3.3.3 - Decision-making techniques

A moving average smooths short-term fluctuations so the underlying direction of a time series is easier to see. Use the number of consecutive observations named in the question and keep the original unit.

For annual percentages 65, 66 and 72, the three-period moving average is (65 + 66 + 72) / 3 = 67.67%. Then move the window forward one period and repeat; do not reuse a three-year total as though it were a single observation.

Compare successive moving averages: a rising series indicates an upward trend after irregular variation has been smoothed. The calculation describes the historical trend; it does not by itself explain why sales changed.

A scatter graph plots paired observations. The direction and closeness of the points show correlation; a line of best fit represents the general relationship and can be extended to estimate a future value.

Identify the input value, move to the line of best fit, then read the estimated output from the other axis. Interpolation stays within observed data; extrapolation extends beyond it and assumes the past relationship continues.

If the fitted line links advertising expenditure to sales, a future advertising budget can be mapped to an estimated sales figure. State it as an estimate and use the axis scale and units precisely.

Quantitative forecasting converts historical data into a numerical trend, but its apparent precision depends on the relevance, quality and stability of the data and assumptions.

A forecast is more useful when past forecasts were accurate, the data are recent and comparable, and the business tests alternative assumptions. It is less useful in a rapidly changing market or over a long extrapolation distance.

The simple payback period is the time taken for forecast net cash inflows to recover the initial investment. A shorter payback normally means the cash is recovered sooner and is exposed to uncertainty for less time.

An investment of £120,000 returning £30,000 each year has a payback of £120,000 / £30,000 = 4 years. If £15,000 remains after year 3 and year 4 brings £30,000, payback is 3 + 15,000/30,000 = 3.5 years, or about 3 years 6 months.

Compare the result with the firm's target payback and with alternatives calculated on the same basis. Faster recovery can support liquidity, but does not establish which project creates the most total return.

Average accounting rate of return (ARR) compares the average annual profit generated by a project with its initial investment and expresses the result as a percentage.

ARR (%) = (average annual profit / initial investment) × 100, where average annual profit = total forecast profit over the project's life / number of years.

If total forecast profit is £287,550 over 6 years and the initial investment is £150,000, average annual profit is £47,925 and ARR = (£47,925 / £150,000) × 100 = 31.95%.

A higher ARR is normally preferred and should be compared with the firm's required return or other projects. The percentage helps compare projects of different scale, provided profit definitions and time periods are consistent.

Discounted cash flow recognises that money received later is worth less than money received now. Net present value (NPV) compares the present value of forecast net cash flows with the initial cost.

If the discounted cash inflows total £21,635 and the machine costs £10,000 now, NPV = £21,635 − £10,000 = £11,635. A positive NPV means the forecast return exceeds the return represented by the chosen discount rate.

With comparable risk and assumptions, a higher positive NPV is financially more attractive; a negative NPV fails to meet the chosen discount rate. The result remains a forecast, not cash already earned.

Investment appraisal figures are useful only when their meaning is matched to the decision. Payback focuses on recovery time, ARR on average profit relative to investment, and NPV on value after discounting future cash flows.

First confirm that figures use comparable time periods, costs and assumptions. Then connect the result to the firm's objective: a cash-constrained firm may value rapid payback, while a long-term investor may give greater weight to NPV.

A method can rank alternatives differently because it measures a different feature. Use the figures together with project scale, risk, finance and strategic fit rather than searching for one universally decisive number.

All investment appraisal methods simplify an uncertain future. Their usefulness depends on the accuracy of cash-flow or profit forecasts and on whether the technique matches the firm's objective.

Forecast error matters more for a large, long-lived or irreversible project. Sensitivity testing, comparison of methods, experienced estimates and qualitative analysis can improve the decision, but cannot remove uncertainty.

A decision tree displays alternative choices and uncertain outcomes in a sequence. It makes the assumptions visible so managers can compare options consistently.

