AP29 — Accounting, Break-even Analysis, and Investment Appraisal

Learning scope and sources

• Learning index: apply Major Category 9 (Corporate and Legal Affairs), Middle Category 22 (Corporate Activities), Section 3 Accounting and Finance from the 2026 IPA Applied Information Technology Engineer (AP) Syllabus Ver.7.2.
• Exact PDF-page/printed-footer mappings: 130/126, 131/127, 132/128.
• Official material: Syllabus PDF · Overview · Revision information
• Checked: 2026-10-21. This is an independent study guide and claims no affiliation with or endorsement by IPA.

One synthetic case

Consider Lumen Devices, a fictional company evaluating a compact monitoring terminal. No personal or real-company data is used. Unless stated otherwise, amounts are in million yen and every figure belongs to this one case.

1. Read the financial statements by purpose

• The balance sheet (B/S) is a point-in-time view: assets = liabilities + net assets. Current assets include cash and receivables; fixed assets include equipment and software. Liabilities are obligations, while net assets are the residual interest.
• The income statement (P/L) is a period view. Sales − cost of sales = gross profit; gross profit − selling, general and administrative expenses = operating profit. Non-operating income and expenses lead to ordinary profit; extraordinary items and taxes then lead toward net income.
• The cash-flow statement (C/F) explains cash movement through operating, investing, and financing activities. Buying equipment is normally an investing cash outflow; borrowing is a financing cash inflow. Profit and cash are not identical because accrual accounting records items such as credit sales and depreciation without matching cash in the same period.
• The statement of changes in net assets explains movements such as profit, dividends, and new share issues within net assets.

Suppose Lumen has current assets of 180, current liabilities of 120, total assets of 500, and net assets of 200. Its current ratio is 180 ÷ 120 × 100 = 150%, and its equity ratio is 200 ÷ 500 × 100 = 40%. These ratios provide views of short-term safety and capital stability; they do not alone prove profitability or liquidity quality.

2. Separate fixed and variable cost

The terminal sells for ¥50,000 per unit. Variable cost is ¥30,000 per unit, and monthly fixed cost is ¥8,000,000.

• Unit contribution margin = price − unit variable cost = 50,000 − 30,000 = ¥20,000
• Contribution-margin ratio = 20,000 ÷ 50,000 = 40%
• Total contribution margin = sales − total variable cost
• Profit = total contribution margin − fixed cost

Variable cost changes with activity within the assumed relevant range. Fixed cost remains constant in total over that range, but fixed cost per unit falls as volume rises. Contribution margin is not operating profit: it must first cover fixed cost.

3. Calculate break-even point, target sales, and margin of safety

Break-even is where profit is zero.

• Break-even volume = fixed cost ÷ unit contribution margin = 8,000,000 ÷ 20,000 = 400 units
• Break-even sales = fixed cost ÷ contribution-margin ratio = 8,000,000 ÷ 0.40 = ¥20,000,000
• Volume for a target profit of ¥4,000,000 = (8,000,000 + 4,000,000) ÷ 20,000 = 600 units
• Sales for that target profit = (8,000,000 + 4,000,000) ÷ 0.40 = ¥30,000,000

At actual sales of ¥25,000,000, the margin of safety is 25,000,000 − 20,000,000 = ¥5,000,000, and the margin-of-safety ratio is 5,000,000 ÷ 25,000,000 × 100 = 20%. It shows how far sales may fall before reaching break-even.

If price and volume assumptions stay unchanged, an increase in fixed cost raises the break-even point. An increase in unit variable cost reduces contribution margin and also raises the break-even point. These are model-based comparisons; the simple model assumes linear revenue/cost behavior, a stable sales mix, and no material inventory distortion within the relevant range.

4. Evaluate an investment with discounted cash flow

At t=0, Lumen can invest ¥10 million and expects after-tax cash inflows of ¥6 million at the end of each of the next two years. The analysis uses a 10% annual discount rate, million-yen units, and rounds final results to three decimal places. It assumes no tax effects beyond the stated after-tax flows, no terminal value, and no working-capital change:

• Year 1 present value = 6 ÷ 1.10 = 5.455
• Year 2 present value = 6 ÷ 1.10² = 4.959
• NPV = −10 + 6 ÷ 1.10 + 6 ÷ 1.10² = +0.413 million yen (calculated from unrounded intermediate values, then rounded)

Under the NPV rule, accept a standalone project when NPV is positive because discounted inflows exceed the initial outlay. The discount rate should reflect the risk and financing context; WACC is a weighted cost of debt and equity often used as a reference for company-wide investment appraisal.

