Which branch gets the ₹5 crore: paid versus incurred claims
FY24 figures for three branches of a general insurer. Branch A: gross written premium ₹120 crore, claims paid ₹78 crore, commission ₹12 crore, operating expenses ₹18 crore; premium grew 8.0% over FY23 premium of ₹111.1 crore. Branch B: premium ₹40 crore, claims paid ₹26 crore, commission ₹5 crore, expenses ₹7 crore; premium grew 22.0% over ₹32.8 crore. Branch C: premium ₹60 crore, claims ₹30 crore, commission ₹6 crore, expenses ₹9 crore; premium grew 5.0% over ₹57.1 crore. The audit note records that Branch B's ₹26 crore is claims paid; claims incurred in the year were ₹31 crore, because ₹5 crore of outstanding claims on a single corporate group policy were provided for and remain unpaid. The zonal head has ₹5 crore for digital and agent-incentive spend, and no branch may take more than 40% of it. The board's instruction is 'profitable growth'; the regional sales head wants 'the fastest-growing branch rewarded'.
1. Compute the combined ratio for each branch on a consistent basis and rank them. State the trap in the data and the underwriting result in rupees.
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Formula: combined ratio = (claims incurred + commission + operating expenses) ÷ gross written premium. Using paid claims instead of incurred claims mixes two different measures and flatters any branch with a large outstanding-claims provision.
- A: (78 + 12 + 18) ÷ 120 = 108 ÷ 120 = 90.0%; underwriting result +₹12 crore.
- B: (31 + 5 + 7) ÷ 40 = 43 ÷ 40 = 107.5%; underwriting result −₹3 crore. On paid claims it would read (26+5+7) ÷ 40 = 95%, which is the trap in this set - the audit note adds ₹5 crore of incurred-but-unpaid claims and flips the branch from 'acceptable' to loss-making.
- C: (30 + 6 + 9) ÷ 60 = 45 ÷ 60 = 75.0%; underwriting result +₹15 crore.
Ranking by combined ratio: C (75.0%) best, A (90.0%) second, B (107.5%) worst. Ranking by underwriting profit: C ₹15 crore, A ₹12 crore, B −₹3 crore - the same order. Note the twist that C earns more underwriting profit than A despite writing half A's premium; a small, well-priced book beats a large, thin one. Growth ranking is the reverse: B 22.0%, A 8.0%, C 5.0%.
2. Recommend the split of the ₹5 crore subject to the 40% cap, using the numbers to justify your allocation and your treatment of Branch B.
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Cap first: 40% of ₹5 crore is ₹2 crore, so no branch can take more.
Marginal economics: each ₹1 crore of new premium at C creates about ₹0.25 crore of margin (100 − 75 = 25%); at A, ₹0.10 crore; at B, it destroys ₹0.075 crore. So growth money should follow combined ratio, not growth rate, unless there is a specific reason.
Recommended split: C ₹2.0 crore; A ₹1.5 crore; B ₹0.5 crore; reserve ₹1.0 crore.
Reasoning. C gets the cap: best combined ratio (75%) and the largest underwriting profit (₹15 crore), yet the slowest growth at 5.0%, so it is the one place where distribution spend is likely to convert into profitable premium. A gets the second-largest share because its 90% combined ratio still earns margin and it delivers the biggest absolute premium increase (+₹8.9 crore, against B's +₹7.2 crore); B's 22% is a base effect off ₹32.8 crore. B gets only ₹0.5 crore and should be told it is conditional on repricing or exiting the loss-making corporate group policy: paying agents to sell more of a 107.5% book increases the loss. The ₹1.0 crore reserve releases to B only if its combined ratio falls below 100%. Answering 'give it all to B because it grew fastest' is the error this case is built to catch.
3. Name the single additional data point that would most change your recommendation, and explain why it ranks above other data you might request.
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The renewal terms and loss history of Branch B's single corporate group policy. It explains most of B's ₹5 crore incurred-but-unpaid claims and B's ₹3 crore underwriting loss; if the policy renews at a corrected rate, B's combined ratio can fall below 100% quickly, and the reserve should be released. If it is being exited, B's future loss ratio improves without any spend at all, and the ₹0.5 crore is better used elsewhere.
Why this outranks the obvious alternatives:
- Line-of-business mix by branch is useful but second order; it explains the ratio rather than changing the decision this quarter.
- Expense detail - how much of A's ₹18 crore is fixed - would change the picture only if a large share is overhead that cannot be cut.
- Past digital spend and its conversion rate would sharpen the allocation, but we are choosing where to spend next, and a loss-making book remains loss-making at any conversion rate.
The judgement being tested: one concentrated exposure is driving an average, and averages hide it. Request the policy-level loss triangle for that account, its renewal date, and the pricing assumption used in the ₹5 crore provision, then hold the reserve decision to those answers.