Edexcel A-level Business (9BS0) · 3.3 Decision-making techniques
Mini-Lesson
Decision-making techniques
This mini-lesson covers Edexcel 3.3 Decision-making techniques: 3.3.1 quantitative sales forecasting (moving averages, scatter graphs and extrapolation), 3.3.2 investment appraisal (payback, ARR and NPV), 3.3.3 decision trees (expected values) and 3.3.4 critical path analysis (EST, LFT and total float). Every calculation on this specification appears here.
Work through each screen, answer the questions as you go (multiple choice, calculations and sorting tasks) and collect ⭐ stars. Press Start when you are ready.
3.3.1 · Quantitative sales forecasting
Moving averages, scatter graphs and extrapolation
A moving average smooths out short-run fluctuations to reveal the underlying trend. Edexcel uses the three-period (or four-quarter) moving average.
three-period moving average = (period 1 + period 2 + period 3) ÷ 3Each average is plotted against the middle period of the three, which is why the trend line is shorter than the data series.
Worked example
Monthly sales (000 units): Jan 120 · Feb 132 · Mar 150 · Apr 141
Jan–Mar average = (120 + 132 + 150) ÷ 3 = 402 ÷ 3 = 134 (plotted against February)
Feb–Apr average = (132 + 150 + 141) ÷ 3 = 423 ÷ 3 = 141 (plotted against March)
The trend is rising — the underlying direction of travel, once monthly noise is removed.
Scatter graphs and the line of best fit show the correlation between two variables (for example advertising spend and sales). Extrapolation extends the line of best fit beyond the data to forecast the future.
Limitations: extrapolation assumes the past pattern continues, which is exactly what fails at a turning point. Correlation is not causation. And no time-series method can predict a shock — a new competitor, a recession or a change in the law.
Calculate
Your turn — moving average
1Monthly sales are 120, 132 and 150 thousand units. Calculate the three-period moving average, in thousands of units.
000 units
Hint: (120 + 132 + 150) ÷ 3.
3.3.2 · Investment appraisal
The project under appraisal
All three appraisal techniques are applied to the same project throughout this lesson:
Project data — a new machine
Initial cost (year 0): £240,000
Net cash flow — Year 1: £80,000 · Year 2: £100,000 · Year 3: £120,000 · Year 4: £100,000
Total inflows over four years = 80 + 100 + 120 + 100 = £400,000
payback = the time taken for cumulative net cash flow to equal the initial outlayWithin a year: (outlay still to be recovered ÷ that year's cash flow) × 12 months
Payback — worked
Cumulative after Year 1 = £80,000 · after Year 2 = £180,000 → still £60,000 short.
Year 3 brings in £120,000, so the remaining £60,000 arrives after 60,000 ÷ 120,000 = 0.5 of Year 3 (6 months).
Payback = 2.5 years.
Calculate
Your turn — payback
2Initial cost £240,000. Net cash flows: Y1 £80,000, Y2 £100,000, Y3 £120,000. Calculate the payback period, in years (to 1 decimal place).
years
Hint: After 2 years £180,000 is recovered; £60,000 remains. 60,000 ÷ 120,000 = 0.5 of year 3.
3.3.2 · Investment appraisal
Average (Accounting) Rate of Return
ARR (%) = (average annual profit ÷ initial investment) × 100average annual profit = (total net cash inflows − initial investment) ÷ number of years
ARR — worked
Total inflows = £400,000 · initial investment = £240,000
Total profit over the project = 400,000 − 240,000 = £160,000
Average annual profit = 160,000 ÷ 4 = £40,000
ARR = (40,000 ÷ 240,000) × 100 = 16.67%
Interpretation: compare the ARR with the firm's criterion rate (its target return) and with the interest rate — if the firm can earn 5% risk-free, a 16.67% return for taking business risk looks attractive. ARR's weakness is that it ignores the timing of cash flows: £100,000 in Year 4 is treated as being worth exactly as much as £100,000 in Year 1.
Calculate
Your turn — ARR
3Total net cash inflows over 4 years are £400,000; the initial investment is £240,000. Calculate the average rate of return, as a percentage to 2 decimal places.
Money in the future is worth less than money today (it could have been earning interest, and it is less certain). Discounting converts each future cash flow into its present value.
present value = net cash flow × discount factor NPV = total present values − initial investmentDecision rule: accept the project if NPV is positive. Between two projects, choose the higher NPV.
