Module 07 · Solutions

Warm-up

E07.01 Interest expense is the cost of goods, deposits/borrowings are operating liabilities, loan growth is the business's investing flow, and leverage is regulated — so EBITDA, FCFF, EV and WACC have no meaning. Replacements: NII (revenue), PPOP (EBITDA), earnings and book value (FCF), equity value and P/B (EV), cost of equity (WACC).

E07.02 NIM: NII ÷ average interest-earning assets (or loans). Cost-to-income: opex ÷ (NII + fees). Credit cost: provisions ÷ average loans. GNPA/NNPA: gross / net (of stage-3 provisions) non-performing loans ÷ loans. PCR: stage-3 provisions ÷ stage-3 loans. Slippages: loans newly turning NPA. CRAR: (Tier-1 + Tier-2) ÷ RWA. ALM: maturity matching of assets and liabilities. Stages 1/2/3: performing / 30+ dpd (SICR) / 90+ dpd credit-impaired.

E07.03 EV: net worth + PV of in-force profits. VNB: PV of profits on the year's new policies. VNB margin: VNB ÷ APE. Persistency: share of policies still in force at 13/25/37/61 months. Combined ratio: (claims + expenses) ÷ premium. Float: premiums held before claims are paid. TER: fund expense ratio charged to investors. Take rate: platform revenue ÷ transaction value.

E07.04 Cyclicals show low P/Es at earnings peaks and high/meaningless P/Es at troughs; use P/B and EV/tonne (or EV/replacement cost) at troughs, and P/E on normalised earnings.

E07.05 Contribution margin: revenue − variable costs per unit. Rule of 40: growth % + margin % ≥ 40. Implied terminal multiple: EV grown at the discount rate ÷ terminal-year EBITDA. Holdco discount: 1 − price/NAV. NAV: PV of project cash flows + assets − debt. Regulated equity base: the equity on which a regulator allows a return. ARPU: revenue per user per month.

E07.06 Provisioning moves from incurred-loss (IRAC) to expected credit loss (stages 1/2/3) under RBI's 2026 Directions, effective 1-Apr-2027 with a glide path to 31-Mar-2031.

Core

E07.07 NII 631.1 (9.24%); fees 0.74; opex −3.53; PPOP 6.45; credit cost −1.77; PBT 4.68; tax −1.18; RoA 3.51%; leverage 6,831.4/1,590.55 = 4.29x; RoE 15.1%.

E07.08 Slippages ≈ 200.7 − 150.3 + 84.6 = ₹135.0 Cr = 2.1% of average loans (higher than the 1.9% credit cost: write-offs consumed existing provisions).

E07.09 RWA grows 20%/yr: 6,642 → 11,477 after three years. Equity: PAT 239.5 growing 15% with 12.5% retained… retained = 87.5% × (275.4 + 316.7 + 364.2) = 837.0 → equity 2,532; Tier-1 ratio 2,532/11,477 = 22.1%; CRAR = (2,532 + 140)/11,477 = 23.3%. Falling ~1.4 pp a year; the 15% floor binds in roughly eight more years at these rates — sooner if growth stays 20% while RoE stays 15% (internal accrual ~13%).

E07.10 Justified P/B: g 6%: (0.151 − 0.06)/(0.07) = 1.30x; g 7%: 0.081/0.06 = 1.35x; g 8%: 0.071/0.05 = 1.42x. Implied RoE at 402/154.1 = 2.61x: 8 + 2.61 × 5 = 21.0%.

E07.11 Value ≈ ₹2,093 Cr → ₹190/share, P/B 1.23x (code in 07.1 §6.2).

E07.12 Credit cost 4.5% × 6,350 = 285.8; extra interest 1% × 5,082 = 50.8. PBT = 440.6 − 50.8 − 285.8 = 104.0; PAT = 77.8; RoE = 77.8/1,590.55 = 4.9%.

E07.13 Structural value = Σ VNB₁…₅ discounted + terminal: VNB grows 15%: 1,207.5, 1,388.6, 1,596.9, 1,836.5, 2,112.0; PVs at 12%: 1,078.1, 1,107.0, 1,136.6, 1,167.1, 1,198.4 = 5,687.2; TV = 2,112.0 × 1.05/(0.07) = 31,680 → PV 17,976; structural ≈ ₹23,660 Cr; appraisal ≈ ₹38,660 Cr; P/EV ≈ 2.58x.

E07.14 Revenue = 1,50,000 × 0.0055 + 1,00,000 × 0.0010 = 825 + 100 = 925; profit = ₹375 Cr. An 8-bp cut removes ₹120 Cr → ₹255 Cr (−32%).

E07.15 EBIT = 4,500 − 1,200 = ₹3,300 Cr. Options −40% (−1,200): EBIT ₹2,100 Cr (−36% on a 27% revenue fall).

