Investment feasibility and downside testing IDER in-house training materials Hypothetical cases and figures for teaching the methods. Learning objectives Reconstruct incremental project cash from operating assumptions. Calculate downside value, liquidity needs and switching values. Translate uncertainty into evidence requests and conditional investment decisions. Basic understanding of revenue, costs, profit and spreadsheet arithmetic. Appraise the decision, not the spreadsheet Incremental cash flows Five-year investment case Hypothetical figures: GHS millions Imagine an investment committee considering a processing line. Your task is to identify which commercial conditions justify committing scarce capital, and which conditions would reverse that recommendation. We will construct an incremental cash model, challenge its downside and specify evidence that management must obtain before approval. Every amount in this case is hypothetical and expressed in millions of Ghana cedis unless stated otherwise. Keep a calculator and a blank assumptions register beside you. For each number, ask what operational event creates the cash movement, when that movement occurs and who can verify it. That discipline turns a valuation exercise into an investment decision that another practitioner can inspect and reproduce. Compare the project with a credible alternative Continue without the line Identify incremental changes Separate operating and financing choices Begin with the counterfactual: what happens if the organisation does not buy the line? Existing overhead that continues under either option does not become an incremental cost merely because accounting allocates it to the project. Conversely, using a building already owned can have an opportunity cost if it displaces a credible rental income. Ignore expenditure that cannot now be recovered, but include avoidable future implementation costs. Model project cash before financing when applying a project discount rate; adding loan proceeds and subtracting debt service would mix valuation perspectives. Document these boundaries before collecting data. Otherwise two competent analysts can calculate different values simply because they are valuing different decisions. Build assumptions from operating evidence Volume × realised price Variable and fixed cash costs Timing, source and accountable owner Our base case sells one hundred thousand units annually at one hundred cedis each. Variable cash cost is sixty cedis per unit and annual fixed cash cost is one point six million. Do not treat those entries as equally certain. Reconcile volume with production capacity, customer commitments and achievable utilisation. Derive realised price after discounts, returns and channel deductions. Separate genuinely variable inputs from costs that change only when another shift or machine is required. Give every material assumption a source, observation date, plausible range and owner. For new markets, a signed expression of interest is weaker evidence than repeat paid orders. The model should make that distinction visible to the decision maker. Convert accounting earnings into project cash Annual revenue 10.00; variable costs 6.00 Fixed costs 1.60; depreciation 0.80 Tax 25%; maintenance 0.20; extra NWC 0.10 (10 − 6 − 1.6 − 0.8) × 0.75 + 0.8 − 0.2 − 0.1 = 1.70 Revenue of ten million less variable costs of six million, fixed cash costs of one point six million and depreciation of eight hundred thousand leaves operating profit of one point six million. Apply our illustrative twenty five percent tax rate to obtain one point two million after tax. Add depreciation back because it reduced profit without consuming current cash. Then deduct two hundred thousand of maintenance investment and one hundred thousand of additional working capital. The result is one point seven million of annual project cash. Notice that adding depreciation back does not make equipment free: its initial purchase appears separately. Actual tax allowances, payment timing and loss treatment must replace these simplified assumptions in a live appraisal. Investment also finances the cash cycle Initial equipment 4.00 Initial working capital 0.60 Annual extra working capital 0.10 The equipment requires four million today, but the project also needs six hundred thousand tied up in receivables and inventories, net of supplier credit. Initial cash outflow is therefore four point six million. Each year's additional one hundred thousand of working capital is already deducted from operating cash in our bridge. After five years the accumulated working capital balance is one point one million. We assume only six hundred thousand is recoverable at closure; the remainder is not a hidden extra terminal receipt. Build receivable, inventory and payable schedules in a practical model so that sales growth drives funding needs. Treat recovery as an evidence question, including ageing, obsolete stock and collection costs. Keep timing and the discount basis consistent Five annual cash receipts of 1.70 Year-five recovery 0.60 Illustrative discount rate 15% NPV = −4.60 + Σ[1.70 / 1.15^t] + 0.60 / 1.15^5 = 1.397 Place the initial four point six million outflow at time zero. Discount each of five annual receipts of one point seven million by fifteen percent, then discount the separate six hundred thousand recovery from the end of year five. The resulting net present value is approximately one point four million. This measures value relative to our assumed required return, not the balance of money available to pay bills. The fifteen percent rate is an illustrative project assumption, not an official public appraisal rate or a recommended financing quote. Match nominal cash flows with a nominal rate and ensure currency and inflation assumptions agree. Monthly timing may materially change the result when construction or sales ramp up slowly. Pause: volume falls to 80,000 units Price and unit cost remain unchanged Fixed costs, tax basis and other flows unchanged Calculate annual cash and explain the mechanism Pause the recording and rebuild the cash bridge for eighty thousand units. Retain the same selling price, variable cost per unit, fixed cash costs, depreciation, maintenance investment and