| Time | Cash flow | Discount factor | Present value | Calculation |
|---|
| Year | Opening amount | Return | Closing amount |
|---|
These exercises combine the financial statements, ratio analysis, the time value of money, NPV, and capital budgeting. They illustrate the type of reasoning that may be required in the final exam. The final exam may combine the material in different ways.
Northline Retail is fictional. All figures are classroom assumptions.
Show the calculation and explain what the result means for the decision. Solutions are not published here.
| Exercise | Main material tested |
|---|---|
| 1 | The income statement, balance sheet, and cash flow statement |
| 2 | Profitability, liquidity, leverage, efficiency, and operating cash flow |
| 3 | Timelines, present value, and NPV |
| 4 | Incremental cash flows and project appraisal |
| 5 | NPV, IRR, payback, and scenario changes |
| 6 | Integrated diagnosis and recommendation |
Exercises 1 and 2 share the same financial statements. Exercises 3 to 5 can be used independently. Exercise 6 uses evidence from the preceding exercises.
Northline Retail reports the following summary for FY2026.
| Item | €m |
|---|---|
| Sales | 800 |
| Cost of goods sold | (480) |
| Gross profit | 320 |
| Operating expenses | (240) |
| Operating profit | 80 |
| Interest expense | (15) |
| Tax | (13) |
| Net profit | 52 |
| Assets | €m | Liabilities and equity | €m |
|---|---|---|---|
| Cash | 30 | Payables | 140 |
| Receivables | 90 | Short-term debt | 60 |
| Inventory | 160 | Long-term debt | 260 |
| Non-current assets | 520 | Equity | 340 |
| Total assets | 800 | Total liabilities and equity | 800 |
| Item | €m |
|---|---|
| Cash flow from operating activities | +40 |
| Cash flow from investing activities | (110) |
| Cash flow from financing activities | +50 |
| Net change in cash | (20) |
| Opening cash balance | 50 |
| Closing cash balance | 30 |
A manager says: “Northline earned €52 million, so its cash must have increased by €52 million.”
Use Northline's FY2026 statements from Exercise 1 together with the following opening balances:
Compare your results with the following classroom reference values for similar retailers.
| Measure | Reference value |
|---|---|
| Operating margin | 9.0% |
| Current ratio | 1.60 |
| Quick ratio | 0.90 |
| Liabilities to assets | 50.0% |
| Inventory days | 85 days |
| Asset turnover | 1.10 |
| Operating cash flow as a share of sales | 8.0% |
Northline can invest €200,000 in a customer-ordering system. The expected cash flows are shown below.
| Time | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Cash flow | -€200,000 | +€70,000 | +€90,000 | +€110,000 |
Northline uses a 7% discount rate.
Northline is considering an automated returns system. Finance has collected the following information:
Northline uses a 9% discount rate.
Northline can finance either of two systems for the same distribution centre. The systems perform the same function, so it can install only one. Each system lasts four years and has no terminal cash flow.
| Time | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Project Alpha | -€1,000,000 | +€350,000 | +€350,000 | +€350,000 | +€350,000 |
| Project Beta | -€300,000 | +€110,000 | +€110,000 | +€110,000 | +€110,000 |
Northline uses a 10% discount rate.
An analyst prepares the following note using the information from Exercises 1 to 5:
€40m - €110m + €50m = -€20m
Opening cash of €50 million therefore fell to €30 million.
The manager has confused an accounting result with a movement in cash. Net profit was positive, operating cash flow was lower than profit, and investment spending caused total cash to fall despite the financing inflow.
Gross margin = €320m / €800m = 40.0%
Operating margin = €80m / €800m = 10.0%
Net margin = €52m / €800m = 6.5%
Northline's operating margin is one percentage point above the 9.0% reference value.
Current assets equal cash, receivables, and inventory:
Current assets = €30m + €90m + €160m = €280m
Current liabilities equal payables and short-term debt:
Current liabilities = €140m + €60m = €200m
Current ratio = €280m / €200m = 1.40
Quick ratio = (€280m - €160m) / €200m = 0.60
The current ratio is below the 1.60 reference value. The quick ratio is also below its 0.90 reference because a large share of current assets consists of inventory.
Total liabilities = €140m + €60m + €260m = €460m
Liabilities to assets = €460m / €800m = 57.5%
Equity to assets = €340m / €800m = 42.5%
Northline uses more liability financing than the 50.0% reference value.
Average inventory = (€140m + €160m) / 2 = €150m
Inventory turnover = €480m / €150m = 3.20 times
Inventory days = 365 / 3.20 = 114.1 days
Inventory remains in the business about 29 days longer than the 85-day reference value.
Average total assets = (€740m + €800m) / 2 = €770m
Asset turnover = €800m / €770m = 1.04
Operating cash flow as a share of sales = €40m / €800m = 5.0%
Both measures are below their reference values.
Conditional approval can be defended. Northline's 10.0% operating margin is above the reference value and operating cash flow remains positive. The strongest concern is liquidity: the quick ratio is 0.60, inventory takes approximately 114 days to sell, and operating cash flow represents only 5.0% of sales. Leverage is also higher than the reference value. Before lending, the bank should examine how long different inventory items have remained unsold, the collection of receivables, and a cash-flow forecast showing how Northline would service the new debt. Approval or rejection could also be defended if the decision uses the evidence consistently and states the condition that changes the conclusion.
| Time | Cash flow | Present value at 7% |
|---|---|---|
| 0 | -€200,000 | -€200,000.00 |
| 1 | +€70,000 | +€65,420.56 |
| 2 | +€90,000 | +€78,609.49 |
| 3 | +€110,000 | +€89,792.77 |
Using the unrounded present values:
NPV = +€33,822.81
The project has a positive NPV. On the stated cash-flow estimates and 7% required return, the NPV rule supports acceptance.
