The calculation-heavy chapters of NISM Series XV (8, 9, 10, 12 and 15) carry 51 of the 100 marks. Take one of the two free 20-question numerical tests below (you need a free account), then use the formula sheet to fix whatever you got wrong. Scoring copies the real exam: +1 for a correct answer, −0.25 for a wrong one.
Two free 20-question tests, 40 different calculation questions in all: ratios, valuation, corporate actions, risk and return, technical analysis and more. Every answer comes with the formula, the working and the common mistake when you finish.
NISM publishes the marks for each chapter but not how many questions are numerical, so use the chapter marks below as your guide. The last column shows how many numerical questions BullWiser has written for each chapter (200 in the full bank, 40 of them in the two free tests).
| Chapter | NISM marks | What gets calculated | Our questions |
|---|---|---|---|
| 3. Terminology | 2 | Market cap, enterprise value, EPS, dividend yield, bond current yield | 20 |
| 5. Economic Analysis | 5 | Inflation, real rates, GDP, fiscal deficit, CRR, multiplier | 10 |
| 6. Industry Analysis | 8 | Market share, HHI, capacity utilisation, industry growth | 5 |
| 8. Financial Analysis | 12 | Liquidity, leverage, DuPont, working-capital days, free cash flow | 40 |
| 9. Corporate Actions | 5 | Bonus, split, rights issue, buyback, ex-dividend price | 15 |
| 10. Valuation Principles | 12 | DDM, CAPM, WACC, DCF, terminal value, multiples | 45 |
| 11. Commodities | 5 | Cost of carry, basis, cash-and-carry arbitrage | 5 |
| 12. Risk and Return | 7 | Returns, standard deviation, beta, Sharpe, Treynor, alpha | 25 |
| 15. Technical Analysis | 15 | Moving averages, RSI, pivots, Fibonacci, pattern targets, position size | 35 |
Marks are from NISM's Series XV syllabus outline. Chapters 1, 2, 4, 7, 13 and 14 are theory chapters, so they have no numerical set here.
Most formulas below are tested in the practice questions, with one worked example each. Amounts are in Rs crore unless stated.
| Measure | Formula | Worked example |
|---|---|---|
| Current ratio | Current assets / Current liabilities | 540 / 300 = 1.80 times |
| Quick ratio | (Current assets − Inventory) / Current liabilities | (540 − 180) / 300 = 1.20 times |
| Debt-equity | Total debt / Shareholders' equity | 480 / 800 = 0.60 times |
| Interest coverage | EBIT / Interest expense | 180 / 30 = 6.0 times |
| ROE | PAT / Average equity | 60 / ((500 + 560)/2) = 11.32% |
| ROCE | EBIT / Capital employed (Equity + Long-term debt, or Total assets − Current liabilities) | 120 / 800 = 15.0% |
| DuPont ROE | Net margin x Asset turnover x Equity multiplier (same basis as ROE: average or closing) | 12% x 1.5 x 2.5 = 45% |
| Inventory days | 365 / (COGS / Average inventory) | 365 / (1,460 / 200) = 50 days |
| Receivable days | Receivables / Sales x 365 (Payable days = Payables / COGS x 365) | 360 / 2,190 x 365 = 60 days |
| Cash conversion cycle | Inventory days + Receivable days − Payable days | 90 + 40 − 50 = 80 days |
| Free cash flow | Cash flow from operations − Capex | 300 − 120 = 180 |
| Sustainable growth | ROE x Retention ratio | 15% x 75% = 11.25% |
