{ "version": 1, "unitConvention": "$ millions unless stated otherwise; rates as decimals", "scope": "16 original questions; 16 parameterized retries; expert review pending", "questions": [ { "id": "ac-capex", "topic": "accounting", "title": "Equipment and cash", "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.", "parameters": { "cost": 144, "life": 6, "tax": 0.25 }, "formulas": { "depreciation": "cost/life", "netIncome": "-cost/life*(1-tax)", "cfo": "cost/life*tax", "cash": "-cost+cost/life*tax", "netPPE": "cost-cost/life", "retainedEarnings": "-cost/life*(1-tax)" }, "workedSolution": [ "Depreciation reduces pre-tax income; apply the tax shield.", "Add depreciation back to net income for CFO; record capex in CFI.", "Cash plus net PP&E movement equals retained earnings movement." ], "misconceptions": [ { "claim": "Depreciation addback creates cash independently of taxes.", "followup": "If there were no current cash tax benefit, what would happen to cash, and why?" } ], "followups": [ "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." ], "retry": { "cost": 180, "life": 6, "tax": 0.3 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "depreciation": 24.0, "netIncome": -18.0, "cfo": 6.0, "cash": -138.0, "netPPE": 120.0, "retainedEarnings": -18.0 }, "retryExpected": { "depreciation": 30.0, "netIncome": -21.0, "cfo": 9.0, "cash": -171.0, "netPPE": 150.0, "retainedEarnings": -21.0 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "depreciation: 144 \u00f7 6 = 24", "net Income: \u2212 144 \u00f7 6 \u00d7 (1 \u2212 0.25) = -18", "cfo: 144 \u00f7 6 \u00d7 0.25 = 6", "cash: \u2212 144 + 144 \u00f7 6 \u00d7 0.25 = -138", "net PPE: 144 \u2212 144 \u00f7 6 = 120", "retained Earnings: \u2212 144 \u00f7 6 \u00d7 (1 \u2212 0.25) = -18" ], "retry": [ "depreciation: 180 \u00f7 6 = 30", "net Income: \u2212 180 \u00f7 6 \u00d7 (1 \u2212 0.3) = -21", "cfo: 180 \u00f7 6 \u00d7 0.3 = 9", "cash: \u2212 180 + 180 \u00f7 6 \u00d7 0.3 = -171", "net PPE: 180 \u2212 180 \u00f7 6 = 150", "retained Earnings: \u2212 180 \u00f7 6 \u00d7 (1 \u2212 0.3) = -21" ] }, "level": "foundation", "retryPrompt": "A warehouse pays 180 in cash for equipment at the start of the year. The equipment has a 6-year straight-line life and no salvage value. At a 30% tax rate, walk through the full first-year changes across all three statements.", "retryAssumptions": "Amounts $m. Six-year straight-line life, no salvage. Book=tax depreciation. 30% tax shield usable immediately. No financing, WC or dividends. The company has sufficient other taxable income to absorb the deduction." }, { "id": "ac-ar", "topic": "accounting", "title": "Revenue that has not been collected", "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, tax 25% paid currently. No other effects.", "parameters": { "revenue": 48, "cost": 18, "tax": 0.25 }, "formulas": { "netIncome": "(revenue-cost)*(1-tax)", "cfo": "(revenue-cost)*(1-tax)-revenue", "ar": "revenue" }, "workedSolution": [ "Pre-tax profit is revenue less costs.", "CFO subtracts the increase in receivables from net income." ], "misconceptions": [ { "claim": "Revenue recognized means cash received.", "followup": "If the customer pays next period, does that create new revenue or reverse the receivable?" } ], "followups": [ "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." ], "retry": { "revenue": 60, "cost": 24, "tax": 0.25 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "netIncome": 22.5, "cfo": -25.5, "ar": 48 }, "retryExpected": { "netIncome": 27.0, "cfo": -33.0, "ar": 60 }, "followupAnswerGuide": "Collection reduces accounts receivable and increases cash/CFO. It is not new revenue or net income when previously recognized correctly.", "numericBridges": { "first": [ "net Income: (48 \u2212 18) \u00d7 (1 \u2212 0.25) = 22.5", "cfo: (48 \u2212 18) \u00d7 (1 \u2212 0.25) \u2212 48 = -25.5", "ar: 48 = 48" ], "retry": [ "net Income: (60 \u2212 24) \u00d7 (1 \u2212 0.25) = 27", "cfo: (60 \u2212 24) \u00d7 (1 \u2212 0.25) \u2212 60 = -33", "ar: 60 = 60" ] }, "level": "foundation", "retryPrompt": "A software vendor