the extra product depends on

• Alternatively it depends on whether incremental revenues exceed incremental cost– Incremental revenue:

– Incremental cost: the shadow price of an additional unit of beginning inventory

• Current acquisition price• Current sales price• Present value of expected future acquisition price• Present value of expected future sales price

• Accounting inventory cost: historical cost but lower of cost or market

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Make or buy

• Options:– Produce an input or intermediate product within the firm– Or purchase from an outside supplier

• Potential disadvantages of outsourcing– Dependency on outside supplier– Loss of proprietary information

• Irreversibility of choice– Hold up problems– Concern for quality

• Short run perspective:– Relatively unambiguous– Is short-run profit higher with insourcing or with outsourcing?

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Two product illustration

• A firm sells two products• Both products run through two production stages with limited

capacity– Subassembly: – Assembly:

• Direct labor and direct material costs in each stage are described by the following LLAs:

• Subassembly: DLS=10q1+10q2

DMS=110q1+200q2

• Assembly: DLA=40q1+80q2

DMA=12q1+15q2

• Overhead LLA: OV=2,000,000+3.5(DLA+DLS)

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Short run profit

• Short run profit equals:

• Optimization problem:

Solution for and is and with = 426,000

Shadow prices on the two constraints are 26 and 227, resp.

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Option for outsourcing

• The firm now has the option to purchase up to 500 parts of product 2 that are otherwise produced in the subassembly stage

• Subassembly: DLS=10q1+10q2

DMS=110q1+200q2

• Assembly: DLA=40q1+80q2+80DMA=12q1+15q2+15

• assuming incremental overhead cost, contribution margin for product 2 becomes:

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Optimization problemwith outsourcing option

• Start with and and P=250• Optimal solutions are , and

• Profit obtained is = 436,500

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Variation in price

• Now we go back to the original setting– no outsourcing – but assume

• We get:(shadow prices: 0, 265)

• Add the outsourcing offer again with P =250

• Results are:

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Reduced form in accounting

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Uncertainty

• Uncertainty is present also with regard to small decisions– How should a manager deal with it

• Ignore it• Consider it implicitly• Include it in the choice model explicitly

• Uncertainty is likely to change the decision problem– With risk neutrality it may add opportunity costs to some choice

• Option value of flexibility– With risk aversion decisions are less likely to be small decisions

• Recall: with small decisions interactions with other projects are low or absent

• Risk aversion causes interdependencies with other projects e.g. if correlation is present