| Measure | Formula | Worked example |
|---|---|---|
| Enterprise value | Market cap + Preferred + Minority interest + Debt − (Cash + Non-operating investments) | 750 + 24 + 60 − 30 − 6 = 798 |
| Dividend per share | Dividend % x Face value | 30% x Rs 2 = Rs 0.60 |
| EPS | (PAT − Preference dividend) / Equity shares | (72 − 8) / 15 = Rs 4.27 |
| Bond current yield | Annual coupon / Market price | 95 / 1,060 = 8.96% |
| Ex-bonus price | Cum price x Existing / (Existing + Bonus) | 1 bonus share for every 2 held (1:2), cum price Rs 600: 600 x 2/3 = Rs 400 |
| Post-split price | Price / (Old face value / New face value) | Rs 10 to Rs 5 at Rs 750: Rs 375 |
| Theoretical ex-rights price | (Existing x Market price + New x Issue price) / Total shares | (5 x 230 + 1 x 150) / 6 = Rs 216.67 |
| Value of a right (per existing share) | Cum-rights price − TERP | 230 − 216.67 = Rs 13.33 |
| EPS after buyback | PAT / (Shares − Shares bought back) | 400 / (20 − 4) = Rs 25 |
| Measure | Formula | Worked example |
|---|---|---|
| Target price | Forward EPS x Target P/E | 24 x 18 = Rs 432 |
| PEG ratio | P/E / Growth rate (%) | 24 / 20 = 1.2 |
| Gordon growth (DDM) | D0 (1 + g) / (ke − g) | 5 x 1.05 / (13% − 5%) = Rs 65.63 |
| CAPM | ke = rf + Beta x (Rm − rf) | 6% + 1.25 x (11% − 6%) = 12.25% |
| WACC | E/V x ke + D/V x kd x (1 − tax) | 0.7 x 15% + 0.3 x 8% x 0.7 = 12.18% |
| Terminal value | Final-year FCF x (1 + g) / (WACC − g) | 80 x 1.06 / (12% − 6%) = 1,413.3 |
| FCFF | EBIT (1 − t) + Depreciation − Capex − Increase in NWC | 400 x 0.75 + 60 − 180 − 30 = 150 |
| FCFE | Net income + Depreciation − Capex − Increase in NWC + Net borrowing | 200 + 50 − 60 − 10 + 40 = 220 |
| EV/EBITDA value per share | (Multiple x EBITDA − Net debt) / Shares | (10 x 250 − 300) / 10 = Rs 220 |
| Justified P/B | (ROE − g) / (ke − g) | (18% − 6%) / (13% − 6%) = 1.71 |
| Justified forward P/E | Payout ratio / (ke − g) | 0.60 / (10% − 6%) = 15 |
| Bond price | Sum of coupon / (1 + y)^t + Face / (1 + y)^n | Rs 100, 8% coupon, 3 years, 10% yield: Rs 95.03 |
| Margin of safety | (Intrinsic value − Price) / Intrinsic value | (500 − 350) / 500 = 30% |
| Measure | Formula | Worked example |
|---|---|---|
| Holding period return | (Sale price − Purchase price + Dividend) / Purchase price | (440 − 400 + 8) / 400 = 12% |
| CAGR | (End value / Start value)^(1/n) − 1 | Rs 1,00,000 to Rs 1,36,800 in 3 years: 11.01% |
| Geometric mean return | [(1 + r1)(1 + r2)...(1 + rn)]^(1/n) − 1 | +25%, −15%, +20%: 8.44% |
| Expected return | Sum of probability x return | 0.4 x 18 + 0.4 x 9 + 0.2 x (−3) = 10.2% |
| Standard deviation (population) | Square root of (Sum of squared deviations / n) | 5, 9, 13, 17: mean 11, variance 20, SD 4.47% (sample SD divides by n − 1: 5.16%) |
| Beta | Covariance (stock, market) / Variance (market) | 270 / 225 = 1.20 |
| Sharpe ratio | (Rp − Rf) / Standard deviation | (18 − 6) / 10 = 1.20 |
| Treynor ratio | (Rp − Rf) / Beta | (14 − 7) / 1.5 = 4.67 |
| Jensen's alpha | Rp − [rf + Beta x (Rm − rf)] | 14 − [7 + 0.9 x 8] = −0.20 percentage points |