E07.16 Mean EBITDA/t 7,620 → normalised EBITDA ₹4,953 Cr; median 6,900 → ₹4,485 Cr. Normalised PAT (mean): (4,953 − 1,800 − 900) × 0.75 = ₹1,690 Cr; P/E 17.8x (median basis: PAT ₹1,339 Cr, 22.4x). EV = 42,000; EV/tonne = ₹6,000 Cr/MT. Sensitivity: 1,000 × 6.5/10 × 0.85 = ₹553 Cr per ₹1,000/t.

E07.17 Demand 9 MT: A + B + C = 8 MT, so D supplies 1 MT and is marginal; price ≈ ₹44k/t; A's cash margin ₹14k/t. Demand 11 MT: A–D = 10 MT, E supplies 1 MT; price ≈ ₹48k/t; A's margin ₹18k/t.

E07.18 EBITDA: −1,087, −824, −434, +49, +646; break-even year 4; cumulative burn to the trough ₹2,345 Cr (after year 3).

E07.19 Year-8 EBITDA = 9,165 × 12% = ₹1,100 Cr; nominal 12,960/1,100 = 11.8x; PV factor 1/1.14⁸ = 0.351 → 33.6x the present value of year-8 EBITDA.

E07.20 ESOPs: 1.03⁴ = 1.1255; round: 4 Cr new shares on ~20.6 Cr (after year-1 ESOPs) ≈ +19.4%; combined factor ≈ 1.1255 × 1.194 ≈ 1.34 — the existing holder owns ~74% of what they owned.

E07.21 Gross = 6,300 + 1,980 + 1,200 = 9,480 → ₹1,896/share; discount = 1 − 950/1,896 = 50%. Build-up: 10 + 15 + 1 + 20 + 5 − 5 = 46% → explained, not "wrong".

E07.22 Royalty ₹225 Cr; pre-royalty PBT = 600/0.75 + 225 = 1,025; royalty = 22% of pre-royalty PBT. Fair royalty 2% = ₹100 Cr; leak ₹125 Cr pre-tax = ₹94 Cr PAT a year; at 30x ≈ ₹2,800 Cr of value.

E07.23 PV projects: 420/1.14^1.5 = 345; 360/1.14² = 277; 1,200/1.14^2.5 = 865 → 1,487; + 600 + 1,875 − 900 = ₹3,062 Cr → ₹153/share. Cap rate 9% (rental 1,667) and C −20% (PV 692): 1,314 + 600 + 1,667 − 900 = ₹2,681 Cr → ₹134.

E07.24 PAT = 4,000 × 15.5% = ₹620 Cr; justified P/B = (0.155 − 0.06)/(0.11 − 0.06) = 1.9x → equity ₹7,600 Cr. At 14%: (0.14 − 0.06)/0.05 = 1.6x → ₹6,400 Cr (−16%).

E07.25 Revenue = 300 mn × 210 × 12 = ₹75,600 Cr; EBITDA ₹37,800 Cr; EV/EBITDA 10.6x; FCF before interest = 37,800 − 35,000 = ₹2,800 Cr. Tariff +15%: revenue +₹11,340 Cr × 90% = +₹10,206 Cr EBITDA (+27%).

Stretch

E07.26 Under clean surplus, dividends = PAT − ΔBook, so the DDM/DCF sum of dividends equals book + PV of (PAT − \(k_e\) × book) after rearrangement. Divergence example: a residual-income terminal that grows RI at 6% while the DCF terminal grows dividends at 6% with a payout inconsistent with RoE and growth (payout ≠ 1 − g/RoE) — the two imply different reinvestment and give different values; fix by deriving payout from g/RoE.

E07.27 For: same currency of returns (RoE), same regulator, same deposit franchise economics; PSU RoEs in FY24–26 matched private peers. Against: government ownership (policy lending, capital calls, OFS overhang, management tenure), lower sustainable RoE through the cycle, and a discount for the probability of non-commercial decisions — a parallel line below the private one, whose gap is the policy-risk premium.

E07.28 (1) Reported EBITDA (with ESOP cost): −6% of revenue. (2) Pre-Ind AS 116 EBITDA (lease payments back in opex): lower still by the lease cost. (3) Free cash flow after leases and capex: the honest number. Use (3) for runway and value, (1) for profitability comparisons, and never the "adjusted" figure.

E07.29 (a) A tariff hike raises expected asset value and lowers its uncertainty — the call moves deeper into the money: large gain. (b) Conversion at a discount transfers value to the government and dilutes the option's per-share claim, but reduces the strike (debt): mixed — per-share value often falls even as survival probability rises. (c) AGR relief lowers the strike directly: gain, largest of the three per rupee of liability removed.

Real-world task

E07.30–32 Rubric: RoA tree ties to reported RoE; roll-forward reconciles; CRAR path shows when capital binds; P/B–RoE plot with implied RoE stated; EV/tonne against a sourced replacement cost; normalised earnings with mean and median; contribution margin rebuilt with the definition stated; implied terminal multiple with the terminal margin justified by a comparable.