# Consolidated Accretive Thinking agent documentation --- # Accretive Thinking agent guide Accretive Thinking is a local practice resource for investment banking and consulting interviews. Start with `llms.txt`; `llms-full.txt` consolidates the agent documentation. No hosted deployment URL is defined. ## Use boundaries - Treat candidate answers and exported practice history as private. Do not transmit them or make external calls unless the user separately asks. - Numeric checks are narrow calculation feedback, not an interview score. Do not infer missing values or grade free-text reasoning as though the checker did. - Do not claim that a candidate is ready for recruiting, interviews, or a job. Explanations and judgment need human review. - The question bank identifies its scenarios as original fictional material based on standard concepts, not copied from course questions. It does not claim these were asked by specific firms. - Voice is optional and separate from the local written loop. It requires server-side `OPENAI_API_KEY` and makes a provider request. Never put a key in browser code or documentation. ## Main files - `index.html`: Accretive Thinking home page. - `bank.html`: question-bank practice; `bank.js` and `practice-engine.js` implement the interface and numeric comparisons. - `consulting.html` with `app.js`: consulting case exercise. - `decision-case.html`: decision case. - `learn/`: static topic index, 8 topic pages, and 16 question pages. - `question-bank.json`: question content, inputs, references, and review notes. - `study-cli.mjs`: local `list`, `question`, and `check` commands; no network or API key required. - `grade-answer.mjs`: numeric checker and function-tool definition. - `server.mjs`: loopback-only local HTTP server and optional voice route. - `docs/`: schema and usage reference. When documentation and implementation disagree, use the source files above and update the docs. --- # Accretive Thinking: agent entry point Accretive Thinking is a local practice resource for investment banking and consulting interviews. No hosted deployment URL is defined. ## Read in this order 1. [Agent guide](AGENT-GUIDE.txt) — safe-use boundaries and source map. 2. [Agent reference](docs/README.md) — product pages, CLI, and local API. 3. [Question-bank reference](docs/question-bank.md) — schema, topics, provenance, and grading limits. 4. [Practice loop](docs/practice-loop.md) — human-led workflow and exact checker semantics. 5. [Question references](docs/questions/index.md) — per-question material in Markdown. 6. [Full agent documentation](llms-full.txt) — consolidated text version. ## Key files - [Home page](index.html): Accretive Thinking landing page. - [Question practice](bank.html): written practice from the question bank. - [Question bank JSON](question-bank.json): 16 scenarios, numeric references, and changed-input retries. - `grade-answer.mjs` (local checkout file): deterministic numeric checker and `check_answer` function-tool schema. - `study-cli.mjs` (local checkout file): offline `list`, `question`, and `check` commands. - [Learning pages](learn/index.html): static topic index with 8 topic pages and 16 individual question pages. - [Consulting case](consulting.html): the separate consulting exercise. - [Decision case](decision-case.html): commercial decision exercise. - `server.mjs` (local checkout file): loopback-only API, default port 8767, plus optional voice-session endpoint. The checker assesses supplied numeric answers and an explicit concept selection only. It does not grade prose or spoken reasoning, and it makes no readiness determination. See the [agent guide](AGENT-GUIDE.txt). --- # Accretive Thinking agent reference Accretive Thinking is a local practice resource. It has no specified hosted deployment URL; the included server binds to `127.0.0.1`. ## Product and source files - [`../index.html`](../index.html): Accretive Thinking home page. - [`../bank.html`](../bank.html), [`../bank.js`](../bank.js), [`../practice-engine.js`](../practice-engine.js): question-bank practice UI and matching behavior. - [`../consulting.html`](../consulting.html), [`../app.js`](../app.js): separate consulting case. - [`../decision-case.html`](../decision-case.html): commercial decision exercise. - [`../learn/index.html`](../learn/index.html): learning index. `../learn/` contains 8 topic pages and 16 question pages. - [`../question-bank.json`](../question-bank.json): versioned question bank and numeric references. - `study-cli.mjs` (local