Skip to content

Drill — speed ratios & mental maths

Why this drill: in a meeting, on a call or reading a results release, you rarely have time to open a spreadsheet. Analysts who can compute a margin, a CAGR, an implied multiple or a dilution in their heads catch errors and spot opportunities in real time. The arithmetic is simple; speed and accuracy come from practice.

Take: any time; repeat monthly. Format: four rounds of eleven questions, 6 minutes per round, no calculator (pen and paper allowed). Score one mark per answer within 2% (or the stated rounding) of the key. Target: 36/44 in under 24 minutes. Record your score and time in your learning journal and retake the rounds you miss.

Tools you will want in your head

Rule of 72 (doubling time ≈ 72 ÷ rate); \(1.1^{n}\) for n = 2, 3, 5, 7, 10 (1.21, 1.33, 1.61, 1.95, 2.59); \(1.15^{5} ≈ 2.0\); \(1.2^{5} ≈ 2.5\); a fall of x needs a rise of x/(1 − x) to recover; earnings yield = 1/P/E; value of a growing perpetuity = CF₁/(r − g); duration ≈ 1/(r − g); P/B = P/E × RoE.

Round A — margins, percentages and per-share (6 minutes)

  1. Revenue ₹1,250 Cr, EBITDA ₹175 Cr. EBITDA margin?
  2. Gross margin 38%, opex 24% of sales, D&A 4% of sales. EBIT margin?
  3. Sales rise 10%; costs (80% of sales) rise 8%. EBIT growth from a 20% margin base?
  4. Fixed costs 30, variable costs 50% of sales. Sales go from 100 to 110. EBIT change?
  5. Price +5%, volume −2%. Revenue change?
  6. A 20% fall followed by a 20% rise. Net change?
  7. A stock falls 60%. What rise gets it back?
  8. PAT ₹90.5 Cr on 6.0 Cr shares. EPS?
  9. A 10% position falls 50%. Portfolio impact?
  10. ₹25 lakh as a percentage of ₹1 crore?
  11. ₹2,340 crore in US$ million at ₹88 to the dollar?

Round B — growth and compounding (6 minutes)

  1. Rule of 72: how long does money take to double at 12%?
  2. ₹100 becomes ₹250 in five years. CAGR?
  3. 15% a year for ten years. Multiple?
  4. Revenue ₹612 Cr → ₹1,318 Cr in five years. CAGR?
  5. 20% a year for three years. Multiple?
  6. EPS grows 12% a year for five years while the P/E falls from 40× to 30×. Annual price return?
  7. Discount ₹1,000 due in five years at 12%.
  8. ₹1 lakh crore in ₹ billion?
  9. Ten crore rupees in millions of rupees?
  10. Expected return: 25% chance of −35%, 50% of +23%, 25% of +60%.
  11. Kelly fraction for a bet that wins 1:1 with 60% probability?

Round C — multiples (6 minutes)

  1. Price ₹390, EPS ₹15.08. P/E?
  2. P/E 25×. Earnings yield?
  3. Market cap ₹2,340 Cr, net debt ₹140.5 Cr, lease liabilities ₹18.2 Cr. EV?
  4. EV ₹2,499 Cr, EBITDA ₹181.9 Cr. EV/EBITDA?
  5. Book value per share ₹154.1, price ₹402. P/B?
  6. P/B 2.5×, RoE 15%. P/E?
  7. Dividend ₹4, price ₹390. Dividend yield?
  8. P/E 30×, expected growth 20%. PEG?
  9. Payout 60%, r 12%, g 6%. Justified forward P/E?
  10. RoE 18%, r 12%, g 6%. Justified P/B?
  11. Max-loss rule: 2% portfolio loss budget, 40% bear-case loss. Maximum position?

Round D — perpetuities, dilution and portfolios (6 minutes)

  1. A perpetuity of ₹10 a year at 10%. Value?
  2. Growing perpetuity: next cash flow ₹10, r 12%, g 5%. Value?
  3. Duration of that perpetuity?
  4. If r rises from 12% to 13% (g 5%), by how much does its value change?
  5. Terminal value: next year's FCF ₹243 Cr, WACC 12.19%, g 5.5%.
  6. A company with 100 Cr shares issues 10 Cr new shares. Dilution of existing holders?
  7. QIP of ₹300 Cr at ₹300 a share; 10 Cr shares before. New share count and dilution?
  8. 1 Cr options with strike ₹200; share price ₹400. Treasury-stock-method dilution in shares?
  9. Buyback of 5% of shares at 20× earnings, funded with cash earning 7% pre-tax (tax 25%). EPS accretion or dilution?
  10. Rights issue 1-for-4 at ₹200; share price ₹300. Theoretical ex-rights price?
  11. Ten equal positions, each with 30% volatility, pairwise correlation 0.5. Portfolio volatility?

Answer key

← Drill · Unidentified industries · Module index · Module 15 · Capstone →