Short-Term Decisions, Investment Appraisal and Cash Planning Toolkit

Learning objectives

By the end of this chapter, you will be able to:

• Identify the costs and revenues that matter for short-term choices and exclude amounts that will not change.
• Apply contribution analysis to prioritise products when a resource is limited.
• Assess capital projects using payback and net present value (NPV), and interpret the results.
• Prepare a cash budget that reflects the timing of receipts and payments, highlighting funding needs or surpluses.
• Recognise and correct common analytical errors in short-term decisions, investment appraisal, and cash planning.

Overview & key concepts

Short-term decisions, investment appraisal, and cash planning are practical toolkits that support management choices:

• Short-term decisionsfocus on what changes if one option is chosen over another.
• Investment appraisalevaluates whether longer-term cash movements justify an initial outlay.
• Cash planningchecks whether the organisation can meet obligations as they fall due, even if a decision appears profitable.

A recurring theme is the difference between profit and cash:

• A decision may increase profit (or contribution) but still create a cash shortage if receipts lag behind payments.
• Investment appraisal is cash-based (discounted cash flows), even though depreciation will later be recognised in the financial statements.

Relevant costs and relevant revenues

A cost or revenue is relevant only if it meets both conditions:

1. It relates to the future, and
2. It differs between the alternatives being compared.

Typical relevant items include:

• Incremental variable costs(materials, direct labour, variable overheads) that arise only if the option is taken.
• Incremental fixed costsincurred specifically because of the decision (for example, a one-off set-up cost).
• Incremental revenues(such as the selling price of a special order).

Items that are usually not relevant:

• Past expenditure that cannot be changed by the decision.
• Fixed costs that will be paid regardless of the option selected.
• Accounting allocations (such as absorbed overhead) unless the underlying cash flow genuinely changes.

Exam approach: start by listing every item mentioned in the scenario, then cross out sunk costs, committed costs, and allocations unless the decision changes the cash flow.

Relevant costing edge cases

Short-term decisions often include “twists” that test whether you can identify the real economic cost of using a resource.

Materials

• If materials must be purchased for the decision: use thecurrent purchase price(what it will cost to obtain them now).
• If materials are already in inventory: the relevant cost depends on the best alternative use:
  • If they have aresale value, using them means giving up that cash receipt (use the resale value, net of selling costs).
  • If they are needed elsewhere and would then have to be replaced, use thereplacement cost.
  • If they haveno alternative use, the relevant cost may be nil (unless there is a disposal cost).

Labour

• If labour is paid anyway and there is genuine idle time: the relevant cost may be only the incremental element (for example, overtime premium or additional temporary staff).
• If labour is fully utilised (or scarce): the relevant cost includes theopportunity costof what labour would otherwise produce (lost contribution).

Fixed costs

• Unavoidable/committed fixed costsare normally irrelevant for a one-off short-term decision.
• Avoidable fixed costs(costs that can be prevented by choosing an option) are relevant.
• Additional fixed costscaused by the decision (for example, hiring a supervisor for a one-off contract) are relevant.

Notional costs and absorbed overhead

Do not include “fair share” overhead charges or bookkeeping allocations unless the decision causes a real change in cash outflow.

Opportunity cost

An opportunity cost is the value sacrificed by using a limited resource in one way rather than in its best available alternative use.

This becomes critical when:

• capacity is fully used (or effectively constrained), or
• the decision forces you to give up sales or production elsewhere.

Limiting factors and contribution optimisation

A limiting factor (constraint) is a scarce resource that caps output (for example, machine hours, skilled labour hours, or a key raw material).

Standard approach:

• Contribution per unit= Selling price − Variable cost
• Contribution per constrained unit= Contribution per unit ÷ units of limiting factor per unit
• Rank products by contribution per constrained unit (highest first).
• Allocate the scarce resource in that order, subject to demand limits.

Practical signpost (multiple constraints): identify the binding constraint first (the one that is fully used after meeting any stated requirements). If more than one constraint binds, the ranking approach may need adaptation.

Special orders and spare capacity

A special order should be assessed using incremental cash flows, but the conclusion depends on capacity:

• If there is spare capacity, accept the order if it creates positive incremental contribution (unless qualitative issues override).
• If capacity is constrained, include theopportunity costof displaced contribution.