The expected receipts recover the €200,000 investment, provide the required 7% annual return, and create approximately €33,823 of additional value measured at time 0. The NPV is a valuation result, so it does not create a separate €33,823 receipt.
The revised timeline is:
| Time | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Cash flow | -€200,000 | +€70,000 | €0 | +€200,000 |
Revised NPV = +€28,680.14
Moving €90,000 from time 2 to time 3 reduces NPV by €5,142.68. The amount received is unchanged, but waiting an additional year reduces its value at time 0. The revised NPV remains positive.
| Item | Treatment | Cash flow | Timing | Reason |
|---|---|---|---|---|
| Equipment | Include | -€320,000 | 0 | Northline pays it only if the project proceeds |
| Installation | Include | -€30,000 | 0 | The project requires the installation |
| Staff training | Include | -€20,000 | 0 | The project causes the training cost |
| Feasibility study cost | Exclude | €0 | None | The €45,000 has already been paid and cannot be changed by the decision |
| Demand forecasts from the study | Use in the forecast | €0 | None | The information may change expected future cash flows |
| Labour savings | Include | +€150,000 | 1 to 4 | The project reduces future cash payments |
| Software support | Include | -€25,000 | 1 to 4 | The payment arises because the project proceeds |
| Rental income given up | Include | -€18,000 | 1 to 4 | Accepting the project removes a cash inflow Northline could otherwise keep |
| Allocated overhead | Exclude | €0 | None | Total company cash overhead remains unchanged |
| Depreciation | Exclude in this case | €0 | None | Depreciation creates no direct cash payment and the case excludes tax |
| Equipment sale | Include | +€40,000 | 4 | Selling the equipment creates a terminal cash receipt |
| Removal cost | Include | -€10,000 | 4 | The project creates a terminal cash payment |
Time 0 = -€320,000 - €30,000 - €20,000 = -€370,000
Annual operating cash flow = €150,000 - €25,000 - €18,000 = +€107,000
Year 4 total = €107,000 + €40,000 - €10,000 = +€137,000
| Time | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Cash flow | -€370,000 | +€107,000 | +€107,000 | +€107,000 | +€137,000 |
At a 9% discount rate:
NPV = -€2,097.22
IRR = approximately 8.75%
NPV is negative and IRR is below the 9% required return. Both rules support rejection on the stated assumptions.
By the end of year 3, Northline has recovered €321,000 and still needs €49,000. Assuming the €107,000 operating cash flow arrives evenly during year 4:
Payback = 3 years + €49,000 / €107,000 = 3.46 years
Payback shows that the initial outlay is recovered during year 4. Northline has provided no maximum acceptable payback, so the measure does not produce an independent accept-or-reject conclusion. The project is close to financial break-even, which makes the cash-flow assumptions worth investigating.
| Measure | Project Alpha | Project Beta |
|---|---|---|
| NPV at 10% | +€109,452.91 | +€48,685.20 |
| IRR | 14.96% | 17.30% |
| Payback | 2.86 years | 2.73 years |
Both projects have positive NPVs and IRRs above the 10% required return. If the projects were independent and Northline could undertake both, both would satisfy the NPV and IRR rules.
The projects are mutually exclusive in this exercise. NPV ranks Alpha first because it creates approximately €60,768 more value. IRR and payback rank Beta first because it produces a higher percentage return and recovers its smaller initial outlay sooner.
Under the base-case assumptions and without a funding constraint, Northline should select Project Alpha because it has the higher NPV.
The revised Alpha cash flows are:
| Time | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Cash flow | -€1,000,000 | +€175,000 | +€350,000 | +€350,000 | +€350,000 |
| Measure | Revised Project Alpha | Project Beta |
|---|---|---|
| NPV at 10% | -€49,638.00 | +€48,685.20 |
| IRR | 7.89% | 17.30% |
| Payback | 3.36 years | 2.73 years |
The new information reverses the NPV ranking. If the implementation team's forecast is more credible than the base case, Northline should choose Project Beta. Before approval, management should request evidence supporting Alpha's installation schedule and the €350,000 annual cash-flow estimate, particularly the amount achievable in year 1. Since Beta is now the recommended project, the same scrutiny applies to its €300,000 initial cost and €110,000 annual cash flows.
The analyst's note contains the following problems:
Northline should select Project Beta unless management can provide convincing evidence that Project Alpha will achieve the base-case rollout. Alpha creates more value under the original forecast, with an NPV of €109,453 compared with €48,685 for Beta. The implementation team's forecast changes Alpha's year 1 cash flow and reduces its NPV to -€49,638. Beta then has the higher NPV, IRR, and speed of recovery. The decision therefore depends on the timing and amount of Alpha's first-year cash benefit. Before committing funds, management should provide a tested installation schedule and evidence supporting the operational savings expected during the rollout. Northline should also examine its liquidity because the quick ratio, inventory days, and operating cash flow are weaker than the reference values.