Source: Demski, Managerial Uses of Accounting Information, 2nd ed., Ch. 8–12 + supplementary notes on projections
Difficulty: Intermediate to Advanced | Prerequisites: Unit 1 (Ch. 1–7) study notes on product cost assessment; basic probability (expected value, conditional probability, Bayes' theorem)
This is the second pillar of the course: using accounting data to make decisions. Unit 1 taught you how costs are measured and allocated. This unit asks what you should do with those numbers when you face a choice. The progression runs from how to frame a decision consistently (Ch. 8), through incorporating uncertainty and probability (Ch. 9), to strategic settings where competitors react to your choices (Ch. 10), to the practical mechanics of small, everyday decisions (Ch. 11) and large, capital‐budgeting decisions (Ch. 12). If you are behind, make sure you are comfortable with relevant vs. irrelevant costs from Unit 1 before starting here.
Good decisions require identifying which costs and revenues change between alternatives (relevant costs), incorporating uncertainty through expected‐value calculations, and recognising that strategic competitors may respond to your choices. Small decisions (make/buy, special orders) use marginal analysis. Large decisions (capital investment) use net present value. Both depend on getting the cost inputs right, which is why Unit 1 matters here.
Relevant cost
A cost that differs between decision alternatives. In simple terms, if a cost stays the same no matter what you choose, ignore it for that decision.
Irrelevant cost
A cost that does not change between alternatives. Sunk costs and allocated fixed overhead that will not change are the usual culprits.
Consistent framing
Demski's principle that a decision analysis must compare alternatives on the same basis: same time horizon, same cost categories, same assumptions. Mixing full cost for one option and marginal cost for another produces nonsense.
Expected value
The probability‐weighted average of all possible outcomes. EV = Σ [probability of outcome × value of outcome]. The standard tool for incorporating uncertainty into a decision.
Bayes' theorem
A rule for updating probabilities when new information arrives. P(A|B) = P(B|A) × P(A) / P(B). In this course, you use it to revise your estimate of a state of the world after observing a signal.
Prior probability
Your initial belief about the likelihood of each state of the world, before new information arrives.
Posterior probability
Your revised belief after incorporating new information via Bayes' theorem.
Strategic interaction
A setting where your payoff depends not just on your own action but on what competitors do. Pricing, capacity, and market‐entry decisions typically fall here.
Omitted variable
A relevant factor left out of the formal analysis. In small‐decision problems (Ch. 11), omitted variables can flip the conclusion, so you need to know what the model is not capturing.
Net present value (NPV)
The sum of discounted future cash flows minus the initial investment. If NPV > 0, the project adds value. The central tool for large, long‐horizon decisions.
Contribution margin
Selling price minus variable cost per unit. In simple terms, it is how much each unit contributes toward covering fixed costs and generating profit.
Special order
A one‐time order at a price below the normal selling price. Accept it when the price exceeds the incremental (variable) cost and there is spare capacity.
Make-or-buy decision
Whether to produce a component in‐house or purchase it from an outside supplier. Compare the relevant costs of each option, including opportunity costs of capacity.
The framing principle
Before comparing alternatives, define the decision frame: what is being decided, what are the alternatives, what time horizon applies, and what costs and revenues change.
Two common errors: including irrelevant costs that do not differ between alternatives, and omitting opportunity costs that do differ.
Sunk costs and the framing discipline
Sunk costs enter neither alternative (they have already been spent), so they drop out of a properly framed analysis.
Students who include sunk costs are not framing consistently: they are mixing past commitments into a forward‐looking comparison.
Full cost vs. marginal cost in framing
A decision frame that uses fully allocated product costs may include fixed overhead that will not change. This overstates the cost of continuing an activity and can lead to incorrect drop decisions.
A properly framed analysis uses only the costs that differ, which usually means marginal or incremental costs.
Incorporating uncertainty into decisions
Most real decisions involve unknown future states (demand could be high or low, a competitor could enter or not). The standard approach is to assign probabilities to each state and compute the expected value of each alternative.
Decision trees
Map out the sequence of decisions and chance events. At each chance node, compute the expected value by weighting outcomes by their probabilities. At each decision node, choose the alternative with the highest expected value.
Value of information
Perfect information would tell you the true state of the world before you decide. The expected value of perfect information (EVPI) is the difference between the expected payoff with perfect information and the expected payoff without it.
Imperfect information (a market study, a test, an audit) has value only if it changes your decision. If you would choose the same alternative regardless of the signal, the information is worthless for that decision.