Displacement rule under a single constraint: keep the activity with the higher contribution per limiting factor, and reduce the lower-ranked activity first, subject to demand limits and any minimum commitments.

Investment appraisal techniques

Payback period

The payback period measures how long it takes for a project’s cash inflows to build up to the point that they cover the initial cash spent.

If payback occurs part-way through a year:

Payback (years) = full years before recovery + (unrecovered amount at start of recovery year ÷ cash inflow in recovery year)

Payback is often expressed in years and months in workings. A decimal expression is acceptable if used consistently.

Limitations:

• Ignores the time value of money.
• Ignores cash flows after payback.

Net present value (NPV)

NPV asks a practical question: if every expected project cash flow is translated into today’s money (using a rate that reflects the return required for the risk), does the project leave the business better off after paying for it?

Method:

• Convert each future cash flow into a present value using a discount factor based on timing.
• The initial outlay is usually “today’s money”, so it is not discounted.
• Add present values of inflows and outflows to find NPV.

Interpretation:

• Apositive NPVmeans the project’s expected cash returns, valued in today’s terms, more than cover the upfront cost at the required return.
• Anegative NPVmeans the project does not generate enough value (in present value terms) at that required return.
• If projects are mutually exclusive and risk is similar, the higher NPV indicates the greater increase in value based on the estimates used.

Rounding policy for clear workings: state the rounding used for discount factors (for example, 4 decimal places) and round present values consistently (for example, to the nearest £). For marginal projects, small rounding differences can change the final few pounds.

Investment cash flow checklist (exam-style coverage)

In more detailed appraisal questions, cash flows commonly include:

• Initial outlay, including delivery/installation and any directly attributable start-up costs.
• Working capital investment (cash outflow at start and recovery at the end).
• Incremental operating cash flows (only the movements that change because of the project).
• Residual value and disposal costs at the end of the project.
• Tax impacts and timing (where applicable), including any relevant tax relief mechanisms.
• Inflation assumptions and whether the discount rate is consistent with the cash flows (nominal with nominal, real with real).
• Timing conventions (end-of-year, mid-year, or specific dates).
• Exclusion of non-incremental allocations (for example, head office cost apportionments) unless the decision changes the cash flow.

Mutually exclusive projects with different lives (signpost)

Where alternatives have different useful lives and can be repeated, a value-per-year approach (such as an equivalent annual measure) may be appropriate. Where repeatability is not realistic, comparisons should reflect the actual decision context.

Cash planning and cash budgets

A cash budget is a time-based map of money in and money out. It follows cash timing, not accounting recognition:

• Sales appear when customers are expected to pay.
• Costs appear when the business expects to settle them.

A practical build method:

1. Start with cash available at the beginning of the period.
2. Add cash expected to be collected during the period (including receipts from earlier credit sales).
3. Subtract cash expected to be paid (suppliers, wages, overheads, tax, capital spending, finance costs).
4. The result is the closing cash position, indicating whether funding is needed or whether surplus cash can be managed.

Exam warning: build cash receipts and payments from the stated credit terms and payment lags—lifting figures from an income statement-style schedule without adjusting timing is a common cause of errors.

Worked example

Narrative scenario

XYZ Ltd manufactures two products—Alpha and Beta—using a single production line. The line is available for 1,000 machine hours per quarter.

Product data:

• Alpha: selling price£50, variable cost£30, machine time2 hours per unit, maximum demand300 units
• Beta: selling price£70, variable cost£45, machine time3 hours per unit, maximum demand200 units

A customer has offered a special order for 100 units of Alpha at £45 per unit. The order is additional to regular demand, but it uses production capacity.

Separately, XYZ Ltd is considering new machinery costing £49,000, expected to generate £15,000 net cash inflow each year for four years. The discount rate is 8.6%.

Required

1. Calculate contribution per unit and contribution per machine hour for Alpha and Beta.
2. Determine the optimal quarterly production plan given the machine-hour limit.
3. Evaluate the incremental financial impact of accepting the special order.
4. Calculate the payback period and NPV for the machinery investment.
5. Prepare a cash budget for thequarter of purchase, incorporating the production plan and the investment outlay.