| Two-asset portfolio risk | Square root of (w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2) | 60/40, 12% and 20%, ρ = 0.5: 13.17% |
| Real return (Fisher) | (1 + nominal) / (1 + inflation) − 1 | 1.11 / 1.05 − 1 = 5.71%. Approximation: 11 − 5 = 6%; if both appear, pick the option closest to the exact figure |
| Coefficient of variation | Standard deviation / Mean return | 18 / 16 = 1.125 |
| Measure | Formula | Worked example |
|---|---|---|
| Simple moving average | Sum of closing prices / n | (316 + 323 + 304 + 319 + 314) / 5 = 315.2 |
| Exponential moving average | Close x k + Previous EMA x (1 − k), k = 2 / (n + 1) | 9-day, k = 0.2: 220 x 0.2 + 210 x 0.8 = 212 |
| RSI | 100 − 100 / (1 + RS), RS = Average gain / Average loss | RS = 2.4 / 0.6 = 4: RSI = 80 |
| Pivot, S1, R1 | P = (H + L + C) / 3; S1 = 2P − H; R1 = 2P − L | H 612, L 594, C 600: P = 602, S1 = 592, R1 = 610 |
| Fibonacci retracement | High − (High − Low) x 38.2% / 50% / 61.8% | 200 to 350: 350 − 150 x 0.618 = 257.30 |
| Head-and-shoulders target | Neckline − (Head − Neckline) | Head 450, neckline 400: 350 |
| Rectangle breakout target | Resistance + (Resistance − Support) for an upside breakout; Support − height for a downside break | Support 360, resistance 390: 420 |
| Bollinger Bands | SMA +/− 2 x Standard deviation | SMA 240, SD 8: 224 to 256 |
| MACD line | 12-day EMA − 26-day EMA | 455.2 − 451.4 = 3.8 |
| Rate of change | (Close − Close n days ago) / Close n days ago x 100 | (475 − 450) / 450 = 5.56% |
| Stochastic %K | (Close − Lowest low) / (Highest high − Lowest low) x 100 | (315 − 300) / (360 − 300) = 25 |
| True range | Greatest of (H − L), |H − Prev close|, |L − Prev close| | Prev close 250, H 262, L 254: 12 |
| On-balance volume | Add volume on up-closes, subtract on down-closes | +3L − 2L + 4L − 3L = +2 lakh shares |
| Reward-to-risk | (Target − Entry) / (Entry − Stop-loss) | (240 − 200) / (200 − 190) = 4 : 1 |
| Position size | (Capital x Risk %) / (Entry − Stop-loss) | (5,00,000 x 2%) / 20 = 500 shares |
| Measure | Formula | Worked example |
|---|---|---|
| Inflation from an index | (CPI this year − CPI last year) / CPI last year | (160.9 − 152.4) / 152.4 = 5.58% |
| Real GDP growth | (1 + nominal growth) / (1 + deflator inflation) − 1 | 1.12 / 1.05 − 1 = 6.67% |
| GDP at market prices | GVA at basic prices + Product taxes − Product subsidies | 220 + 22 − 10 = 232 lakh crore |
| Investment multiplier | 1 / (1 − MPC) | MPC 0.9: 10, so Rs 800 cr adds Rs 8,000 cr |
| Cash reserve requirement | CRR x NDTL | Illustrative 3% x 18,00,000 = 54,000 crore (the RBI changes CRR, so use the rate given in the question) |
| HHI | Sum of squared market shares (in %, scale 0 to 10,000) | 45, 25, 20, 10: 3,150 |
| Capacity utilisation | Actual output / Installed capacity | 9 / 12 = 75% |
| Cost-of-carry futures price | Spot + Storage + Financing cost | 8,000 + 300 + 320 = 8,620 |
| Basis | Spot price − Futures price | 62,400 − 62,700 = −300 (negative basis = contango). Some texts define basis as futures minus spot, so follow the question |
The solved-examples page gives the formula, solved questions from the free test, extra worked examples and the mistakes that cost marks for each topic below.