additional working capital. Use the illustrative tax rule from the base case. First calculate revenue and total variable costs; then work through operating profit, tax and cash. Do not reduce every spreadsheet row by twenty percent. Write one sentence explaining why a twenty percent volume decline can cause a larger percentage decline in project cash. Finally predict whether the original positive net present value will necessarily survive. Your answer should identify the mechanism before you inspect the numerical solution on the following slide. Fixed commitments amplify the volume shock Annual operating profit 0.80 Annual project cash 1.10 Revised NPV −0.614 (8 − 4.8 − 1.6 − 0.8) × 0.75 + 0.8 − 0.2 − 0.1 = 1.10 At eighty thousand units, revenue is eight million and variable cost is four point eight million. Deduct fixed cash costs of one point six million and depreciation of eight hundred thousand: operating profit becomes eight hundred thousand. After illustrative tax, profit is six hundred thousand. Add depreciation, deduct maintenance and extra working capital, and annual project cash is one point one million. Cash has fallen by approximately thirty five percent despite volume falling twenty percent because fixed commitments did not contract with sales. Discounting the lower cash receipts and the same terminal recovery gives a negative net present value of about six hundred and fourteen thousand. This is a commercially meaningful reversal, not merely a smaller spreadsheet output. Stress variables that move together Volume 80,000; price 90 Variable cost per unit 66 Current tax floor: zero 7.20 − 5.28 − 1.60 − 0.20 − 0.10 = 0.02 One variable at a time is useful for diagnosis, but a market shock rarely respects that convenience. Suppose demand weakens to eighty thousand units, competitive pressure reduces price to ninety cedis and imported inputs raise variable cost to sixty six cedis. Revenue becomes seven point two million and variable cost five point two eight million. After fixed costs and depreciation, operating profit is negative four hundred and eighty thousand. Under our simplified rule there is no current tax and no immediate cash refund for the loss. Adding depreciation and deducting maintenance and additional working capital leaves only twenty thousand of annual cash. Assign joint scenarios a defensible narrative; multiplying unrelated worst cases can also mislead. Positive value does not prevent a cash crisis Build a monthly cash calendar Locate the lowest cash balance Test committed funding and headroom Annual cash totals can conceal the moment a business runs out of money. A customer might pay in December while imported materials and wages must be paid in March. Build a monthly schedule from invoice dates, contractual credit periods, seasonal inventory and construction milestones. Carry the opening cash balance forward and identify the most negative cumulative position before funding. Then test available facilities against actual draw conditions, expiry dates and covenants. A promising project can still fail because funding arrives too late or cannot be drawn when needed. Keep this liquidity question separate from project value: a loan can bridge timing, but its existence does not repair an investment whose underlying commercial economics destroy value. Find the assumption that reverses the decision Required annual cash ≈ 1.283 Implied annual volume ≈ 86,109 Check the tax and capacity region Required volume ≈ (1.283 + 1.300) million / 30 ≈ 86,109 A switching value translates sensitivity into a useful research target. In this case, annual cash of about one point two eight three million makes net present value zero, holding terminal recovery and all other assumptions fixed. Within the positive taxable profit region, project cash equals thirty cedis times annual units, less one point three million. Dividing the required cash plus that fixed amount by thirty gives roughly eighty six thousand one hundred and nine units. This is the minimum volume implied by this simplified valuation, not a guaranteed safe production target. Check whether the formula crosses tax, capacity or cost step changes. Then ask commercial researchers whether evidence supports sustainable paid demand above that threshold. Use uncertainty to choose the next investigation Test the highest-impact weak assumption Price the cost of delay and learning Specify a staged commitment Do not commission more research merely because uncertainty exists. Compare the decision impact of each uncertain assumption with the cost and speed of obtaining better evidence. If attainable volume is close to the switching threshold, a paid pilot with representative customers may matter more than refining a minor maintenance estimate. Specify in advance what result would support launch, redesign or deferral. Where possible, negotiate staged equipment orders or a smaller initial capacity to reduce irreversible exposure. Such flexibility has practical value, but describe its conditions rather than attaching an unsupported premium. Assign each evidence gap an owner and deadline so that the investment committee can see what remains unknown at the point of commitment. Pause: halve the terminal recovery Recovery falls from 0.60 to 0.30 Base annual cash remains 1.70 Calculate the present-value reduction For the second exercise, return to the base operating case. Suppose an inventory review shows that only three hundred thousand, rather than six hundred thousand, can be recovered at the end of year five. Calculate the reduction in present value and the revised net present value. Resist subtracting three hundred thousand directly from today's value, because the lost receipt occurs five years from now. Then write a short explanation of why this correction matters even when the recommendation remains positive. Identify one item of documentary evidence you would request to support the revised recovery estimate. Pause now and complete both the calculation and the evidence request before advancing to the worked response. Discount the lost receipt at its actual date Lost future receipt 0.30 Present-value reduction 0.149 Revised NPV 1.248 0.30 / 1.15^5 = 0.149; revised NPV = 1.248 The lost receipt is three