Bayes' theorem in practice
Start with prior probabilities for each state. Observe a signal. Use Bayes' theorem to compute posterior probabilities. Re‐evaluate the decision with the posteriors.
The Bayesian Ralph problems walk you through this process step by step. Parts A and C are assigned, so work through them carefully.
Risk aversion
Expected value assumes the decision maker is risk‐neutral. A risk‐averse decision maker may prefer a lower‐expected‐value option if it carries less variance. This is relevant but secondary to the expected‐value mechanics in most of the assigned problems.
When competitors matter
In a strategic setting, your optimal action depends on what others do. A pricing decision that ignores competitor response may look profitable in isolation but trigger a price war.
Game-theoretic basics
Two players, two or more strategies each, payoffs that depend on the combination of choices. You do not need to be a game theory expert, but you need to read a payoff matrix and identify dominant strategies and Nash equilibria.
Ralph's Heirloom Partition and Strategic Disclosure problems
These problems require you to think about how information released to competitors (or withheld from them) affects outcomes. The key insight: information has strategic value because it changes what others do.
Connecting back to cost data
The cost numbers you share (or that leak through pricing) can reveal your cost structure to competitors. This is why firms sometimes use full‐cost pricing even when marginal‐cost pricing would be more "correct" in a textbook sense: full‐cost prices are harder for competitors to reverse‐engineer.
The typical small‐decision problems
Make or buy, accept or reject a special order, keep or drop a product line, add or drop a shift, allocate a scarce resource among competing uses.
The decision rule
Compare incremental revenues with incremental costs. If the incremental revenue exceeds the incremental cost (including opportunity cost), go ahead.
Omitted variables
The formal model captures quantifiable costs and revenues. But qualitative factors (quality risk from outsourcing, customer goodwill from keeping a loss‐making product, employee morale) may matter. The textbook asks you to recognise these as omitted variables and discuss how they might change the conclusion.
Missing data and projections
When data for a relevant cost is unavailable, you must project it. The supplementary notes on projections cover techniques for estimating costs from incomplete data. The key skill: separating what you know from what you are guessing, and being explicit about your assumptions.
Unobservable costs
Some costs (the true opportunity cost of capacity, the reputational cost of a quality failure) cannot be directly observed. You still need to include them in the frame, even if the number is approximate.
Standard costing and the plug
When standard costing is used, the difference between actual and applied overhead (the "plug" or variance) must go somewhere. Homework problem 11‐15 asks you to think about what role this plug plays in a decision context. The point: if standard costs are used for decision making, the variance may contain information about whether the standards are still accurate.
Capital budgeting and NPV
Large decisions commit resources over multiple periods. The standard tool is net present value: discount all future incremental cash flows to the present, subtract the initial outlay.
NPV > 0 means the project earns more than the cost of capital. Accept it.
Cash flows, not profits
NPV uses cash flows, not accounting profits. Depreciation is not a cash flow (it is an allocation of a past expenditure). Taxes are a cash flow. Working‐capital changes are cash flows.
Ralph's NPV problems (Parts A and B)
These walk you through a capital‐budgeting analysis. Part A sets up the cash flows; Part B introduces complications. Work both carefully.
Long-run framing
Ralph's long‐run frame problems (Parts A and B) extend the analysis to settings where the firm's cost structure can change over time. In the long run, capacity is adjustable, so fixed costs become relevant costs.
The long‐run frame asks: if we can redesign our operations, what is the most efficient configuration? This loops back to the economic theory of cost from Chapter 2, where all inputs are variable in the long run.
Expected value
EV = Σ P(state_i) × Payoff(state_i)
Bayes' theorem
P(State | Signal) = P(Signal | State) × P(State) / P(Signal), where P(Signal) = Σ P(Signal | State_j) × P(State_j) over all states j.
Expected value of perfect information (EVPI)
EVPI = EV(with perfect info) – EV(best decision without info). This is the most you should pay for a perfect forecast.
Net present value
NPV = Σ [Cash flow_t / (1 + r)^t] for t = 0, 1, 2, ..., n, where r is the discount rate. Cash flow at t = 0 is typically the initial investment (a negative number).
Contribution margin
CM = Price – Variable cost per unit.
Break-even volume
Q* = Fixed costs / Contribution margin per unit. This is the volume at which total revenue equals total cost.