recognizes 60 of credit revenue and pays associated cash operating costs of 24. None of the revenue has been collected. At a 25% tax rate, calculate net income, CFO and the receivable created.", "retryAssumptions": "All amounts $m; no opening receivable, revenue not collected, costs paid, tax 25% paid currently. No other effects." }, { "id": "ac-deferred", "topic": "accounting", "title": "Customer prepays", "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.", "parameters": { "receipt": 72 }, "formulas": { "cash": "receipt", "deferredRevenue": "receipt", "revenue": "0", "cfo": "receipt" }, "workedSolution": [ "Cash and the contract liability rise equally.", "No service has been delivered, so no revenue is recognized yet." ], "misconceptions": [ { "claim": "Cash receipt must be revenue.", "followup": "After three of the twelve months, how much revenue and liability remain if service is even?" } ], "followups": [ "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." ], "retry": { "receipt": 96 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "cash": 72, "deferredRevenue": 72, "revenue": 0, "cfo": 72 }, "retryExpected": { "cash": 96, "deferredRevenue": 96, "revenue": 0, "cfo": 96 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "cash: 72 = 72", "deferred Revenue: 72 = 72", "revenue: 0 = 0", "cfo: 72 = 72" ], "retry": [ "cash: 96 = 96", "deferred Revenue: 96 = 96", "revenue: 0 = 0", "cfo: 96 = 96" ] }, "level": "foundation", "retryPrompt": "A customer pays 96 upfront for twelve months of evenly delivered service. At receipt, before any service is delivered, what are the effects on cash, deferred revenue, revenue and CFO?", "retryAssumptions": "Amounts $m. No tax, cost or financing effects at receipt. Treat customer advance as operating cash flow." }, { "id": "ac-inventory", "topic": "accounting", "title": "Inventory on supplier credit", "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.", "parameters": { "purchase": 36 }, "formulas": { "inventory": "purchase", "accountsPayable": "purchase", "cfo": "0" }, "workedSolution": [ "Inventory increases assets; payable increases liabilities.", "CFO has equal negative inventory and positive payable adjustments." ], "misconceptions": [ { "claim": "Inventory increase always means a cash outflow.", "followup": "What happens to CFO when the payable is subsequently paid without selling inventory?" } ], "followups": [ "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?" ], "retry": { "purchase": 52 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "inventory": 36, "accountsPayable": 36, "cfo": 0 }, "retryExpected": { "inventory": 52, "accountsPayable": 52, "cfo": 0 }, "followupAnswerGuide": "Paying the supplier reduces cash and accounts payable by 36 and creates a 36 operating cash outflow without changing inventory or net income. Retry 52.", "numericBridges": { "first": [ "inventory: 36 = 36", "accounts Payable: 36 = 36", "cfo: 0 = 0" ], "retry": [ "inventory: 52 = 52", "accounts Payable: 52 = 52", "cfo: 0 = 0" ] }, "level": "foundation", "retryPrompt": "A retailer buys 52 of inventory entirely on supplier credit. Before any sale or payment, what are the changes in inventory, accounts payable and CFO?", "retryAssumptions": "Amounts $m, no tax or other changes. Accounts payable is operating." }, { "id": "ev-bridge", "topic": "valuation", "title": "From operations to shareholders", "prompt": "A logistics company has EBITDA 84, a 7.5x EV/EBITDA multiple, debt 210, excess cash 54 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.", "parameters": { "ebitda": 84, "multiple": 7.5, "debt": 210, "cash": 54, "shares": 30 }, "formulas": { "ev": "ebitda*multiple", "equity": "ebitda*multiple-debt+cash", "price": "(ebitda*multiple-debt+cash)/shares" }, "workedSolution": [ "Apply an enterprise multiple to EBITDA.", "Subtract debt and add excess cash, then divide by diluted shares." ], "misconceptions": [ { "claim": "Adding debt increases equity value.", "followup": "If 40 of new debt is retained as cash with no other changes, what happens to equity and