Solution

1) Contribution per unit and per machine hour

Alpha (regular sales)

• Contribution per unit = £50 − £30 =£20
• Contribution per machine hour = £20 ÷ 2 =£10.00 per hour

Beta

• Contribution per unit = £70 − £45 =£25
• Contribution per machine hour = £25 ÷ 3 =£8.33 per hour

Ranking by contribution per machine hour:

1. Alpha (£10.00)
2. Beta (£8.33)

2) Optimal production plan (continuous units and whole units)

Optimal plan (continuous units for ranking logic)

• Alpha to maximum demand: 300 units × 2 hours =600 hours
• Remaining hours: 1,000 − 600 =400 hours
• Beta: 400 ÷ 3 =133.33 units

Optimal plan (whole units for a realistic production plan)

• Beta units =133 units(uses 399 hours), leaving1 hour idle

3) Special order (100 units of Alpha at £45)

Step 1: Incremental contribution from the order

• Special order contribution per unit = £45 − £30 =£15
• Total special order contribution = 100 × £15 =£1,500

Step 2: Capacity impact (effectively constrained capacity)
Special order machine hours required: 100 × 2 = 200 hours.

The production line is effectively constrained. Even allowing for the 1 hour idle created by whole-unit rounding, the order still requires a substantial additional 199 hours.

Which product is displaced (and why)?
Under a single machine-hour constraint, capacity should remain allocated to the activity earning the higher contribution per machine hour. Alpha already has the higher contribution per hour and is produced to its demand limit. Therefore, the capacity needed for the special order would be released by reducing Beta first (subject to any minimum commitments, which are not stated here).

Opportunity cost of displaced Beta contribution (approx.)

• Beta contribution per hour ≈ £8.33
• Displaced hours = 200
• Opportunity cost ≈ 200 × £8.33 =£1,666(rounded)

Net impact (approx.)

• Net impact ≈ £1,500 − £1,666 =£(166) adverse

Conclusion:
With capacity constrained, the order is not financially attractive at £45 per unit because it earns £7.50 contribution per machine hour (£15 ÷ 2), below Beta’s £8.33 per machine hour.

Production plan if the order is accepted (whole units basis)

• Alpha regular: 300 units → 600 hours
• Alpha special order: 100 units → 200 hours
• Remaining for Beta: 1,000 − 800 = 200 hours →66 units(198 hours)

Total contribution if accepted (whole units basis):

• Alpha regular: 300 × £20 = £6,000
• Alpha special: 100 × £15 = £1,500
• Beta: 66 × £25 = £1,650
• Total =£9,150

Without the order (whole units basis):

• Alpha: £6,000
• Beta: 133 × £25 = £3,325
• Total =£9,325

Difference = £9,150 − £9,325 = £(175) adverse (indivisibility/rounding explains the small difference from the hourly estimate).

4) Investment appraisal (machinery)

Terminology convention used here: “net cash inflow” refers to the annual net cash benefit generated by the investment.

Rounding policy used here: discount factors rounded to 4 decimal places; present values rounded to the nearest £.

Payback period

Initial investment = £49,000
Annual net cash inflow = £15,000

Cumulative inflows:

• End of Year 1: £15,000
• End of Year 2: £30,000
• End of Year 3: £45,000
• End of Year 4: £60,000

Unrecovered after Year 3 = £49,000 − £45,000 = £4,000
Fraction of Year 4 = £4,000 ÷ £15,000 = 0.27 years

Payback period ≈ 3.27 years

NPV at 8.6%

Discount factors (8.6%):

• Year 1: 1 / 1.086 =0.9208
• Year 2: 1 / 1.086² =0.8479
• Year 3: 1 / 1.086³ =0.7807
• Year 4: 1 / 1.086⁴ =0.7189

Present value of net cash inflows:

• Year 1: £15,000 × 0.9208 =£13,812
• Year 2: £15,000 × 0.8479 =£12,718
• Year 3: £15,000 × 0.7807 =£11,711
• Year 4: £15,000 × 0.7189 =£10,784

Total PV of net cash inflows = £49,025
NPV = £49,025 − £49,000 = £25 (positive)

Because the result is marginal, small rounding differences can change the final few pounds.

5) Cash budget (quarter of purchase)

The cash budget below covers the quarter in which production occurs and the machinery is purchased. The investment appraisal benefits are annual; they would only appear in the cash budget if the benefits are expected to be received within the budget period.