Special‐order decisions happen constantly in manufacturing (an overseas customer wants a one‐time batch at a discounted price) and services (a hotel considering a group rate below rack rate). Make‐or‐buy decisions drive entire supply chains: automotive companies continually reassess which components to produce in‐house vs. outsource. NPV analysis underlies every capital budget in corporate finance, from building a new plant to launching a product line. Bayesian updating is the foundation of diagnostic medicine, fraud detection, and quality control, though those fields rarely call it by that name.
Students include allocated fixed overhead as a relevant cost in make‐or‐buy decisions. If the overhead will not go away when you outsource, it is irrelevant to the comparison.
Students assume all information is worth acquiring. Information has value only if it could change your decision. If one alternative dominates regardless of the signal, the information is worthless for that choice.
Students confuse accounting profit with cash flow in NPV calculations. Depreciation is an accounting entry, not a cash outflow. Include it only for its tax‐shield effect (depreciation × tax rate = cash saved).
Students forget opportunity cost. If accepting a special order uses capacity that would otherwise produce regular‐priced units, the forgone contribution margin on those units is a cost of the special order.
⚠️ Exams are problems and short essay, cumulative. Expect to frame a decision by identifying relevant costs, compute expected values, and apply Bayes' theorem.
⚠️ Be able to set up and solve a Bayesian updating problem from scratch (prior → likelihood → posterior → revised decision). The Bayesian Ralph assignment is direct exam preparation.
⚠️ NPV problems will require you to identify incremental cash flows (not accounting profits), discount them, and state the accept/reject conclusion.
⚠️ Short‐essay questions may ask you to discuss omitted variables or strategic considerations that a purely numerical analysis misses. Practice articulating these in two or three clear sentences.
⚠️ Ralph's Technology problems (Parts A and C) test your ability to handle projections with incomplete data. Make sure you know the supplementary notes on projections.
True or false: A sunk cost is always irrelevant to a forward‐looking decision. (True.)
Fill in the blank: The expected value of perfect information equals the expected payoff _______ perfect information minus the expected payoff _______ it. (With; without.)
True or false: In an NPV calculation, depreciation expense should be included as a cash outflow. (False. Depreciation is not a cash flow; only its tax‐shield effect matters.)
Fill in the blank: A special order should be accepted when the order price exceeds the _______ cost of filling it. (Incremental / variable.)
True or false: Information always has positive value. (False. Information has zero value if it cannot change the decision you would make.)
Q: A firm can make a component for $12 variable cost per unit. A supplier offers to sell it for $14. Fixed overhead of $5 per unit is currently allocated to the component. Should the firm outsource?
A: The relevant comparison is $12 (variable cost to make) vs. $14 (buy price). The $5 allocated fixed overhead is irrelevant if it will not disappear upon outsourcing. Continue making in‐house.
Q: You have two states of the world (High demand, Low demand) with prior probabilities 0.6 and 0.4. A market study returns a "positive" signal. P(positive | High) = 0.8, P(positive | Low) = 0.3. What is P(High | positive)?
A: P(positive) = 0.8(0.6) + 0.3(0.4) = 0.48 + 0.12 = 0.60. P(High | positive) = 0.8(0.6) / 0.60 = 0.48 / 0.60 = 0.80.
Q: A project costs $100,000 today and generates cash flows of $40,000 per year for four years. The discount rate is 10%. Should you accept?
A: PV of cash flows = 40,000/1.1 + 40,000/1.21 + 40,000/1.331 + 40,000/1.4641 = 36,364 + 33,058 + 30,053 + 27,321 = 126,796. NPV = 126,796 – 100,000 = 26,796 > 0. Accept.
Q: Explain in two sentences why a manager might reject a positive‐NPV project in a strategic setting.
A: If the project signals the firm's intentions to a competitor (e.g. capacity expansion), the competitor may respond aggressively (price war, matching expansion), eroding the projected cash flows. The NPV analysis that ignores this response overstates the project's value.
Q: What is the role of the "plug" in a standard‐costing system, and why does it matter for decisions?
A: The plug is the overhead variance (difference between applied and actual overhead). It matters because a large, persistent variance suggests the standard rates are stale, and decisions based on those rates may be using the wrong cost inputs.
Consistent framing (Ch. 8) is the bridge between cost measurement (Unit 1) and cost‐based decisions (this unit). The uncertainty material (Ch. 9) reappears in performance evaluation (Ch. 13–14), where the question shifts from "what should we decide?" to "how well did the decision turn out, given uncertainty?" Strategic framing (Ch. 10) connects to coordination and incentive design (Ch. 18–19) in Unit 3, where information asymmetry between managers and the firm drives the analysis.
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