NPV — worked at a 10% discount rate
Year 1: 80,000 × 0.91 = £72,800
Year 2: 100,000 × 0.83 = £83,000
Year 3: 120,000 × 0.75 = £90,000
Year 4: 100,000 × 0.68 = £68,000
Total present value = 72,800 + 83,000 + 90,000 + 68,000 = £313,800
NPV = 313,800 − 240,000 = +£73,800 → accept.
Watch the discount rate: a higher rate (because interest rates rose, or the project is riskier) shrinks the present value of distant cash flows and can turn a positive NPV negative. The choice of rate is a judgement — and it drives the answer.
Calculate
Your turn — NPV
4Using discount factors of 0.91, 0.83, 0.75 and 0.68 for years 1–4 and cash flows of £80,000, £100,000, £120,000 and £100,000, with an initial cost of £240,000, calculate the NPV in £.
?A firm with a serious cash-flow problem must choose between two projects. Which appraisal method should carry most weight, and why?
Sort it
Which appraisal technique?
Tap a statement, then tap the investment appraisal technique it describes.
⏱️ Payback
📈 ARR
💸 NPV
3.3.3 · Decision trees
Decision trees and expected values
expected value = Σ (probability × outcome) net gain = expected value − cost of the optionSquares are decision nodes; circles are chance nodes. Probabilities at each chance node must sum to 1.
Work from right to left: calculate the expected value at each chance node, then subtract the cost of each option and compare.
Worked — expected values
Extend existing: EV = (0.7 × 120,000) + (0.3 × 50,000) = 84,000 + 15,000 = £99,000 → net gain = 99,000 − 20,000 = £79,000
Launch new: EV = (0.6 × 200,000) + (0.4 × 40,000) = 120,000 + 16,000 = £136,000 → net gain = 136,000 − 50,000 = £86,000
On expected value, launch new wins by £7,000.
Calculate
Your turn — decision tree
5Launching the new product costs £50,000. Success (probability 0.6) yields £200,000; failure (probability 0.4) yields £40,000. Calculate the net gain of this option, in £.
£
Hint: EV = (0.6 × 200,000) + (0.4 × 40,000) = 136,000. Net gain = 136,000 − 50,000.
Quick check
Evaluating the decision tree
?The new launch has the higher net gain (£86,000 vs £79,000). Why might a cautious board still choose to extend the existing product?
3.3.4 · Critical path analysis
Networks, EST, LFT and total float
Critical path analysis identifies the sequence of activities that determines the minimum project duration. Its purpose is to schedule resources, identify which activities can be delayed and which cannot, and enable just-in-time delivery of materials.
EST (earliest start time) — work left to right, taking the highest preceding finish LFT (latest finish time) — work right to left, taking the lowest value total float = LFT − duration − ESTActivities on the critical path have a total float of zero — any delay to them delays the whole project.
Worked example
Activities: A (4 days, no predecessor) · B (6 days, no predecessor) · C (5 days, after A) · D (2 days, after B) · E (2 days, after C and D)
Path A → C → E = 4 + 5 + 2 = 11 days · Path B → D → E = 6 + 2 + 2 = 10 days
The project duration is the longest path: 11 days. The critical path is A, C, E.
Float on B: E starts at day 9, so D must finish by day 9; D takes 2 days, so D must start by day 7; therefore B must finish by day 7. Float on B = LFT (7) − duration (6) − EST (0) = 1 day.
Calculate
Your turn — project duration
6Using the network above (A 4 days; B 6 days; C 5 days after A; D 2 days after B; E 2 days after C and D), calculate the minimum project duration, in days.
days
Hint: Compare the paths: A+C+E = 11 and B+D+E = 10. The project takes as long as the longest path.
Quick check
Using the float
?Activity B has a total float of 1 day. What does this mean in practice?
Match it
Match the CPA term
Tap a definition on the left, then the critical path analysis term it defines.
Definition
CPA term
Quick check
Limitations of CPA
?Which is the strongest limitation of critical path analysis?
Quick check
Limitations of quantitative forecasting
?A firm extrapolates five years of steadily rising sales and forecasts continued growth. A new low-cost competitor then enters the market. What does this illustrate?
Recap
The big ideas to know
Moving average: (sum of three periods) ÷ 3, plotted against the middle period; extrapolation assumes the trend continues
Payback: time to recover the outlay; part-years = (amount outstanding ÷ that year's cash flow)
ARR: (average annual profit ÷ initial investment) × 100 — ignores the timing of cash flows