Strategy has 9 topics and Management has 3 topics, for a total of 12 topics.
Break-even point and expected value appear more often than anything else in Strategy, and critical path is the single most important Management topic.
📊 Strategy (9 topics)
#12 Break-even point (sales volume)
The point at which sales revenue and total cost are exactly equal, so profit becomes zero.
Break-even sales volume = Fixed costs ÷ Contribution margin (Unit price - Variable cost)- Fixed costs: Costs that arise even when sales are zero (e.g. rent, salaries of permanent staff, depreciation on equipment)
- Unit price: The selling price of one unit
- Variable costs: Costs that rise with the number of units sold (e.g. materials, the purchase cost of goods, outsourcing fees)
Solution steps
- Find the contribution margin
Work out how much is left in your hands when you sell one unit.
Example: at a unit price of ¥1,000 and a variable cost of ¥600, 1,000 - 600 = ¥400 - Divide fixed costs by the contribution margin
Work out how many times that per-unit margin has to repay the large fixed cost before it is paid off.
Example: fixed costs ¥200,000 ÷ ¥400 = 500 units
Common mistakes
- Dividing fixed costs directly by the selling price (unit price)
This ignores variable costs such as materials, so you end up believing you need fewer units than you really do.
Exam pointers
- On the IT Passport, questions that ask for a number of units are by far the most common.
- If the question says "profit becomes zero," that is your signal to find the break-even point.
How to remember
"Fixed cost is the mountain; the contribution margin is one step. How many steps to the summit?"
"Cross the point where it becomes zero, and you see the light."
#13 Expected value (basic)
The average of the possible future outcomes (amounts and so on), weighted by the probability that each one occurs.
Expected value = Outcome1 × Probability1 + Outcome2 × Probability2 + ...- Probability: The likelihood that an event occurs (0.0 to 1.0)
Solution steps
- Calculate "amount × probability"
Do the multiplication for each scenario.
Example: if there is a 10% chance of a ¥1,000,000 loss, 1,000,000 × 0.1 = ¥100,000 - Add up the results of every scenario
Sum every outcome that could occur.
Example: result of scenario A + result of scenario B ...
Common mistakes
- Forgetting to multiply by the probability
Comparing raw loss amounts leads you to over-invest in countermeasures against things that almost never happen.
Exam pointers
- When you are asked "which is the rational choice?", pick the larger expected value for profit and the smaller one for cost.
- Convert figures like "a 2% chance of an accident" into decimals (0.02) before calculating.
How to remember
"Expected value is the pair of glasses that lets you see the future as an average."
"Multiply amount by probability, then add up every branch."
#14 Financial analysis metrics (profitability / efficiency / productivity)
A family of metrics that use the figures in a company's financial statements to analyze the state of the business through profit ratios, turnover ratios, productivity and similar views.
Various ratios (e.g. profit ratio = Profit ÷ Sales revenue × 100)- Operating profit margin: Operating profit ÷ Sales revenue. Shows the earning power of the core business.
- ROE (return on equity): Net income ÷ Shareholders' equity. Shows how efficiently the company grew the shareholders' money.
Solution steps
- Check what is being measured against what
Break the name of the metric apart to decide the denominator and the numerator.
Example: "sales revenue," "operating profit," "margin" → Operating profit ÷ Sales revenue - Find the matching figures in the financial statements
Pull the right items out of the profit and loss statement (P/L) or the balance sheet (B/S).
Example: combine shareholders' equity (B/S) with net income (P/L) to get ROE - Divide, and multiply by 100 if you need a percentage
Calculators are not allowed on the IT Passport, so do the division by hand.
Example: 8,000,000 ÷ 40,000,000 = 0.2 → 20%
Common mistakes
- Confusing gross profit with operating profit
Operating profit is the true strength of the core business, after selling and administrative expenses have been deducted. - Trying to answer a turnover ratio as a percentage
A turnover ratio is not a proportion; it is a count of how many times stock turned over in a year.
Exam pointers
- Labor productivity often appears as an outcome of DX (digital transformation) achieved with IT.
- You may also be asked to read the meaning: a high inventory turnover means fresh, healthy operations, while a low one means a lot of dead stock.
How to remember
"ROE is the ratio of earnings (E) returned on what the owners (O) entrusted to you."
"When you hear 'the ratio of X,' X goes on the bottom and what you want to know goes on top."
#15 Break-even point (sales revenue / variable-cost ratio)
The break-even point found as an amount of money — how much you have to sell to move into profit — rather than as a number of units.