hundred thousand at the end of year five. Divide it by one point one five raised to the fifth power: the present-value reduction is approximately one hundred and forty nine thousand. Subtract this from the base net present value to obtain approximately one point two five million. The model still indicates positive value under the remaining assumptions, but the margin has narrowed. Useful evidence might include an aged receivables schedule with subsequent collections, an inventory disposal assessment or enforceable resale quotations. Distinguish a genuine cash recovery from an accounting book value. Explain the effect separately so that reviewers can see what changed and avoid counting the same impairment twice. Write a recommendation that can be challenged Base, downside and liquidity results Evidence gaps and conditional approval Named controls and review dates A professional investment note should let a reviewer reconstruct the recommendation without trusting the spreadsheet author. State the decision boundary, counterfactual, cash-flow perspective and key operating assumptions. Show the base case beside an economically coherent downside and a monthly funding requirement. Highlight switching values and the evidence supporting assumptions near those thresholds. Distinguish verified facts, management estimates and unresolved questions. Recommend approval, redesign or deferral with explicit conditions, responsible owners and dates. Where implementation proceeds, specify leading indicators such as paid orders, realised margin and collection delays that trigger a review. This creates a link between appraisal and management action instead of leaving the financial model as a document completed only for approval. Apply the method to your next investment review Rebuild one incremental cash bridge Run a coherent downside and a switching test Defend the next evidence-gathering action For independent practice, choose a real investment proposal and rebuild one year's cash bridge from its operating assumptions. Reconcile every adjustment to an identifiable cash event, then inspect the timing of working capital and terminal recovery. Create one coherent downside and calculate a switching value for the weakest material assumption. Explain which further evidence would most improve the decision and what it would cost to obtain. Complete the six questions and two applied tasks accompanying this clinic; use their explanations to diagnose errors in reasoning, not just arithmetic. A good practitioner can defend why an assumption belongs in the model, how it changes the recommendation and what evidence would justify revising it tomorrow. Check your understanding 1. Which cash flow belongs in an incremental project appraisal? A. An allocated overhead unchanged under both options B. An avoidable future implementation cost C. An unrecoverable past study cost D. Loan proceeds in an unlevered project cash flow 2. What is the base annual project cash flow in GHS millions? A. 1.20 B. 2.00 C. 1.70 D. 2.40 3. At 80,000 units with other assumptions unchanged, annual cash is: A. 1.36 million B. 1.10 million C. 0.80 million D. 1.70 million 4. Why can a positive project NPV coexist with a funding crisis? A. Discounting eliminates working capital B. Annual value does not establish monthly liquidity C. Positive NPV guarantees a credit facility D. Depreciation pays suppliers 5. Halving year-five recovery from 0.60 to 0.30 at 15% reduces current value by approximately: A. 0.300 million B. 0.600 million C. 0.149 million D. 0.075 million 6. What is the best use of a volume switching value near current demand estimates? A. Treat it as a guaranteed sales target B. Raise the discount rate until approval C. Investigate attainable paid demand and decision conditions D. Ignore fixed-cost and tax regions Applied task 1 Rebuild the base and 80,000-unit cash cases and recommend what evidence to obtain before commitment. Applied task 2 Design a monthly liquidity stress and a terminal-recovery verification procedure for this project. Answers and explanations 1. B. Include future cash changes caused by the decision. Unchanged allocations and sunk costs do not qualify; financing must match the valuation perspective. (Slide 2) 2. C. After-tax operating profit 1.20 + depreciation 0.80 − maintenance 0.20 − additional working capital 0.10 = 1.70. (Slide 4) 3. B. Revenue 8 − variable costs 4.8 − fixed costs 1.6 − depreciation 0.8 = profit 0.8; after tax and cash adjustments, cash is 1.1. (Slide 8) 4. B. A project may create value over its life while receipts arrive after unavoidable payments. A monthly funding schedule is required. (Slide 10) 5. C. The lost year-five receipt is discounted: 0.30 / 1.15^5 = 0.149153 million. (Slide 14) 6. C. The switching value identifies a consequential uncertainty. Validate sustainable paid demand and check that the formula remains in the relevant operating and tax region. (Slide 11) Applied task 1 Base cash is 1.70 million and NPV 1.397 million; lower-volume cash is 1.10 million and NPV −0.614 million. Verify sustainable paid demand around the approximate 86,109-unit switching value and inspect cost/tax thresholds before approval. Reconciles profit to cash without double-counting depreciation or capital expenditure. Discounts five annual flows and the separate year-five recovery consistently. Links a specific evidence request to a decision threshold and owner. Applied task 2 Schedule invoice collections, materials, payroll and investment by month, roll forward cash and test committed facility conditions. Reconcile terminal receivables and inventory to recoverable cash using subsequent receipts or supported disposal values; halving recovery reduces NPV by 0.149 million. Distinguishes valuation from timing and funding availability. Identifies evidence and responsible owners for recovery assumptions. States a management response to a projected cash deficit. References HM Treasury — The Green Book (2026) https://www.gov.uk/government/publications/the-green-book-appraisal-and-evaluation-in-central-government General appraisal principles: options, uncertainty and sensitivity. Original hypothetical commercial calculations; the 15% rate is not the Green Book social discount rate.