If annual benefits were assumed to arise evenly through the year, a simple phasing would be £15,000 ÷ 4 = £3,750 per quarter. No timing is stated here, so the budget below includes only the purchase outflow.

Assumption for this illustration: all sales receipts and variable cost payments occur within the quarter.

Cash budget layout

Opening cash balance: £5,000

Cash receipts

• Alpha: 300 × £50 = £15,000
• Beta: 133 × £70 = £9,310
• Total receipts = £24,310

Cash payments

• Alpha variable cost: 300 × £30 = £9,000
• Beta variable cost: 133 × £45 = £5,985
• Machinery purchase: £49,000
• Total payments = £63,985

Net cash movement = £24,310 − £63,985 = £(39,675)
Closing cash balance = £5,000 − £39,675 = £(34,675)

Common pitfalls and misunderstandings

• Ranking products by selling price or contribution per unit instead of contribution per constrained unit.
• Accepting a special order because it shows positive contribution without checking whether it displaces higher-earning output.
• Including absorbed overheads or “fair share” allocations when the cash flow does not change.
• Ignoring opportunity costs when the resource is constrained.
• Mixing profit items into cash budgets (for example, treating depreciation as a cash payment).
• Discounting errors in NPV (wrong timing, wrong discount factors, discounting the initial outflow).
• Rounding too early, which can distort rankings or flip borderline NPVs.
• Treating payback as a value measure rather than a recovery-speed measure.
• Producing a cash budget that ignores credit terms and payment lags.
• Treating non-incremental overhead allocations as project cash flows in investment appraisal.

Summary and further reading

This chapter developed a toolkit for:

• Relevant costing: isolating future cash flows that differ between alternatives.
• Constraint optimisation: maximising total contribution by prioritising contribution per limiting factor.
• Investment appraisal: using payback for cash recovery insight and NPV for value evaluation.
• Cash budgeting: mapping cash timing to anticipate funding needs and manage liquidity.

Further development comes from practising mixed scenarios where capacity, working capital, tax, inflation, and timing assumptions interact and can change the decision.

FAQ

What separates relevant costs from costs that should be ignored?

Relevant costs are future cash flows that differ between the options. Amounts that have already happened or will be the same whichever option is chosen should be excluded.

How do I rank products when capacity is constrained?

Compute contribution per unit, then divide by the scarce resource usage per unit (such as machine hours). Rank from highest to lowest and allocate the scarce resource in that order, subject to demand limits.

Why can a profitable special order be rejected?

If capacity is constrained, the order may displace regular output. The lost contribution from that displaced output is an opportunity cost and must be compared with the order’s incremental contribution.

What does payback tell me that NPV does not?

Payback highlights how quickly cash is recovered, which can help manage liquidity risk. It does not measure total value because it ignores discounting and later cash flows.

Why is NPV usually preferred for investment decisions?

NPV converts expected cash movements into present value terms and compares them with the upfront cost. It captures timing and required return, making it a direct value measure.

How does a cash budget differ from a profit forecast?

A cash budget records expected cash receipts and payments by period. A profit forecast is based on when income and expenses are recognised, which may not match cash movement timing.

Summary (Recap)

This chapter covered how to:

• identify decision-relevant cash flows and exclude costs that do not change,
• maximise returns under constraints using contribution per limiting factor,
• assess investments using payback for recovery speed and NPV for value,
• prepare cash budgets that reflect cash timing and highlight funding requirements.

Glossary

Relevant cost
A future cash outflow (or reduced cash inflow) that differs between decision options.

Sunk cost
A past expenditure that cannot be altered by a current decision.

Opportunity cost
The value forgone by choosing one option instead of the best alternative use of the resource.

Limiting factor (constraint)
A scarce resource that caps output or sales, such as machine hours or skilled labour.

Contribution
Sales revenue minus variable costs; the amount available to cover fixed costs and then generate profit.

Payback period
How long it takes for the project’s cash inflows to accumulate to the point that they cover the initial cash spent.

Net present value (NPV)
The net amount of value today after converting all expected project cash flows into present-day money at the required return, and then deducting the upfront cost.

Cash budget
A period-by-period forecast of cash receipts, cash payments, and resulting cash balances.

Discount rate
The rate used to translate future cash flows into present values, reflecting required return and risk.

Discount factor
The multiplier applied to a future cash flow to express it in present value terms, based on discount rate and timing.