Break-even sales revenue = Fixed costs ÷ (1 - Variable-cost ratio)- Variable-cost ratio: The share of sales revenue taken up by variable costs (e.g. 0.6 if 60% of sales goes to materials)
- Contribution margin ratio: 1 - Variable-cost ratio. The share of sales that remains as margin.
Solution steps
- Find the variable-cost ratio
Divide variable costs by sales revenue to see what share of sales disappears into variable costs.
Example: with sales of ¥10,000,000 and variable costs of ¥6,000,000, 6,000,000 ÷ 10,000,000 = 0.6 - Find the contribution margin ratio
Subtract the variable-cost ratio from 1.
Example: 1 - 0.6 = 0.4 - Divide fixed costs by the contribution margin ratio
Work back to the break-even point as an amount of money.
Example: fixed costs ¥2,000,000 ÷ 0.4 = ¥5,000,000
Common mistakes
- Putting the variable-cost ratio itself in the denominator
That gives you a meaningless calculation — how many times larger variable costs are than fixed costs.
Exam pointers
- If the question mentions a "variable-cost ratio" or "sales revenue," suspect this formula.
- Some easy questions hand you the contribution margin ratio from the start.
How to remember
"The denominator is not the variable-cost ratio itself. Divide by what is left after subtracting it from 1."
"Break-even revenue: take fixed costs back through the margin ratio."
#16 Margin of safety ratio / break-even ratio
A metric for how far current sales revenue sits from the break-even point.
Margin of safety ratio (%) = (Current sales revenue - Break-even sales revenue) ÷ Current sales revenue × 100- Current sales revenue: Total sales revenue, actual or forecast
- Break-even sales revenue: The sales revenue at which profit becomes zero
Solution steps
- Find the gap from the break-even point
Subtract the break-even point from current sales to get your cushion of profit.
Example: sales of ¥10,000,000 against a break-even point of ¥8,000,000 leaves a gap of ¥2,000,000 - Express it as a share of total sales
Divide the cushion by sales revenue to get the ratio.
Example: 2,000,000 ÷ 10,000,000 = 0.2 (20%)
Common mistakes
- Putting break-even sales revenue in the denominator
The baseline is always current sales revenue.
Exam pointers
- The break-even ratio and the margin of safety ratio always add up to 100% (1.0), which is a useful shortcut.
- When you are asked which company is resilient in a downturn, pick the one with the higher margin of safety ratio.
How to remember
"A safe margin is the share made up of the savings you earned (sales - BEP)."
"Add the two ratios, safety and break-even, and you get a perfect 100% circle."
#17 Expected value (decision-making / comparison)
A technique for picking the most favorable option out of several by using expected value.
Expected value of each plan = Σ(Profit × Probability) - Investment costSolution steps
- Work out the expected value of plan A
Calculate (profit on success × probability of success) + (loss on failure × probability of failure).
Example: success ¥5,000,000 (60%) and failure -¥2,000,000 (40%) gives 3,000,000 - 800,000 = ¥2,200,000 - Work out the expected value of plan B
Get the average outcome of the other plan the same way.
Example: (the same procedure as for plan A) - Compare the expected values and decide
For profit choose the larger; for cost or loss choose the smaller.
Example: plan A (¥2.2M) vs plan B (¥2.0M) → go with plan A
Common mistakes
- Comparing only the profit if things go well
Ignoring the probability of failure and the loss it brings will make you misjudge the risk. - Forgetting to subtract the investment (the initial cost)
A large expected profit means nothing if the cost of getting it is larger still.
Exam pointers
- On the IT Passport, comparisons of two investment plans, or of holding more versus less inventory, come up often.
- The phrase "economically rational" is a signal to pick the plan with the best expected value.
How to remember
"Don't chase the dream (the best case). Choose coolly by expected value (the average outcome)."
"Branches multiply, the end adds up. Pick up every route."
#18 ROI / payback period
Metrics for how much profit you got back on the money you put in (ROI), or how many years it takes to recover it (the payback period).
ROI (return on investment) = Profit ÷ Investment × 100- Profit: The pure gain obtained, or expected, from that investment
- Investment: The money put in at the start, such as initial costs and development costs
Solution steps
- Identify the investment and the profit
Pull the money paid at the start (investment) and the money it generated (profit) out of the question.
Example: invest ¥10,000,000 and earn ¥2,000,000 of profit each year - Calculate ROI (how efficient it is)
Profit ÷ Investment × 100 gives the efficiency as a percentage.
Example: 2,000,000 ÷ 10,000,000 × 100 = 20% - Calculate the payback period (how fast it is)
Investment ÷ Profit gives the number of years.