EV?" } ], "followups": [ "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." ], "retry": { "ebitda": 96, "multiple": 8, "debt": 250, "cash": 58, "shares": 32 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "ev": 630.0, "equity": 474.0, "price": 15.8 }, "retryExpected": { "ev": 768, "equity": 576, "price": 18.0 }, "followupAnswerGuide": "Equal debt and excess cash issuance leaves net debt, operating EV and equity value unchanged under the stated no-fee/no-repricing assumptions.", "numericBridges": { "first": [ "ev: 84 \u00d7 7.5 = 630", "equity: 84 \u00d7 7.5 \u2212 210 + 54 = 474", "price: (84 \u00d7 7.5 \u2212 210 + 54) \u00f7 30 = 15.8" ], "retry": [ "ev: 96 \u00d7 8 = 768", "equity: 96 \u00d7 8 \u2212 250 + 58 = 576", "price: (96 \u00d7 8 \u2212 250 + 58) \u00f7 32 = 18" ] }, "level": "foundation", "retryPrompt": "A logistics company has EBITDA of 96, an EV/EBITDA multiple of 8\u00d7, debt of 250, excess cash of 58, and 32 million diluted shares. Calculate EV, equity value and value per share.", "retryAssumptions": "Amounts $m except share price; no preferred, NCI or other claims. Debt at stated value." }, { "id": "ev-dilution", "topic": "valuation", "title": "Treasury stock dilution", "prompt": "A company has 50 million basic shares, 10 million options with strike 8, and stock price 20. 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.", "parameters": { "basic": 50, "options": 10, "strike": 8, "price": 20 }, "formulas": { "newShares": "options-options*strike/price", "dilutedShares": "basic+options-options*strike/price" }, "workedSolution": [ "Exercise produces proceeds; use proceeds to repurchase shares at market price.", "Only the net increment is dilution." ], "misconceptions": [ { "claim": "Every option adds one net diluted share.", "followup": "What if the strike were above the stock price?" } ], "followups": [ "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?" ], "retry": { "basic": 60, "options": 12, "strike": 10, "price": 25 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "newShares": 6.0, "dilutedShares": 56.0 }, "retryExpected": { "newShares": 7.2, "dilutedShares": 67.2 }, "followupAnswerGuide": "Out-of-the-money options add no diluted shares in treasury stock method; do not allow negative dilution.", "numericBridges": { "first": [ "new Shares: 10 \u2212 10 \u00d7 8 \u00f7 20 = 6", "diluted Shares: 50 + 10 \u2212 10 \u00d7 8 \u00f7 20 = 56" ], "retry": [ "new Shares: 12 \u2212 12 \u00d7 10 \u00f7 25 = 7.2", "diluted Shares: 60 + 12 \u2212 12 \u00d7 10 \u00f7 25 = 67.2" ] }, "level": "foundation", "retryPrompt": "A company has 60 million basic shares, 12 million in-the-money options at a $10 strike, and a $25 share price. Calculate net new shares and diluted shares with the treasury stock method.", "retryAssumptions": "All options exercisable and in the money. Ignore taxes and other dilutive securities." }, { "id": "dcf-ufcf", "topic": "dcf", "title": "Unlevered free cash flow", "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.", "parameters": { "ebit": 90, "tax": 0.25, "da": 18, "capex": 26, "nwc": 12 }, "formulas": { "ufcf": "ebit*(1-tax)+da-capex-nwc" }, "workedSolution": [ "Tax operating income, add back noncash D&A, subtract reinvestment.", "UFCF belongs to all capital providers; financing is reflected in WACC." ], "misconceptions": [ { "claim": "Subtract interest in UFCF and discount at WACC.", "followup": "Why don\u2019t we subtract interest expense? How would the cash-flow definition and discount rate change for a levered equity DCF?" } ], "followups": [ "Why don\u2019t we subtract interest expense? How would the 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?" ], "retry": { "ebit": 120, "tax": 0.3, "da": 24, "capex": 35, "nwc": 10 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "ufcf": 47.5 }, "retryExpected": { "ufcf": 63.0 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "ufcf: 90 \u00d7 (1 \u2212 0.25) + 18 \u2212 26 \u2212 12 = 47.5" ], "retry": [ "ufcf: 120 \u00d7 (1 \u2212 0.3) + 24 \u2212 35 \u2212 10 = 63" ] }, "level": "intermediate", "retryPrompt": "A