checkout file): offline CLI. - `grade-answer.mjs` (local checkout file): `gradeAnswer` and `check_answer` function-tool schema. - `server.mjs` (local checkout file): local HTTP routes and optional voice provider request. - [`questions/`](questions/index.md): one Markdown reference per bank question ID. ## Study CLI Run from the demo root (the folder containing `study-cli.mjs`) with Node.js; no server, network, or API key is required: - `node study-cli.mjs list` prints question IDs, topics, titles, and levels. - `node study-cli.mjs question ac-capex` prints the candidate prompt and supporting metadata, omitting expected answers and worked solutions. - `printf '{"depreciation":24,"netIncome":-18}' | node study-cli.mjs check ac-capex first` checks only the supplied answer fields. Use `retry` as the final argument to check retry references. The `check` command reads an answer object from stdin, not command-line arguments. ## Local HTTP API Run from the demo root with `node server.mjs`. The default is `http://127.0.0.1:8767`; set `PORT` before launch to select another port. The server only accepts `localhost` or `127.0.0.1` at that port and binds to loopback. - `GET /api/status` returns `{configured, model}`. `configured` indicates whether the server has `OPENAI_API_KEY`; it does not test the key or prove voice access. - `GET /question-bank.json` returns the question bank. - `POST /api/check` accepts `{question_id, attempt, answers, concept_choice?}`. It requires an `Origin` header matching the requested local host and port. `attempt` is `first` or `retry`; `answers` maps answer field names to numeric values. `concept_choice` is optional and matches only when it equals `0`. Example, after starting the server locally: ```sh curl http://127.0.0.1:8767/api/check \ -H 'Origin: http://127.0.0.1:8767' \ -H 'Content-Type: application/json' \ --data '{"question_id":"ac-capex","attempt":"first","answers":{"depreciation":24,"netIncome":-18}}' ``` - `POST /api/session?focus=` accepts an SDP offer with `Content-Type: application/sdp`. It is disabled without a server-side key and, when enabled, sends the offer to the configured provider. Use this only when voice practice is requested. Request sizes are limited. Never expose a provider key in client code. --- # Question bank reference [`../question-bank.json`](../question-bank.json) has top-level fields `version`, `unitConvention`, `scope`, and `questions`. It currently declares version 1, 16 original questions, 16 parameterized retries, and expert review pending. Amounts are generally in $ millions unless stated; rates are decimals. ## Question record Each record has the same fields: - `id`, `topic`, `title`, `prompt`: stable identifier and candidate-facing scenario. - `assumptions`: constraints needed for the calculation. - `parameters`: original numeric inputs; `retry` contains replacement inputs for the same task. - `formulas`: reference calculation expressions keyed by answer field. - `expected`, `retryExpected`: numeric answer maps, keyed by result field. - `workedSolution`: short calculation/reasoning steps. - `misconceptions`: objects with `claim` and `followup` prompts. - `followups`, `followupAnswerGuide`: prompts and guidance for a human discussion. - `level`: practice difficulty label. - `numericBridges`: optional named intermediate calculation references. - `provenance`: source note; the bank describes scenarios and wording as original fictional material, not copied from course questions. - `reviewStatus`: current review note. It currently says formula-tested and expert review pending. Topics currently represented: accounting (4), DCF (3), valuation (2), mergers (2), LBO (2), comparables (1), financial institutions (1), and real estate (1). This is a demo bank, not evidence of comprehensive coverage. ## Grading semantics `gradeAnswer` in `grade-answer.mjs` (local checkout file) takes `{question_id, attempt, answers, concept_choice?}`. Unknown question IDs, attempts, answer objects, or answer field names are invalid. It compares only supplied numeric fields and returns each field's `provided`, `expected`, `matches`, and diagnostic explanation, plus unanswered expected fields. Missing values are not inferred. The optional concept check reports a match only when `concept_choice === 0`; its explanation comes from the corresponding concept prompt data in `practice-engine.js`. This is only an explicit selection check. It does not grade free-text explanation, spoken reasoning, transcription quality, or interview performance. --- # Practice loop Use the demo as a structured rehearsal with human feedback: 1. Select a scenario and read its prompt and assumptions. Ask the candidate to state their approach before calculating. 