Example: 10,000,000 ÷ 2,000,000 = 5 years
Common mistakes
- Swapping the numerator and the denominator (Investment ÷ Profit)
That gives you the payback period. For ROI, profit is the numerator.
Exam pointers
- When several investment plans are compared and you are asked which is most efficient, pick the highest ROI.
- For "how many years to recover the investment?", keep dividing until the unit is years.
How to remember
"ROI is the return (R) as a share of the money you put in (I)."
"Payback is capital ÷ annual gain. How many years until your savings are whole again?"
#19 Inventory management (reorder point / EOQ)
How to decide the stock level at which you should reorder (the reorder point) and how many units to order at a time (the economic order quantity).
Reorder point = Daily usage × Procurement lead time + Safety stock- Daily usage: Average consumption per day
- Procurement lead time: The number of days from placing the order to delivery
- Safety stock: Extra stock held against swings in demand
How to remember
"The reorder point is usage × waiting days, plus the stock that lets you sleep."
#20 Depreciation
The accounting treatment that turns the value of a fixed asset such as a building or equipment into an expense little by little over the period it is used.
Straight-line method: Annual depreciation = (Acquisition cost - Residual value) ÷ Useful life- Acquisition cost: The price paid when the asset was purchased
- Residual value: The value left after the useful life has passed (often zero)
- Useful life: The period over which the asset can be used
How to remember
"Straight-line is the same every year: subtract residual from acquisition, then divide by the years."
📋 Management (3 topics)
#21 Critical path (PERT)
The longest path to project completion — the chain of tasks that has no slack.
Shortest completion time = max(duration of each path)- Path: A chain of tasks from start to finish
- Slack (float): Latest start - earliest start (zero on the critical path)
How to remember
"The critical path follows the slowest one. It is the longest route."
#22 Person-month calculation
A way of expressing the total work in a project by treating what one person does in one month as a single unit (one person-month).
Total effort (person-months) = Number of people needed × Development period (months)- Number of people: The number of staff assigned to the project
- Development period: The number of months from the start of work to completion
Solution steps
- Grasp the total work in person-months
Start by multiplying people by period.
Example: work that takes 5 people 4 months is 5 × 4 = 20 person-months - Divide according to the condition you are given
If you want to shorten the period, divide the total effort by the period to get the number of people.
Example: to finish 20 person-months of work in 2 months, 20 ÷ 2 = 10 people are needed
Common mistakes
- Answering "how many more people are needed?" with the total headcount you calculated
When the question asks for the number of additional staff, you have to subtract the people you already have.
Exam pointers
- The pattern "how many more people are needed to make up the delay?" comes up often.
- The exam usually assumes you ignore the drop in efficiency that comes from adding staff (Brooks's law), so simple division is enough.
How to remember
"A person-month is a rectangle: people down the side, months across, and the area is the work."
"Work is water, people are cups. How many cups do you need?"
#23 EVM (Earned Value Management)
A technique that manages project progress and cost objectively by converting them into monetary amounts using three measures: PV, EV and AC.
CV (cost variance) = EV - AC / SV (schedule variance) = EV - PV- PV (Planned Value): The budgeted amount of the work that was planned to be finished by now
- EV (Earned Value): The budgeted amount of the work actually finished by now. The earned value.
- AC (Actual Cost): The total cost actually spent up to now
Solution steps
- Use EV (the result) as your baseline
EV is always the lead actor. Put EV on the left, or on top, in every formula.
Example: take EV = ¥400k, PV = ¥500k, AC = ¥450k - Compare against the plan (SV / SPI)
Subtract PV (what should have been done) from EV (what was done).
Example: 400k - 500k = -¥100k (SV). It is negative, so you are behind. - Compare against actual cost (CV / CPI)
Subtract AC (the money paid) from EV (what was done).
Example: 400k - 450k = -¥50k (CV). It is negative, so you are over budget.
Common mistakes
- Comparing PV and AC directly (PV - AC)
Comparing the planned amount with the amount spent tells you nothing about how much work is finished, so it cannot be used to judge progress. - Reversing the order of the subtraction (AC - EV, for example)
The IT Passport definition subtracts from EV, so that negative always means a bad state.
Exam pointers
- Multiple-choice questions asking "which of these best describes the current situation?" are common.
- Learning what the initials stand for (P: planned, E: earned, A: actual) is the shortcut to passing.
How to remember
"EV is king. In subtraction and in division alike, EV is always on the left, or on top."
"C (cost) compares with AC; S (schedule) compares with PV."
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