The IRR is the discount rate that makes NPV zero. Accepting when IRR exceeds the required return is a common rule, but NPV is generally preferable for comparing mutually exclusive projects because IRR can mislead with different project scale, timing, or non-conventional cash flows.

The undiscounted payback period for this project is 1 year + 4 ÷ 6 year = 1.667 years. The discounted payback period (DPP) uses discounted cash flows: after year 1, 4.545 remains, so DPP = 1 + 4.545 ÷ 4.959 = approximately 1.917 years. Payback emphasizes recovery speed but ignores cash flows after the cutoff and, unless discounted, the time value of money.

Term	Canonical distinction
B/S / P/L / C/F	point-in-time financial position / period performance / cash movement
Fixed / variable cost	constant in total within the relevant range / changes with activity
Contribution margin	sales minus variable cost; amount available for fixed cost and profit
Break-even / target-profit sales	zero-profit level / level covering fixed cost plus target profit
NPV / IRR / DPP	value added at a required rate / zero-NPV rate / discounted recovery time
WACC	weighted cost of debt and equity used as a discount-rate reference

Practice questions — all original

Question 1

Which transaction and cash-flow category pairing is correct?

1. Purchase of production equipment for cash — operating cash outflow
2. Proceeds from a new bank loan — financing cash inflow
3. Collection of a trade receivable — investing cash inflow
4. Payment of employee wages — financing cash outflow

Answer: 2

• 1: Incorrect. Buying equipment is normally an investing outflow.
• 2: Correct. Borrowing raises funds and is a financing inflow.
• 3: Incorrect. Collection from customers belongs to operating cash flow.
• 4: Incorrect. Wages are normally an operating outflow.

Question 2

For a product priced at ¥50,000 with unit variable cost of ¥30,000 and fixed cost of ¥8,000,000, what is the break-even volume?

1. 160 units
2. 267 units
3. 400 units
4. 600 units

Answer: 3

• 1: Incorrect. It results from dividing fixed cost by price without using contribution margin.
• 2: Incorrect. It roughly divides fixed cost by variable cost, which is not the formula.
• 3: Correct. 8,000,000 ÷ (50,000 − 30,000) = 400 units.
• 4: Incorrect. This is the volume for a ¥4,000,000 target profit.

Question 3

If actual sales are ¥25,000,000 and break-even sales are ¥20,000,000, what is the margin-of-safety ratio?

1. 5%
2. 10%
3. 20%
4. 25%

Answer: 3

• 1: Incorrect. The ¥5 million difference is not 5% of actual sales.
• 2: Incorrect. It does not follow from the given values.
• 3: Correct. (25 − 20) ÷ 25 × 100 = 20%.
• 4: Incorrect. This divides the margin by break-even sales instead of actual sales.

Question 4

An investment costs ¥10 million now and returns ¥6 million at each year-end for two years. At 10%, which appraisal is correct (rounded)?

1. NPV is about +¥0.413 million, so the NPV rule accepts it.
2. NPV is −¥2 million because discounting must be ignored.
3. NPV is exactly +¥2 million after discounting.
4. NPV cannot be calculated without accounting depreciation.

Answer: 1

• 1: Correct. −10 + 6/1.10 + 6/1.10² ≈ +0.413.
• 2: Incorrect. The undiscounted net inflow is +¥2 million, not −¥2 million.
• 3: Incorrect. +¥2 million is the undiscounted result.
• 4: Incorrect. The stated cash flows and discount rate are sufficient.

Provenance and next installment

All four questions are original. Therefore past-question year/season/AP label/original time band/question number are N/A, translation/adaptation is N/A, and official-answer comparison is N/A. No IPA past question is used. The examples are for exam study, not personal investment advice, and this article does not guarantee a pass.

The next installment is AP30 — AI, statistics, evaluation, and data.