2. Capture each requested numeric result and the candidate's explanation separately. Preserve signs and units; rates use decimals unless entered with a percent sign in the UI. 3. Check only the supplied numeric fields with `gradeAnswer` or the local `/api/check` endpoint. Review diagnostics and unanswered fields; do not fill in omitted answers. 4. Discuss the worked solution and follow-up prompts. Ask the candidate to defend assumptions and explain causal steps. The tool does not grade prose. 5. Use the replacement inputs for a retry after discussion. Treat a repeat match as practice on that calculation, not proof of retention or readiness. 6. End with specific human feedback and a next practice target. Do not issue a readiness score or claim recruiting/interview readiness. ## Function tool `grade-answer.mjs` exports `checkTool`, named `check_answer`. Its parameters are `question_id` (string), `attempt` (`first` or `retry`), and `answers` (object whose values are numbers). All three are required. The tool description instructs agents to confirm ambiguous numbers with the candidate, never infer missing answers, and check reasoning through conversational follow-ups separately. The function schema does not include `concept_choice`; the local HTTP endpoint does accept it. The return value labels itself with a limitation: only supplied numbers and explicit concept selection are checked. A correct numeric match is not an assessment of communication, judgment, or full technical ability. --- # Revenue that has not been collected **ID:** `ac-ar` **Topic:** accounting **Level:** foundation ## Prompt A software vendor records 48 of credit revenue. Associated cash operating costs are 18. Explain earnings and cash impact. ## Assumptions All amounts $m; no opening receivable, revenue not collected, costs paid, tax25% paid currently. No other effects. ## Inputs ### Original - `revenue`: 48 - `cost`: 18 - `tax`: 0.25 ### Retry - `revenue`: 60 - `cost`: 24 - `tax`: 0.25 ## Reference calculations - `netIncome`: original 22.5; retry 27.0. Formula: `(revenue-cost)*(1-tax)` - `cfo`: original -25.5; retry -33.0. Formula: `(revenue-cost)*(1-tax)-revenue` - `ar`: original 48; retry 60. Formula: `revenue` ## Intermediate calculations - `first`: `['netIncome: (48-18)*(1-0.25) = 22.5', 'cfo: (48-18)*(1-0.25)-48 = -25.5', 'ar: 48 = 48']` - `retry`: `['netIncome: (60-24)*(1-0.25) = 27', 'cfo: (60-24)*(1-0.25)-60 = -33', 'ar: 60 = 60']` ## Discussion prompts - If the customer pays next period, does that create new revenue or reverse the receivable? - How could reported earnings grow while operating cash flow deteriorates? Name two facts you would investigate before judging the company. ## Review notes Collection reduces accounts receivable and increases cash/CFO. It is not new revenue or net income when previously recognized correctly. Common misconception: - Revenue recognized means cash received. Follow up: If the customer pays next period, does that create new revenue or reverse the receivable? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Equipment and cash **ID:** `ac-capex` **Topic:** accounting **Level:** foundation ## Prompt A warehouse buys equipment for 144 cash at the start of the year. Walk through the first year across all three statements. ## Assumptions Amounts $m. Six-year straight-line life, no salvage. Book=tax depreciation. 25% tax shield usable immediately. No financing, WC or dividends. The company has sufficient other taxable income to absorb the deduction. ## Inputs ### Original - `cost`: 144 - `life`: 6 - `tax`: 0.25 ### Retry - `cost`: 180 - `life`: 6 - `tax`: 0.3 ## Reference calculations - `depreciation`: original 24.0; retry 30.0. Formula: `cost/life` - `netIncome`: original -18.0; retry -21.0. Formula: `-cost/life*(1-tax)` - `cfo`: original 6.0; retry 9.0. Formula: `cost/life*tax` - `cash`: original -138.0; retry -171.0. Formula: `-cost+cost/life*tax` - `netPPE`: original 120.0; retry 150.0. Formula: `cost-cost/life` - `retainedEarnings`: original -18.0; retry -21.0. Formula: `-cost/life*(1-tax)` ## Intermediate calculations - `first`: `['depreciation: 144/6 = 24', 'netIncome: -144/6*(1-0.25) = -18', 'cfo: 144/6*0.25 = 6', 'cash: -144+144/6*0.25 = -138', 'netPPE: 144-144/6 = 120', 'retainedEarnings: -144/6*(1-0.25) = -18']` - `retry`: `['depreciation: 180/6 = 30', 'netIncome: -180/6*(1-0.3) = -21', 'cfo: 180/6*0.3 = 9', 'cash: -180+180/6*0.3 = -171', 'netPPE: 180-180/6 = 150', 'retainedEarnings: -180/6*(1-0.3) = -21']` ## Discussion prompts - If there were no current cash tax benefit, what would happen to cash, and why? - If a six-year useful life changes to three years with the same tax capacity, what happens to first-year earnings and cash? Separate timing from lifetime economics. ## Review notes Without a current cash tax benefit, CFO has no cash tax saving and cash falls by the full capex. Net income may still reflect deferred taxes if recognition criteria are met; ask the candidate to state that assumption. Common misconception: - Depreciation addback creates cash independently of taxes. Follow up: If there were no current cash tax benefit, what would happen to cash, and why? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Customer prepays **ID:** `ac-deferred` **Topic:** accounting **Level:** foundation ## Prompt A customer pays 72 upfront for twelve months of service. At receipt, before any service is delivered, what changes? ## Assumptions Amounts $m. No tax, cost or financing effects at receipt. Treat customer advance as operating cash flow. ## Inputs ### Original - `receipt`: 72 ### Retry - `receipt`: 96 ## Reference calculations - `cash`: original 72; retry 96. Formula: `receipt` - `deferredRevenue`: original 72; retry 96. Formula: `receipt` - `revenue`: original 0; retry 0. Formula: `0` - `cfo`: original 72; retry 96. Formula: `receipt` ## Intermediate calculations - `first`: `['cash: 72 = 72', 'deferredRevenue: 72 = 72', 'revenue: 0 = 0', 'cfo: 72 = 72']` - `retry`: `['cash: 96 = 96', 'deferredRevenue: 96 = 96', 'revenue: 0 = 0', 'cfo: 96 = 96']` ## Discussion prompts - After three of the twelve months, how much revenue and liability remain if service is even? - Would faster annual prepayments improve reported profit immediately, or mainly cash and liabilities? Explain what service delivery changes. ## Review notes After three months of even service, revenue is 18 and deferred revenue is 54 on the original 72 advance; recognizing it does not create new cash. Retry: 24 revenue and 72 deferred revenue. Common misconception: - Cash receipt must be revenue. Follow up: After three of the twelve months, how much revenue and liability remain if service is even? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Inventory on supplier credit **ID:** `ac-inventory` **Topic:** accounting **Level:** foundation ## Prompt A retailer buys 36 of inventory entirely on supplier credit. Before any sale or payment, explain the cash-flow impact. ## Assumptions Amounts $m, no tax or other changes. Accounts payable is operating. ## Inputs ### Original - `purchase`: 36 ### Retry - `purchase`: 52 ## Reference calculations - `inventory`: original 36; retry 52. Formula: `purchase` - `accountsPayable`: original 36; retry 52. Formula: `purchase` - `cfo`: original 0; retry 0. Formula: `0` ## Intermediate calculations - `first`: `['inventory: 36 = 36', 'accountsPayable: 36 = 36', 'cfo: 0 = 0']` - `retry`: `['inventory: 52 = 52', 'accountsPayable: 52 = 52', 'cfo: 0 = 0']` ## Discussion prompts - What happens to CFO when the payable is subsequently paid without selling inventory? - Could stretching supplier terms temporarily improve CFO without improving profitability? What sustainability risks would you check? ## Review notes Paying the supplier reduces cash and accounts payable by36 and creates a36 operating cash outflow without changing inventory or net income. Retry52. Common misconception: - Inventory increase always means a cash outflow. Follow up: What happens to CFO when the payable is subsequently paid without selling inventory? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Bank price to book **ID:** `bank-pb` **Topic:** financial-institutions **Level:** intermediate ## Prompt A bank has common equity book value900 and90 million shares. A comparable P/B multiple is1.3x. Find implied equity value and share price. ## Assumptions Amounts $m. Book equity is common equity, with no preferred or other adjustments. Illustrative comparable, not investment advice. ## Inputs ### Original - `book`: 900 - `shares`: 90 - `multiple`: 1.3 ### Retry - `book`: 1200 - `shares`: 100 - `multiple`: 1.1 ## Reference calculations - `equity`: original 1170.0; retry 1320.0. Formula: `book*multiple` - `price`: original 13.0; retry 13.2. Formula: `book*multiple/shares` ## Intermediate