Decision-Making Techniques
Unit 3: Business Decisions and Strategy
Decision-Making Techniques
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A moving average replaces each figure with the mean of it and its neighbours, smoothing seasonal ups and downs so the underlying trend shows.
A time series is a set of figures recorded at regular intervals, such as monthly sales. Read raw, it jumps about with the seasons and with one-off events. A moving average takes a fixed number of consecutive figures, finds their mean, then moves on one period and repeats, so the direction underneath shows.
A four-quarter moving average smooths a whole year of seasons at once, but four values have no middle quarter to sit against. So it is centred: average each pair of neighbouring four-quarter averages and write the result against the quarter between them. The specification names both versions (WBS13, 3.3.3.1a).
Real Example: Ride-hailing bookings for an app such as Grab in Kuala Lumpur spike every Friday evening and whenever it rains. A seven-day moving average of daily bookings irons out those spikes, so the operations team can see whether demand is growing or just having a wet week.
Exam Matters: A Calculate question (4 marks, WBS13 Appendix 6) wants the method shown: the three figures added, the division by three, and the answer against the right period. Round consistently, usually to one decimal place, and state the units.
A scatter graph shows whether two variables move together; the line of best fit summarises the link, and extending a line beyond the data is extrapolation.
Plot one variable against another, one dot per period: advertising spend across, sales up. Dots rising from bottom-left to top-right show a positive correlation; falling from top-left to bottom-right, a negative correlation; a shapeless cloud, no correlation. The line of best fit runs through the middle of the dots, with about as many above it as below.
The line is the forecasting tool. Read up from a planned advertising budget to the line and across to the sales axis, and you have a forecast. Extending the line past the last dot, or a moving-average trend past the last period, is extrapolation: it assumes the pattern in the data will carry on.
Correlation is not causation. Two variables can move together because a third drives both: ice-cream and air-conditioner sales both rise with hot weather. Before spending on the strength of a correlation, ask what links the two.
Real Example: Blockbuster's revenue peaked in 2004; a forecaster extrapolating the previous decade's growth would have missed DVD-by-mail, kiosks and streaming. The company filed for bankruptcy protection in September 2010 (source: Blockbuster Inc. annual report for 2004; Chapter 11 petition, 23 September 2010).
Exam Matters: Interpreting a scatter graph is a named WBS13 skill (3.3.3.1b): state the direction and strength of the correlation, use the line of best fit to read off a forecast, and say what extrapolating beyond the data assumes.
Every quantitative forecast assumes the future will behave like the past; the technique cannot see a change it has no data for.
Quantitative methods are a starting point, not a verdict. Firms combine them with qualitative forecasting: sales-force estimates, expert opinion, test markets and consumer panels, which can pick up what the numbers have not yet recorded.
Real Example: Airlines planned their 2020 schedules by extrapolating a decade of steady passenger growth. Global passenger traffic then fell by about two-thirds in 2020 as pandemic travel restrictions took hold (source: IATA press release, 3 February 2021).
Exam Matters: For a Discuss (8 marks) or Assess (12 marks) on forecasting, the strongest evaluation is conditional: quantitative methods work in stable markets with long records, and fail when the market is new, volatile or about to change.
Payback is the time an investment takes to earn back its cost from the net cash inflows it generates; the shorter, the sooner the money is safe.
Investment appraisal is the set of techniques for deciding whether a capital project (a machine, a store, a fleet) is worth its cost. Simple payback asks the plainest question: how long until the cumulative net cash inflow equals the outlay?
Part-year rule: full years before recovery + amount still to recover ÷ cash inflow in the year of recovery. Compare the result with the firm's target, or with the rival project: shortest wins. Payback is simple and favours liquidity, but it ignores every cash flow after the payback point and the timing of cash within it.
Real Example: Supermarkets that swap open chillers for glass-door cabinets pay a known price and save a known amount of electricity each year. Payback is the natural test: the number of years until the saved power bills have repaid the doors.
Exam Matters: A Calculate question (4 marks) is marked on the cumulative table and the part-year fraction as much as on the answer, so show them, then give the result in years and months (WBS13 Appendix 6: workings should be given).
ARR expresses the average annual profit from an investment as a percentage of its initial cost, so it can be set against a target rate or a savings rate.
Average (accounting) rate of return turns a project into a percentage. Unlike payback it uses profit: the total net cash inflow over the project's life minus the initial cost, spread over the years.
Accept the project if the ARR beats the firm's target, or the return the money could earn elsewhere, such as bank interest; between projects, the higher ARR wins. ARR uses the whole life of the project, which payback does not, but it treats a dollar in year four exactly like a dollar in year one.