company has $120 million of EBIT, $24 million of depreciation and amortization, and $35 million of capital expenditures. Its operating working capital increases by $10 million. Assume a 30% tax rate. What is its unlevered free cash flow?", "retryAssumptions": "Enter your answer in millions. Operating working capital excludes cash and financing debt." }, { "id": "dcf-terminal", "topic": "dcf", "title": "Terminal value timing", "prompt": "Year 5 UFCF is 50. Perpetual growth 2%, WACC 10%. Find terminal value at end of year 5 and its present value.", "assumptions": "Amounts $m. Gordon growth, WACC>g, no stub periods. Only discount terminal value, not explicit forecast cash flows.", "parameters": { "fcf": 50, "g": 0.02, "wacc": 0.1, "years": 5 }, "formulas": { "terminal": "fcf*(1+g)/(wacc-g)", "pv": "fcf*(1+g)/(wacc-g)/(1+wacc)**years" }, "workedSolution": [ "Grow year5 cash flow once to obtain year6.", "The terminal value sits at end of year5; discount five years." ], "misconceptions": [ { "claim": "Use year5 FCF directly or discount terminal value six years.", "followup": "What breaks when growth approaches or exceeds WACC?" } ], "followups": [ "What breaks when growth approaches or exceeds WACC?", "How would you challenge a valuation dominated by terminal value before recommending a bid?" ], "retry": { "fcf": 65, "g": 0.025, "wacc": 0.11, "years": 5 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "terminal": 637.5, "pv": 395.8373434502113 }, "retryExpected": { "terminal": 783.8235294117648, "pv": 465.1611144929584 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "terminal: 50 \u00d7 (1 + 0.02) \u00f7 (0.1 \u2212 0.02) = 637.5", "pv: 50 \u00d7 (1 + 0.02) \u00f7 (0.1 \u2212 0.02) \u00f7 (1 + 0.1) ^ 5 = 395.837" ], "retry": [ "terminal: 65 \u00d7 (1 + 0.025) \u00f7 (0.11 \u2212 0.025) = 783.824", "pv: 65 \u00d7 (1 + 0.025) \u00f7 (0.11 \u2212 0.025) \u00f7 (1 + 0.11) ^ 5 = 465.161" ] }, "level": "intermediate", "retryPrompt": "Year 5 UFCF is 65. Perpetual growth is 2.5% and WACC is 11%. Calculate terminal value at the end of year 5, and its present value today.", "retryAssumptions": "Amounts $m. Gordon growth, WACC>g, no stub periods. Only discount terminal value, not explicit forecast cash flows." }, { "id": "dcf-wacc", "topic": "dcf", "title": "Cost of capital", "prompt": "Equity weight 70%, debt 30%, cost of equity 12%, pre-tax debt cost 6%, tax 25%. Calculate WACC.", "assumptions": "Fixed market-value weights; interest deduction usable; no preferred stock. Enter WACC as decimal, not percentage points.", "parameters": { "e": 0.7, "d": 0.3, "ke": 0.12, "kd": 0.06, "tax": 0.25 }, "formulas": { "wacc": "e*ke+d*kd*(1-tax)" }, "workedSolution": [ "Use market-value capital weights.", "Tax-effect only cost of debt." ], "misconceptions": [ { "claim": "Apply a tax discount to equity or use book equity weights.", "followup": "Why might increasing debt eventually raise WACC rather than always reduce it?" } ], "followups": [ "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." ], "retry": { "e": 0.6, "d": 0.4, "ke": 0.14, "kd": 0.07, "tax": 0.3 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "wacc": 0.09749999999999999 }, "retryExpected": { "wacc": 0.10360000000000001 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "wacc: 0.7 \u00d7 0.12 + 0.3 \u00d7 0.06 \u00d7 (1 \u2212 0.25) = 0.0975" ], "retry": [ "wacc: 0.6 \u00d7 0.14 + 0.4 \u00d7 0.07 \u00d7 (1 \u2212 0.3) = 0.1036" ] }, "level": "intermediate", "retryPrompt": "Market-value capital weights are 60% equity and 40% debt. Cost of equity is 14%, pre-tax cost of debt is 7%, and tax is 30%. Calculate WACC.", "retryAssumptions": "Fixed market-value weights; interest deduction usable; no preferred stock. Enter WACC as decimal, not percentage points." }, { "id": "comps-normalize", "topic": "comparables", "title": "Normalize EBITDA", "prompt": "Reported EBITDA is 64 after a one-time cash litigation expense 9. Normalize EBITDA and calculate implied EV at 8x.", "assumptions": "Amounts $m. Expense is included in EBITDA and genuinely nonrecurring. No