calculations - `first`: `['equity: 900*1.3 = 1170', 'price: 900*1.3/90 = 13']` - `retry`: `['equity: 1200*1.1 = 1320', 'price: 1200*1.1/100 = 13.2']` ## Discussion prompts - Why are EV/EBITDA and industrial-company net-debt bridges often poor starting points for banks? - What sustainable ROE and asset-quality evidence would you want before calling a bank trading below book cheap? ## Review notes Funding liabilities, including deposits, are integral to a bank business; interest is an operating input. Use consistent equity metrics with capital adequacy, asset quality and sustainable ROE rather than mechanically subtracting deposits from P/B equity value. Common misconception: - Subtract bank deposits as ordinary corporate net debt from P/B value. Follow up: Why are EV/EBITDA and industrial-company net-debt bridges often poor starting points for banks? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Normalize EBITDA **ID:** `comps-normalize` **Topic:** comparables **Level:** intermediate ## Prompt Reported EBITDA is64 after a one-time cash litigation expense9. Normalize EBITDA and calculate implied EV at8x. ## Assumptions Amounts $m. Expense is included in EBITDA and genuinely nonrecurring. No other adjustments. ## Inputs ### Original - `reported`: 64 - `expense`: 9 - `multiple`: 8 ### Retry - `reported`: 78 - `expense`: 6 - `multiple`: 7.5 ## Reference calculations - `normalized`: original 73; retry 84. Formula: `reported+expense` - `ev`: original 584; retry 630.0. Formula: `(reported+expense)*multiple` ## Intermediate calculations - `first`: `['normalized: 64+9 = 73', 'ev: (64+9)*8 = 584']` - `retry`: `['normalized: 78+6 = 84', 'ev: (78+6)*7.5 = 630']` ## Discussion prompts - What evidence would you need before accepting management’s recurring restructuring addback? - How would your recommendation change if the same supposedly one-off expense appeared in each of the last three years? ## Review notes Review recurrence, cash evidence, historical addbacks and business economics; repeated ordinary restructuring may be recurring even if management calls it one-time. Consistency across comparables matters. Common misconception: - Add back every cost labeled exceptional. Follow up: What evidence would you need before accepting management’s recurring restructuring addback? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Terminal value timing **ID:** `dcf-terminal` **Topic:** dcf **Level:** intermediate ## Prompt Year5 UFCF is50. Perpetual growth2%, WACC10%. Find terminal value at end of year5 and its present value. ## Assumptions Amounts $m. Gordon growth, WACC>g, no stub periods. Only discount terminal value, not explicit forecast cash flows. ## Inputs ### Original - `fcf`: 50 - `g`: 0.02 - `wacc`: 0.1 - `years`: 5 ### Retry - `fcf`: 65 - `g`: 0.025 - `wacc`: 0.11 - `years`: 5 ## Reference calculations - `terminal`: original 637.5; retry 783.8235294117648. Formula: `fcf*(1+g)/(wacc-g)` - `pv`: original 395.8373434502113; retry 465.1611144929584. Formula: `fcf*(1+g)/(wacc-g)/(1+wacc)**years` ## Intermediate calculations - `first`: `['terminal: 50*(1+0.02)/(0.1-0.02) = 637.5', 'pv: 50*(1+0.02)/(0.1-0.02)/(1+0.1)**5 = 395.837']` - `retry`: `['terminal: 65*(1+0.025)/(0.11-0.025) = 783.824', 'pv: 65*(1+0.025)/(0.11-0.025)/(1+0.11)**5 = 465.161']` ## Discussion prompts - What breaks when growth approaches or exceeds WACC? - How would you challenge a valuation dominated by terminal value before recommending a bid? ## Review notes The standard perpetual-growth formula requires WACC greater than growth. Near equality implies an unstable enormous terminal value; at or above WACC the conventional perpetuity model is not economically valid. Common misconception: - Use year5 FCF directly or discount terminal value six years. Follow up: What breaks when growth approaches or exceeds WACC? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Unlevered free cash flow **ID:** `dcf-ufcf` **Topic:** dcf **Level:** intermediate ## Prompt A company has $90 million of EBIT, $18 million of depreciation and amortization, and $26 million of capital expenditures. Its operating working capital increases by $12 million. Assume a 25% tax rate. What is its unlevered free cash flow? ## Assumptions Enter your answer in millions. Operating working capital excludes cash and financing debt. ## Inputs ### Original - `ebit`: 90 - `tax`: 0.25 - `da`: 18 - `capex`: 26 - `nwc`: 12 ### Retry - `ebit`: 120 - `tax`: 0.3 - `da`: 24 - `capex`: 35 - `nwc`: 10 ## Reference calculations - `ufcf`: original 47.5; retry 63.0. Formula: `ebit*(1-tax)+da-capex-nwc` ## Intermediate calculations - `first`: `['ufcf: 90*(1-0.25)+18-26-12 = 47.5']` - `retry`: `['ufcf: 120*(1-0.3)+24-35-10 = 63']` ## Discussion prompts - How would your cash-flow definition and discount rate change for a levered equity DCF? - If growth requires a larger working-capital investment, why might higher revenue growth reduce near-term cash flow? ## Review notes Levered cash flow reflects interest and net borrowing and is discounted at cost of equity to equity value. Keep cash-flow definition and discount rate consistent; do not simply swap rates. Common misconception: - Subtract interest in UFCF and discount at WACC. Follow up: How would your cash-flow definition and discount rate change for a levered equity DCF? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Cost of capital **ID:** `dcf-wacc` **Topic:** dcf **Level:** intermediate ## Prompt Equity weight70%, debt30%, cost of equity12%, pre-tax debt cost6%, tax25%. Calculate WACC. ## Assumptions Fixed market-value weights; interest deduction usable; no preferred stock. Enter WACC as decimal, not percentage points. ## Inputs ### Original - `e`: 0.7 - `d`: 0.3 - `ke`: 0.12 - `kd`: 0.06 - `tax`: 0.25 ### Retry - `e`: 0.6 - `d`: 0.4 - `ke`: 0.14 - `kd`: 0.07 - `tax`: 0.3 ## Reference calculations - `wacc`: original 0.09749999999999999; retry 0.10360000000000001. Formula: `e*ke+d*kd*(1-tax)` ## Intermediate calculations - `first`: `['wacc: 0.7*0.12+0.3*0.06*(1-0.25) = 0.0975']` - `retry`: `['wacc: 0.6*0.14+0.4*0.07*(1-0.3) = 0.1036']` ## Discussion prompts - Why might increasing debt eventually raise WACC rather than always reduce it? - Would you use the same WACC for a safe contracted asset and a speculative expansion? Explain the cash-flow risk you are pricing. ## Review notes Higher leverage can increase default risk, borrowing costs and required equity returns, reduce tax shield usability, and change weights. A fixed-cost-of-capital thought experiment is not a universal optimization. Common misconception: - Apply a tax discount to equity or use book equity weights. Follow up: Why might increasing debt eventually raise WACC rather than always reduce it? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # From operations to shareholders **ID:** `ev-bridge` **Topic:** valuation **Level:** foundation ## Prompt A logistics company has EBITDA 84, a 7.5x EV/EBITDA multiple, debt210, excess cash54 and 30 million diluted shares. Find EV, equity value and per-share value. ## Assumptions Amounts $m except share price; no preferred, NCI or other claims. Debt at stated value. ## Inputs ### Original - `ebitda`: 84 - `multiple`: 7.5 - `debt`: 210 - `cash`: 54 - `shares`: 30 ### Retry - `ebitda`: 96 - `multiple`: 8 - `debt`: 250 - `cash`: 58 - `shares`: 32 ## Reference calculations - `ev`: original 630.0; retry 768. Formula: `ebitda*multiple` - `equity`: original 474.0; retry 576. Formula: `ebitda*multiple-debt+cash` - `price`: original 15.8; retry 18.0. Formula: `(ebitda*multiple-debt+cash)/shares` ## Intermediate calculations - `first`: `['ev: 84*7.5 = 630', 'equity: 84*7.5-210+54 = 474', 'price: (84*7.5-210+54)/30 = 15.8']` - `retry`: `['ev: 96*8 = 768', 'equity: 96*8-250+58 = 576', 'price: (96*8-250+58)/32 = 18']` ## Discussion prompts - If 40 of new debt is retained as cash with no other changes, what happens to equity and EV? - If the quoted multiple rises by one turn with EBITDA and net debt fixed, quantify the equity-value effect per share. ## Review notes Equal debt and excess cash issuance leaves net debt, operating EV and equity value unchanged under the stated no-fee/no-repricing assumptions. Common misconception: - Adding debt increases equity value. Follow up: If 40 of new debt is retained as cash with no other changes, what happens to equity and EV? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Treasury stock dilution **ID:** `ev-dilution` **Topic:** valuation **Level:** foundation ## Prompt A company has 50 million basic shares, 10 million options with strike8, and stock price20. Using treasury stock method, find net new shares and diluted shares. ## Assumptions All options exercisable and in the money. Ignore taxes and other dilutive securities. ## Inputs ### Original - `basic`: 50 - `options`: 10 - `strike`: 8 - `price`: 20 ### Retry - `basic`: 60 - `options`: 12 - `strike`: 10 - `price`: 25 ## Reference calculations - `newShares`: original 6.0; retry 7.2. Formula: `options-options*strike/price` - `dilutedShares`: original 56.0; retry 67.2. Formula: `basic+options-options*strike/price` ## Intermediate calculations - `first`: `['newShares: 10-10*8/20 = 6', 'dilutedShares: 50+10-10*8/20 = 56']` - `retry`: `['newShares: 12-12*10/25 = 7.2', 'dilutedShares: 60+12-12*10/25 = 67.2']` ## Discussion prompts - What if the strike were above the stock price? - At a much higher share price, how does the net dilution from these same options change, and why? ## Review notes Out-of-the-money options add no diluted shares in treasury stock method; do not allow negative dilution. Common misconception: - Every option adds one net diluted share. Follow up: What if the strike were above the stock price? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Cash available for debt paydown **ID:** `lbo-debt` **Topic:** lbo **Level:** intermediate ## Prompt An LBO generates EBITDA80, cash interest20, cash taxes10, capex15, increase in NWC5. How much is available for optional debt paydown? ## Assumptions Amounts $m. No other cash flows, mandatory amortization, fees or minimum cash requirement. D&A irrelevant because cash taxes given. ## Inputs ### Original - `ebitda`: 80 - `interest`: 20 - `taxes`: 10 - `capex`: 15 - `nwc`: 5 ### Retry - `ebitda`: 100 - `interest`: 26 - `taxes`: 12 - `capex`: 18 - `nwc`: 7 ## Reference calculations - `paydown`: original 30; retry 37. Formula: `ebitda-interest-taxes-capex-nwc` ## Intermediate calculations - `first`: `['paydown: 80-20-10-15-5 = 30']` - `retry`: `['paydown: 100-26-12-18-7 = 37']` ## Discussion prompts - What if a minimum cash covenant requires retaining 8 of this cash? - If interest rates rise, explain both the immediate cash-paydown impact and the possible exit-equity consequence. ## Review notes Retaining8 reduces optional paydown from30 to22 on the original inputs; the retry generates37 and leaves29 if the same minimum-cash increment applies. Common misconception: - EBITDA is cash available to repay debt. Follow up: What if a minimum cash covenant requires retaining 8 of this cash? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Exit equity and sponsor return **ID:** `lbo-return` **Topic:** lbo **Level:** intermediate ## Prompt Entry EV500 funded with debt300 and sponsor equity200. At exit after five years EV600, debt180, no excess cash. Find equity proceeds, MOIC and IRR. ## Assumptions Amounts $m. No interim distributions, fees, other claims or additional equity. IRR as decimal. ## Inputs ### Original - `ev`: 600 - `debt`: 180 - `entryEquity`: 200 - `years`: 5 ### Retry - `ev`: 720 - `debt`: 160 - `entryEquity`: 250 - `years`: 4 ## Reference calculations - `proceeds`: original 420; retry 560. Formula: `ev-debt` - `moic`: original 2.1; retry 2.24. Formula: `(ev-debt)/entryEquity` - `irr`: original 0.15996225865400127; retry 0.2233817698125049. Formula: `((ev-debt)/entryEquity)**(1/years)-1` ## Intermediate calculations - `first`: `['proceeds: 600-180 = 420', 'moic: (600-180)/200 = 2.1', 'irr: ((600-180)/200)**(1/5)-1 = 0.159962']` - `retry`: `['proceeds: 720-160 = 560', 'moic: (720-160)/250 = 2.24', 'irr: ((720-160)/250)**(1/4)-1 = 0.223382']` ## Discussion prompts - If MOIC stays fixed but holding period shortens, what happens to IRR? - Can an attractive IRR conceal a modest absolute cash profit? Compare timing, leverage and MOIC. ## Review notes For a fixed MOIC greater than1 and no interim cash flows, shorter duration increases annualized IRR. State assumptions; IRR and MOIC measure different dimensions. Common misconception: - Use EV growth as the equity return or divide MOIC by years. Follow up: If MOIC stays fixed but holding period shortens, what happens to IRR? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Cash acquisition EPS **ID:** `ma-eps` **Topic:** mergers **Level:** intermediate ## Prompt Acquirer net income120, shares40. Target net income24. Cash purchase300 funded from excess cash earning4% pre-tax. Tax25%. Find pro forma EPS and accretion. ## Assumptions Amounts $m. Full-year ownership, no synergies, fees, purchase accounting amortization or new shares. Enter accretion as decimal. ## Inputs ### Original - `ani`: 120 - `shares`: 40 - `tni`: 24 - `price`: 300 - `rate`: 0.04 - `tax`: 0.25 ### Retry - `ani`: 150 - `shares`: 50 - `tni`: 30 - `price`: 400 - `rate`: 0.05 - `tax`: 0.25 ## Reference calculations - `standalone`: original 3.0; retry 3.0. Formula: `ani/shares` - `proforma`: original 3.375; retry 3.3. Formula: `(ani+tni-price*rate*(1-tax))/shares` - `accretion`: original 0.125; retry 