Real Example: Fixed-deposit rates at banks in Singapore or Pakistan are the benchmark a small firm reaches for: a machine returning 12% a year on average clears the bar when deposits pay 4%, and fails it when they pay 15%.
Exam Matters: State the formula, show total profit, the average and the percentage. A correct method with one arithmetic slip still earns method marks under the own figure rule (WBS13 mark schemes), so never write the answer alone.
NPV discounts each future cash flow to its value today and subtracts the cost; a positive result means the project earns more than the firm's required rate.
A dollar next year is worth less than a dollar now, because today's dollar could be invested and grow. Discounted cash flow applies that idea: a discount factor for each year, at the firm's chosen rate, converts a future cash flow into its present value. The factors are given in the question.
NPV = sum of (cash flow × discount factor) − initial cost. Positive, the project beats the discount rate; negative, reject; between projects, the highest NPV wins. NPV alone prices the timing of every cash flow, but it rests on long-range forecasts and on the choice of rate, and a higher rate can turn an accept into a reject.
Real Example: Mining companies appraise a new mine with discounted cash flow because the outlay comes first and the returns arrive over decades; a project that looks profitable in total can show a negative NPV once cash flows twenty years out are discounted.
Exam Matters: Set the working out as a table: year, cash flow, discount factor, present value, with the cost in year 0 at a factor of 1. The paper supplies the factors (WBS13, 3.3.3.2c); the skill is applying them and interpreting the sign.
The three techniques answer different questions, so they can disagree; a decision weighs the figures against risk, liquidity and factors no calculation captures.
When they disagree, ask why. A project with a slow payback but a high NPV earns late; a firm short of cash may still refuse it. A tie on ARR can hide a big difference in timing that NPV reveals. Then add what the numbers omit: the forecasts may be wrong, the capital may be needed elsewhere, and the workforce, the brand and the environment appear in none of the three.
Real Example: Airlines buying aircraft that will fly for twenty-five years cannot decide on payback alone, which would reject almost any aircraft; they lean on NPV over the whole life, then weigh fuel prices, route demand and financing that no single figure settles.
Exam Matters: A 20-mark Evaluate on an investment decision (WBS13 Section B or C) is levels-marked: calculate what the data allow, compare the methods, bring in non-financial factors, and end with a recommendation that states the criterion it rests on.
A decision tree draws a choice as branches: squares where the manager decides, circles where chance decides, with probabilities and payoffs on the ends.
A decision tree maps a decision from left to right. A decision node, drawn as a square, is a point where the manager chooses between options. A chance node, drawn as a circle, is a point where the outcome is uncertain. From each chance node run branches, one per possible outcome, and the probabilities on them add up to 1.
Kopi Kita must choose between launching its own bottled cold brew and licensing the recipe to a drinks firm. Launching costs $200,000 and faces high demand (0.6, payoff $500,000) or low demand (0.4, payoff $100,000). Licensing costs $20,000, with strong uptake (0.5, $250,000) or weak (0.5, $150,000). The diagram at the chapter check-in draws it.
Real Example: Pharmaceutical firms draw decision trees for drug development, because each trial phase is a chance node with a known historical success rate; only about 8% of the candidates that enter human trials reach approval (source: BIO, Clinical Development Success Rates 2011–2020).
Exam Matters: Construct (4 marks) means an accurately labelled diagram (WBS13 Appendix 6): squares and circles in the right places, probabilities on chance branches adding to 1, costs on option branches, payoffs at the ends. Label everything, since the marks sit on the labelled elements.
Work the tree from right to left: expected value at each chance node, then subtract each option's cost and choose the highest net gain at the decision node.
The expected monetary value (EMV) of a chance node is the weighted average of its payoffs: multiply each payoff by its probability and add them. It is what the branch would return on average if the situation were repeated many times.
Where a tree has more than one decision node, roll each back in turn; the value carried into an earlier node is the best net gain available beyond it.
Real Example: Oil companies decide whether to drill an exploration well this way: the well is a cost on the decision branch, the chance node holds the probabilities of a dry hole, a small find and a large one, and the well is drilled only if the net gain is positive.
Exam Matters: Show every product and sum. A Calculate answer with the right EMVs and the wrong final choice still carries method marks under the own figure rule (WBS13 mark schemes). State the choice in words, with the net gain figure that justifies it.
A decision tree is only as sound as its probabilities and payoffs, and it ignores risk attitude and anything that cannot be given a number.
Used well, a tree forces a manager to name the options, the uncertainties and their odds, and to compare them on one scale. Used badly, it lends false precision to a guess.