Draw choices from left to right. After each choice, add its possible outcomes, label probabilities and returns, and check that mutually exclusive probabilities at each chance node sum to 1. Put any initial cost on the relevant option.

Work back from right to left after calculating expected values. The tree helps compare alternatives, but the final recommendation should also test whether the inputs and omitted qualitative factors are credible.

Expected monetary value (EMV) is the probability-weighted average financial outcome. Calculate it at each chance node, then deduct the initial cost of the option to compare net expected values.

EMV at a chance node = Σ(probability × financial outcome). Net expected value of an option = EMV − initial investment cost.

Option A has a 0.4 probability of £7m and a 0.6 probability of −£1m: EMV = (0.4 × £7m) + (0.6 × −£1m) = £2.2m. If a separate initial cost exists, subtract it once after weighting the outcomes.

On the quantitative evidence alone, choose the option with the highest net expected value. Then consider the range of outcomes, affordability, time, strategic fit and reliability of the probabilities before making a recommendation.

A decision tree structures uncertainty and makes alternatives comparable, but its numerical result is only as credible as the estimated probabilities, returns and choices included.

The technique is strongest for clearly defined alternatives with defensible probabilities and comparable monetary consequences. It is weaker for novel, long-term decisions dominated by human response or external shocks.

Critical path analysis (CPA) represents a project as linked activities with durations and dependencies. Its purpose is to identify the minimum completion time and the activities that cannot be delayed without delaying the whole project.

CPA can coordinate a building project, factory change or marketing launch. Managers can see where a delayed critical activity will affect every dependent activity and where resources might be reallocated.

A project network links activities in dependency order. Complete a semi-finished network, calculate timings through it, and identify the route whose activities determine the minimum project duration.

A delay to a critical activity delays the project unless time is recovered elsewhere on the critical path. A non-critical activity may be delayed only up to its available float before it becomes critical or affects a successor.

Earliest start time (EST) is found by a forward pass; latest finish time (LFT) is found by a backward pass. Together they show how much an activity can slip without delaying the project.

If an activity starts from an event with EST 8, lasts 4 weeks and ends at an event with LFT 16, total float = 16 − 4 − 8 = 4 weeks. Zero float indicates a critical activity.

The start event normally has EST 0. At the final event, EST and LFT equal the minimum project duration. At a merge use the largest forward value; at a split use the smallest backward value.

CPA is a planning model. Errors in activity duration, dependencies or resource assumptions can make the calculated completion date and float misleading.

CPA is more useful for familiar, divisible projects with reliable estimates and active monitoring. Managers should update the network, build contingencies and combine timing information with cost, quality and risk controls.

Contribution is the amount remaining after variable costs are deducted from sales revenue. It first contributes toward fixed costs; only contribution above total fixed costs becomes profit.

Contribution isolates the extra amount generated by a product or decision before fixed cost allocation. This helps analyse product mix, pricing, special orders and whether limited capacity should be used for one option rather than another.

Contribution must be calculated with consistent units. Find per-unit contribution for a single product decision or total contribution when assessing the overall result.

Contribution per unit = selling price per unit − variable cost per unit. Total contribution = contribution per unit × output. Profit = total contribution − fixed costs.

If a product sells for £50, variable cost is £32 and 4,000 units are sold, contribution per unit is £18 and total contribution is £72,000. With fixed costs of £55,000, profit is £17,000.

Higher total contribution provides more toward fixed costs and profit, but output, capacity use and any additional fixed cost must be included. When a scarce resource constrains output, compare contribution per unit of that limiting factor.

Contribution analysis asks how a decision changes revenue and variable cost, then whether the resulting contribution is sufficient given fixed costs, capacity and alternatives.

A special order at £28 with variable cost £22 adds £6 contribution per unit if spare capacity exists. It may help cover fixed costs, but displacement of regular sales or an added fixed setup cost could reverse the decision.

Use contribution for the incremental financial effect, then test demand, capacity, opportunity cost, quality and strategy. The recommendation should state which assumptions make the decision worthwhile.