Spoiler warning: if you want to test yourself first, take the tests above before reading the tables. Each row links to the full method where we have a solved-examples section for that topic.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 3 | Book value per share and P/B | 3.94 times | Shares = 60 ÷ 10 = 6 crore. Net worth = 60 + 260 = Rs 320 crore. Book value per share = 320 ÷ 6 = Rs 53.33. P/B = 210 ÷ 53.33 = 3.94 times. |
| 3 | Price-to-earnings ratio | Rs. 264 | 22 × 12 = Rs 264. |
| 5 | Real interest rate | 4.81% | 1.09 ÷ 1.04 − 1 = 1.0481 − 1 = 4.81%. |
| 8 | Free cash flow | Rs. 520 crore | 640 − 120 = Rs 520 crore. |
| 8 | Interest coverage ratio | 2.67 times | 240 ÷ 90 = 2.67 times. |
| 8 | Return on equity | 12.50% | Average equity = (700 + 740) ÷ 2 = 720. ROE = 90 ÷ 720 = 12.50%. |
| 8 | Fixed asset and total asset turnover | 2.00 times | 2,400 ÷ 1,200 = 2.00 times. |
| 9 | Holding after bonus | 240 shares | Bonus shares = 200 × 1 ÷ 5 = 40. Total = 200 + 40 = 240 shares. |
| 9 | Stock split | Rs. 375.00 | 10 ÷ 5 = 2, so each share becomes 2 shares. 750 ÷ 2 = Rs 375. |
| 10 | CAPM cost of equity | 12.25% | 6% + 1.25 × (11% − 6%) = 6% + 6.25% = 12.25%. |
| 10 | EV/Sales multiple | Rs. 80.00 | EV = 1.5 × 800 = 1,200. Equity value = 1,200 − 400 = 800. Per share = 800 ÷ 10 = Rs 80. |
| 10 | Margin of safety | 30.0% | (600 − 420) ÷ 600 = 180 ÷ 600 = 30.0%. |
| 10 | PEG ratio | 0.90 times | 18 ÷ 20 = 0.90. |
| 11 | Contango and backwardation identification | Contango, with a positive cost of carry reflected in the higher deferred prices | 84 < 86 < 88, so the curve slopes upward: contango. The higher deferred prices reflect the cost of carry (storage, insurance and financing). |
| 12 | Portfolio expected return | 7.50% | 0.25 × 12% + 0.75 × 6% = 3.00% + 4.50% = 7.50%. |
| 12 | Sharpe ratio | 1.20 | (18 − 6) ÷ 10 = 1.20. |
| 12 | Treynor ratio | 8.75 | (14 − 7) ÷ 0.8 = 8.75 percentage points per unit of beta. |
| 15 | Pivot points | Rs. 610.00 | P = (612 + 594 + 600) ÷ 3 = 602.00. S1 = 2P − H = 592.00. R1 = 2P − L = 610.00. |
| 15 | Rectangle breakout target | Rs. 220 | Height = 200 − 180 = 20. Target = 200 + 20 = Rs 220. |
| 15 | Percentage retracement and support break | Rs. 450 | 500 × (1 − 0.10) = Rs 450. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 3 | Current yield of a bond | 7.21% | Annual coupon = 7.5% × 1,000 = Rs 75. Current yield = 75 ÷ 1,040 = 7.21%. |
| 3 | Enterprise value | Rs. 798.0 crore | 750 + 24 + 60 − 30 − 6 = Rs 798 crore. |
| 5 | Inflation from a price index | 5.58% | (160.9 − 152.4) ÷ 152.4 = 8.5 ÷ 152.4 = 5.58%. |
| 6 | Herfindahl-Hirschman Index | 3,150 | 45² + 25² + 20² + 10² = 2,025 + 625 + 400 + 100 = 3,150. |
| 8 | Cash conversion cycle | 80 days | 75 + 50 − 45 = 80 days. |
| 8 | Current ratio | 1.93 times | 540 ÷ 280 = 1.93 times. |
| 8 | DuPont analysis | 45.0% | 12% × 1.5 × 2.5 = 45.0%. |
| 8 | Return on capital employed | 10.91% | Capital employed = 800 + 300 = 1,100. ROCE = 120 ÷ 1,100 = 10.91%. |
| 9 | Ex-bonus price | Rs. 428.57 | A 2:5 bonus means 5 shares become 7. 600 × 5 ÷ 7 = Rs 428.57. |
| 9 | Rights issue TERP | Rs. 126.67 | Take 2 existing shares and 1 new share. (2 × 140 + 1 × 100) ÷ 3 = 380 ÷ 3 = Rs 126.67. |
| 10 | EV/EBITDA valuation | Rs. 84.00 | EV = 8 × 300 = 2,400. Equity value = 2,400 − 300 = 2,100. Per share = 2,100 ÷ 25 = Rs 84. |