0.09999999999999987. Formula: `((ani+tni-price*rate*(1-tax))/shares)/(ani/shares)-1` ## Intermediate calculations - `first`: `['standalone: 120/40 = 3', 'proforma: (120+24-300*0.04*(1-0.25))/40 = 3.375', 'accretion: ((120+24-300*0.04*(1-0.25))/40)/(120/40)-1 = 0.125']` - `retry`: `['standalone: 150/50 = 3', 'proforma: (150+30-400*0.05*(1-0.25))/50 = 3.3', 'accretion: ((150+30-400*0.05*(1-0.25))/50)/(150/50)-1 = 0.1']` ## Discussion prompts - Can a deal be EPS-accretive but destroy value? Explain without relying only on EPS. - How would a higher cash yield change the accretion result, holding everything else fixed? Explain the opportunity cost. ## Review notes Yes. Accretion can result from financing and earnings-yield differences even if price exceeds economic value. Evaluate incremental risk-adjusted cash flows versus consideration; EPS is not NPV. Common misconception: - EPS accretion proves the deal creates value. Follow up: Can a deal be EPS-accretive but destroy value? Explain without relying only on EPS. **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Purchase accounting residual **ID:** `ma-goodwill` **Topic:** mergers **Level:** intermediate ## Prompt Consideration for all equity is250; fair value of identifiable assets330 and assumed liabilities140. Find acquired net assets and goodwill. ## Assumptions Amounts $m. No NCI, prior holding, deferred taxes or other adjustments. Consideration is equity purchase price. ## Inputs ### Original - `price`: 250 - `assets`: 330 - `liabilities`: 140 ### Retry - `price`: 310 - `assets`: 400 - `liabilities`: 160 ## Reference calculations - `netAssets`: original 190; retry 240. Formula: `assets-liabilities` - `goodwill`: original 60; retry 70. Formula: `price-(assets-liabilities)` ## Intermediate calculations - `first`: `['netAssets: 330-140 = 190', 'goodwill: 250-(330-140) = 60']` - `retry`: `['netAssets: 400-160 = 240', 'goodwill: 310-(400-160) = 70']` ## Discussion prompts - How could recognition of a new identifiable intangible and related deferred tax liability affect goodwill? - Does a larger goodwill balance automatically mean the buyer overpaid? What evidence would establish that? ## Review notes A newly recognized intangible increases identifiable assets, tending to reduce goodwill; a related DTL increases liabilities, partially offsetting that reduction. Net change depends on fair value and tax basis. Common misconception: - Subtract gross assets without liabilities or confuse equity price with EV. Follow up: How could recognition of a new identifiable intangible and related deferred tax liability affect goodwill? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json). --- # Property value and financing **ID:** `re-cap` **Topic:** real-estate **Level:** intermediate ## Prompt A fictional property produces stabilized annual NOI6.3 at a6% cap rate, with mortgage65. Estimate unlevered property value and equity value. ## Assumptions Amounts $m. NOI excludes financing, tax and depreciation. No cash, transaction costs or other claims. Cap-rate approximation, no growth forecast. ## Inputs ### Original - `noi`: 6.3 - `cap`: 0.06 - `debt`: 65 ### Retry - `noi`: 8.4 - `cap`: 0.07 - `debt`: 72 ## Reference calculations - `value`: original 105.0; retry 120.0. Formula: `noi/cap` - `equity`: original 40.0; retry 48.0. Formula: `noi/cap-debt` ## Intermediate calculations - `first`: `['value: 6.3/0.06 = 105', 'equity: 6.3/0.06-65 = 40']` - `retry`: `['value: 8.4/0.07 = 120', 'equity: 8.4/0.07-72 = 48']` ## Discussion prompts - If cap rates rise with NOI flat, what happens to property value? What other diligence would you need? - Which matters more for a proposed bid: current NOI or the reliability of stabilized NOI? Explain the diligence you would request. ## Review notes Value falls with higher cap rate and fixed positive NOI. Verify leases, occupancy, recurring capex, taxes, market rents, refinancing and whether NOI is truly stabilized. Common misconception: - Deduct mortgage interest from NOI then capitalize at an unlevered cap rate. Follow up: If cap rates rise with NOI flat, what happens to property value? What other diligence would you need? **Provenance:** Original fictional scenario and wording; standard finance concepts. Not copied from course questions. **Review status:** Formula-tested; expert review pending Numeric references support calculation practice only. They do not grade explanations or establish interview readiness. Source: [`../../question-bank.json`](../../question-bank.json).