Real Example: A film studio deciding whether to make a sequel can put probabilities on a hit and a flop, but the payoff of a hit depends on a release date years away and on what rivals release that week; the tree organises the argument without settling it.
Exam Matters: Analyse (6 marks) asks for two limitations developed in context (WBS13 Appendix 6). Tie each to the case: which probability is a guess here, which payoff is furthest ahead, whether this firm could survive the worst branch.
Critical path analysis draws a project as a network of dependent activities to find the shortest time it can take and the activities that cannot slip.
A project is a set of activities, each with a duration and dependencies: wiring cannot start until the strip-out is finished. Critical path analysis (CPA) draws them as a network. Each activity is an arrow; each node is a circle where activities start and finish, split into three: the node number on top, the earliest start time (EST) bottom-left, the latest finish time (LFT) bottom-right.
The critical path is the longest route through the network from start to finish. Its length is the minimum time the whole project can take, and every activity on it has zero float: delay one and the project finishes late. Activities off the path have float, spare time they can absorb.
Real Example: Critical path methods date from the late 1950s: DuPont used them to schedule chemical-plant maintenance shutdowns and the US Navy for the Polaris missile programme (sources: Kelley and Walker, "Critical-Path Planning and Scheduling", 1959; Malcolm and others, Operations Research, 1959).
Exam Matters: The paper gives a network to complete and interpret (WBS13, 3.3.3.4b). Be able to say what a node's three numbers mean, why the longest route is the critical one, and what float lets a manager do.
A forward pass fills in the earliest start times, a backward pass the latest finish times, and float is the gap between them less the activity's duration.
Critical path: A–B–D–F, 10 days. C and E can each slip two days.
Real Example: Shipyards in South Korea sequence hull, wiring and fit-out work with network diagrams; float on the painting tasks shows which crews can move to critical hull work without delaying delivery.
Exam Matters: Calculate (4 marks) asks for a float or a node value: show the subtraction with the three numbers named. Identify the critical path by listing its activities and its length, and check that each has zero float.
CPA assumes the durations and dependencies are right and the resources are there; a project that breaks those assumptions has a different critical path.
A strength sits inside each limit. Because the network is explicit, a change can be re-planned quickly, float shows where slack exists, and the critical activities are known before trouble arrives.
Real Example: The Sydney Opera House was planned to open in 1963 and opened in 1973, after design changes and construction difficulties; a network drawn in 1959 could not hold once the work itself changed (source: Sydney Opera House, "Our story", sydneyoperahouse.com).
Exam Matters: For a Discuss (8 marks) on CPA, weigh the limits against the purpose: the more uncertain the durations and the more shared the resources, the less the network can promise, but even then it shows which slips matter.
Contribution is what each sale leaves after its variable cost; added up, it pays the fixed costs, and whatever remains is profit.
Contribution per unit = selling price − variable cost per unit. It is not profit: fixed costs have not yet been paid. Total contribution = contribution per unit × units sold, and profit = total contribution − fixed costs.
The purpose of contribution is to separate the costs a sale causes from the costs the firm carries anyway. That is what makes it a decision tool: it shows what a product, an order or a branch really adds. In Unit 2 the same idea gave the break-even output (fixed costs ÷ contribution per unit); here the interest is in choices.
Real Example: Budget airlines such as AirAsia price this way: once a flight is scheduled, its fuel, crew and airport charges are fixed for that flight, so nearly every dollar of an extra seat sold is contribution, which is why late seats can be sold cheaply and still be worth selling.
Exam Matters: A 4-mark Calculate can ask for contribution per unit, total contribution or the resulting profit; write the formula, substitute the figures and state the units. A Define (2 marks) needs the price-minus-variable-cost idea and what contribution goes towards.
Whenever fixed costs will be paid whatever the firm decides, the right comparison is contribution: take the option that adds the most of it.
The tool's limit is its assumption: fixed costs must really be fixed and capacity really spare. An order that needs overtime, a new machine or a second shift has changed the costs, and the simple comparison no longer holds.
Real Example: Hotels release unsold rooms to last-minute apps at prices well below the rack rate. A room's variable cost, cleaning and laundry, is small, so a cheap booking still adds contribution, provided it does not tempt full-price guests to wait for the discount.
Exam Matters: An Assess (12 marks in Unit 3, WBS13 Appendix 6) on a special order is levels-marked: calculate the contribution the order adds, then weigh capacity, the effect on regular customers and whether fixed costs really stay fixed, and reach a judgement.
A moving average replaces each figure with the mean of it and its neighbours, smoothing seasonal ups and downs so the underlying trend shows.
A scatter graph shows whether two variables move together; the line of best fit summarises the link, and extending a line beyond the data is extrapolation.