other adjustments.", "parameters": { "reported": 64, "expense": 9, "multiple": 8 }, "formulas": { "normalized": "reported+expense", "ev": "(reported+expense)*multiple" }, "workedSolution": [ "Add back a genuinely nonrecurring EBITDA expense.", "Apply the multiple consistently to the normalized metric." ], "misconceptions": [ { "claim": "Add back every cost labeled exceptional.", "followup": "What evidence would you need before accepting management\u2019s recurring restructuring addback?" } ], "followups": [ "What evidence would you need before accepting management\u2019s recurring restructuring addback?", "How would your recommendation change if the same supposedly one-off expense appeared in each of the last three years?" ], "retry": { "reported": 78, "expense": 6, "multiple": 7.5 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "normalized": 73, "ev": 584 }, "retryExpected": { "normalized": 84, "ev": 630.0 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "normalized: 64 + 9 = 73", "ev: (64 + 9) \u00d7 8 = 584" ], "retry": [ "normalized: 78 + 6 = 84", "ev: (78 + 6) \u00d7 7.5 = 630" ] }, "level": "intermediate", "retryPrompt": "Reported EBITDA is 78, after an included genuinely one-time litigation expense of 6. Calculate normalized EBITDA and implied EV at 7.5\u00d7.", "retryAssumptions": "Amounts $m. Expense is included in EBITDA and genuinely nonrecurring. No other adjustments." }, { "id": "ma-eps", "topic": "mergers", "title": "Cash acquisition EPS", "prompt": "Acquirer net income 120, shares 40. Target net income 24. Cash purchase 300 funded from excess cash earning 4% pre-tax. Tax 25%. 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.", "parameters": { "ani": 120, "shares": 40, "tni": 24, "price": 300, "rate": 0.04, "tax": 0.25 }, "formulas": { "standalone": "ani/shares", "proforma": "(ani+tni-price*rate*(1-tax))/shares", "accretion": "((ani+tni-price*rate*(1-tax))/shares)/(ani/shares)-1" }, "workedSolution": [ "Subtract after-tax foregone interest from combined earnings.", "Divide by unchanged shares; compare to standalone EPS." ], "misconceptions": [ { "claim": "EPS accretion proves the deal creates value.", "followup": "Can a deal be EPS-accretive but destroy value? Explain without relying only on EPS." } ], "followups": [ "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." ], "retry": { "ani": 150, "shares": 50, "tni": 30, "price": 400, "rate": 0.05, "tax": 0.25 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "standalone": 3.0, "proforma": 3.375, "accretion": 0.125 }, "retryExpected": { "standalone": 3.0, "proforma": 3.3, "accretion": 0.09999999999999987 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "standalone: 120 \u00f7 40 = 3", "proforma: (120 + 24 \u2212 300 \u00d7 0.04 \u00d7 (1 \u2212 0.25)) \u00f7 40 = 3.375", "accretion: ((120 + 24 \u2212 300 \u00d7 0.04 \u00d7 (1 \u2212 0.25)) \u00f7 40) \u00f7 (120 \u00f7 40) \u2212 1 = 0.125" ], "retry": [ "standalone: 150 \u00f7 50 = 3", "proforma: (150 + 30 \u2212 400 \u00d7 0.05 \u00d7 (1 \u2212 0.25)) \u00f7 50 = 3.3", "accretion: ((150 + 30 \u2212 400 \u00d7 0.05 \u00d7 (1 \u2212 0.25)) \u00f7 50) \u00f7 (150 \u00f7 50) \u2212 1 = 0.1" ] }, "level": "intermediate", "retryPrompt": "The acquirer has net income of 150 and 50 million shares. Target net income is 30. A cash purchase of 400 uses excess cash earning 5% pre-tax, with a 25% tax rate. Calculate standalone EPS, pro forma EPS and accretion.", "retryAssumptions": "Amounts $m. Full-year ownership, no synergies, fees, purchase accounting amortization or new shares. Enter accretion as decimal." }, { "id": "ma-goodwill", "topic": "mergers", "title": "Purchase accounting residual", "prompt": "Consideration for all equity is 250; fair value of identifiable assets 330 and assumed liabilities 140. Find acquired net assets and goodwill.", "assumptions": "Amounts $m. No NCI, prior holding, deferred taxes or other adjustments. Consideration is equity purchase price.", "parameters": { "price": 250, "assets": 330, "liabilities": 140 }, "formulas": { "netAssets": "assets-liabilities", "goodwill": "price-(assets-liabilities)" }, "workedSolution": [ "Goodwill is the residual over fair value of identifiable net assets." ], "misconceptions": [ { "claim": "Subtract gross assets without liabilities or confuse equity price with EV.", "followup": "How could recognition of a new identifiable intangible and related deferred tax liability affect goodwill?" } ], "followups": [ "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?" ], "retry": { "price": 310, "assets": 400, "liabilities": 160 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "netAssets": 190, "goodwill": 60 }, "retryExpected": { "netAssets": 240, "goodwill": 70 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "net Assets: 330 \u2212 140 = 190", "goodwill: 250 \u2212 (330 \u2212 140) = 60" ], "retry": [ "net Assets: 400 \u2212 160 = 240", "goodwill: 310 \u2212 (400 \u2212 160) = 70" ] }, "level": "intermediate", "retryPrompt": "The buyer pays 310 for all equity. Identifiable assets have fair value of 400, with assumed liabilities of 160. Calculate identifiable net assets and goodwill.", "retryAssumptions": "Amounts $m. No NCI, prior holding, deferred taxes or other adjustments. Consideration is equity purchase price." }, { "id": "lbo-return", "topic": "lbo", "title": "Exit equity and sponsor return", "prompt": "Entry EV 500 funded with debt 300 and sponsor equity 200. At exit after five years EV 600, debt 180, no excess cash. Find equity proceeds, MOIC and IRR.", "assumptions": "Amounts $m. No interim distributions, fees, other claims or additional equity. IRR as decimal.", "parameters": { "ev": 600, "debt": 180, "entryEquity": 200, "years": 5 }, "formulas": { "proceeds": "ev-debt", "moic": "(ev-debt)/entryEquity", "irr": "((ev-debt)/entryEquity)**(1/years)-1" }, "workedSolution": [ "Exit equity is EV less remaining debt.", "MOIC ignores timing; IRR annualizes the return." ], "misconceptions": [ { "claim": "Use EV growth as the equity return or divide MOIC by years.", "followup": "If MOIC stays fixed but holding period shortens, what happens to IRR?" } ], "followups": [ "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." ], "retry": { "ev": 720, "debt": 160, "entryEquity": 250, "years": 4 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "proceeds": 420, "moic": 2.1, "irr": 0.15996225865400127 }, "retryExpected": { "proceeds": 560, "moic": 2.24, "irr": 0.2233817698125049 }, "followupAnswerGuide": "For a fixed MOIC greater than 1 and no interim cash flows, shorter duration increases annualized IRR. State assumptions; IRR and MOIC measure different dimensions.", "numericBridges": { "first": [ "proceeds: 600 \u2212 180 = 420", "moic: (600 \u2212 180) \u00f7 200 = 2.1", "irr: ((600 \u2212 180) \u00f7 200) ^ (1 \u00f7 5) \u2212 1 = 0.159962" ], "retry": [ "proceeds: 720 \u2212 160 = 560", "moic: (720 \u2212 160) \u00f7 250 = 2.24", "irr: ((720 \u2212 160) \u00f7 250) ^ (1 \u00f7 4) \u2212 1 = 0.223382" ] }, "level": "intermediate", "retryPrompt": "The sponsor invests 250 of equity. After 4 years, exit EV is 720, remaining debt is 160, and excess cash is zero. Calculate equity proceeds, MOIC and IRR.", "retryAssumptions": "Amounts $m. No interim distributions, fees, other claims or additional equity. IRR as decimal." }, { "id": "lbo-debt", "topic": "lbo", "title": "Cash available for debt paydown", "prompt": "An LBO generates EBITDA 80, cash interest 20, cash taxes 10, capex 15, increase in NWC 5. 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.", "parameters": { "ebitda": 80, "interest": 20, "taxes": 10, "capex": 15, "nwc": 5 }, "formulas": { "paydown": "ebitda-interest-taxes-capex-nwc" }, "workedSolution": [ "Move from EBITDA to actual cash after financing costs, taxes and reinvestment." ], "misconceptions": [ { "claim": "EBITDA is cash available to repay debt.", "followup": "What if a minimum cash covenant requires retaining 8 of this cash?" } ], "followups": [ "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." ], "retry": { "ebitda": 100, "interest": 26, "taxes": 12, "capex": 18, "nwc": 7 