| 10 | Gordon growth model | Rs. 106.00 | D1 = 8 × 1.06 = 8.48. Value = 8.48 ÷ (14% − 6%) = 8.48 ÷ 0.08 = Rs 106. |
| 10 | Terminal value | Rs. 1,040.0 crore | 80 × 1.04 ÷ (12% − 4%) = 83.2 ÷ 0.08 = Rs 1,040 crore. |
| 10 | WACC | 11.20% | 0.70 × 13% + 0.30 × 10% × (1 − 0.30) = 9.10% + 2.10% = 11.20%. |
| 11 | Cost of carry futures price | Rs. 8,620.00 | Storage = 50 × 6 = 300. Financing = 8,000 × 8% × 6/12 = 320. Futures price = 8,000 + 300 + 320 = Rs 8,620. |
| 12 | CAGR of an investment | 9.01% | 1,41,200 ÷ 1,00,000 = 1.412. 1.412^(1/4) = 1.0901. CAGR = 9.01%. |
| 12 | Jensen alpha | -0.20% | Required return = 7% + 0.9 × (15% − 7%) = 7% + 7.2% = 14.20%. Alpha = 14% − 14.20% = −0.20%. |
| 12 | Standard deviation of returns | 4.47% | Mean = (5 + 9 + 13 + 17) ÷ 4 = 11. Squared deviations = 36 + 4 + 4 + 36 = 80. Variance = 80 ÷ 4 = 20. SD = √20 = 4.47%. |
| 15 | Fibonacci retracement | Rs. 257.30 | Range = 350 − 200 = 150. 350 − 150 × 0.618 = 350 − 92.70 = Rs 257.30. |
| 15 | Relative Strength Index | 80.0 | RS = 2.40 ÷ 0.60 = 4. RSI = 100 − 100 ÷ 5 = 100 − 20 = 80. |
Yes. Chapters such as Financial Analysis, Valuation Principles, Corporate Actions, Risk and Return and Technical Analysis need calculations, and together they carry 51 of the 100 marks. NISM does not publish how many questions are numerical. The 5 case-based sets of 4 questions each may also involve calculations.
NISM's general candidate instructions say candidates may bring their own physical calculator, which must be silent and have no connectivity, and that rough sheets are provided by the invigilator. The Series XV pages do not mention calculators separately, so confirm the rules in your registration or admit instructions before exam day.
The pass mark is 60 out of 100 and the exam lasts 120 minutes. Each wrong answer costs 25% of the question's marks, so 0.25 for a 1-mark question. Unanswered questions score zero.
You get 1 mark for each correct answer and lose 0.25 for each wrong answer, the same scheme as the exam. Skipped questions score zero.
Yes. Two 20-question numerical tests (40 solved questions) are free with a free BullWiser account, which takes a few seconds to create. The full bank of 200 numerical questions, served 25 at a time and favouring questions you have not seen, comes with BullWiser XV mock access, a one-time payment of Rs 199 per series.
Yes. Yes. Every question in the two free tests shows the correct answer, the formula, the step-by-step working and the common mistake when you finish. The solutions are also published on this page, so you can read them without taking the test.
Learn the formula for each topic, work through solved examples, then practise under exam scoring. BullWiser's solved-examples page covers each numerical topic (Sharpe and Treynor ratios, CAPM, valuation multiples, financial ratios, bonus, split and rights issues, pivot points and breakout targets, contango and backwardation, and the Fisher equation) with the formula, solved questions and the mistakes that cost marks.
No. BullWiser prepared them from the standard formulas taught in the NISM workbook, and each has a worked explanation. BullWiser is not affiliated with NISM.
Take the full-length XV mock (free first attempt, 80 MCQs and 5 case sets), read the XV notes and question bank, or start with the chapters that carry the most numericals: Technical Analysis, Valuation Principles and Financial Analysis.