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "paydown": 30 }, "retryExpected": { "paydown": 37 }, "followupAnswerGuide": "Retaining 8 reduces optional paydown from 30 to 22 on the original inputs; the retry generates 37 and leaves 29 if the same minimum-cash increment applies.", "numericBridges": { "first": [ "paydown: 80 \u2212 20 \u2212 10 \u2212 15 \u2212 5 = 30" ], "retry": [ "paydown: 100 \u2212 26 \u2212 12 \u2212 18 \u2212 7 = 37" ] }, "level": "intermediate", "retryPrompt": "EBITDA is 100, cash interest is 26, cash taxes are 12, capex is 18, and operating NWC increases by 7. Calculate cash available for optional debt paydown.", "retryAssumptions": "Amounts $m. No other cash flows, mandatory amortization, fees or minimum cash requirement. D&A irrelevant because cash taxes given." }, { "id": "bank-pb", "topic": "financial-institutions", "title": "Bank price to book", "prompt": "A bank has common equity book value 900 and 90 million shares. A comparable P/B multiple is 1.3x. 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.", "parameters": { "book": 900, "shares": 90, "multiple": 1.3 }, "formulas": { "equity": "book*multiple", "price": "book*multiple/shares" }, "workedSolution": [ "P/B is an equity multiple, so it directly implies equity value." ], "misconceptions": [ { "claim": "Subtract bank deposits as ordinary corporate net debt from P/B value.", "followup": "Why are EV/EBITDA and industrial-company net-debt bridges often poor starting points for banks?" } ], "followups": [ "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?" ], "retry": { "book": 1200, "shares": 100, "multiple": 1.1 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "equity": 1170.0, "price": 13.0 }, "retryExpected": { "equity": 1320.0, "price": 13.2 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "equity: 900 \u00d7 1.3 = 1170", "price: 900 \u00d7 1.3 \u00f7 90 = 13" ], "retry": [ "equity: 1200 \u00d7 1.1 = 1320", "price: 1200 \u00d7 1.1 \u00f7 100 = 13.2" ] }, "level": "intermediate", "retryPrompt": "A bank has common book equity of 1200, 100 million common shares, and an illustrative P/B multiple of 1.1\u00d7. Calculate implied common equity value and share price.", "retryAssumptions": "Amounts $m. Book equity is common equity, with no preferred or other adjustments. Illustrative comparable, not investment advice." }, { "id": "re-cap", "topic": "real-estate", "title": "Property value and financing", "prompt": "A fictional property produces stabilized annual NOI 6.3 at a 6% cap rate, with mortgage 65. 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.", "parameters": { "noi": 6.3, "cap": 0.06, "debt": 65 }, "formulas": { "value": "noi/cap", "equity": "noi/cap-debt" }, "workedSolution": [ "Capitalize stabilized unlevered NOI; subtract mortgage for equity." ], "misconceptions": [ { "claim": "Deduct mortgage interest from NOI then capitalize at an unlevered cap rate.", "followup": "If cap rates rise with NOI flat, what happens to property value? What other diligence would you need?" } ], "followups": [ "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." ], "retry": { "noi": 8.4, "cap": 0.07, "debt": 72 }, "provenance": "Original fictional scenario and wording; standard finance concepts. Not copied from course questions.", "reviewStatus": "Formula-tested; expert review pending", "expected": { "value": 105.0, "equity": 40.0 }, "retryExpected": { "value": 120.0, "equity": 48.0 }, "followupAnswerGuide": "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.", "numericBridges": { "first": [ "value: 6.3 \u00f7 0.06 = 105", "equity: 6.3 \u00f7 0.06 \u2212 65 = 40" ], "retry": [ "value: 8.4 \u00f7 0.07 = 120", "equity: 8.4 \u00f7 0.07 \u2212 72 = 48" ] }, "level": "intermediate", "retryPrompt": "A fictional property has stabilized annual NOI of 8.4, a 7% cap rate, and a mortgage balance of 72. Calculate unlevered property value and equity value.", "retryAssumptions": "Amounts $m. NOI excludes financing, tax and depreciation. No cash, transaction costs or other claims. Cap-rate approximation, no growth forecast." } ] }