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Difficulty: HardInsurance: Principles and Types

A commercial factory building valued at N15,000,000\text{N}15,000,000 is insured against fire with two underwriters: N6,000,000\text{N}6,000,000 with Underwriter Alpha and N4,000,000\text{N}4,000,000 with Underwriter Beta. Both policies contain an average clause. If a fire outbreak causes a loss of N4,500,000\text{N}4,500,000, how much compensation will Underwriter Alpha pay?

  1. N1,800,000\text{N}1,800,000Answer
  2. B
    N2,700,000\text{N}2,700,000
  3. C
    N2,250,000\text{N}2,250,000
  4. D
    N3,000,000\text{N}3,000,000

Answer

The compensation payable by Underwriter Alpha is N1,800,000\text{N}1,800,000.
Because the factory is under-insured (insured for N10,000,000\text{N}10,000,000 out of its N15,000,000\text{N}15,000,000 value) and the policies include an average clause, the policyholder acts as a co-insurer for the uninsured proportion (33.33%33.33\%). Each underwriter pays according to their proportion of the total property value: N6,000,000N15,000,000×N4,500,000=N1,800,000\frac{\text{N}6,000,000}{\text{N}15,000,000} \times \text{N}4,500,000 = \text{N}1,800,000.

Step-by-Step Solution

1
Determine if the property is under-insured
Total Sum Insured = N6,000,000+N4,000,000=N10,000,000\text{N}6,000,000 + \text{N}4,000,000 = \text{N}10,000,000. Actual Property Value = N15,000,000\text{N}15,000,000. Since Total Sum Insured < Actual Property Value, the property is under-insured and the average clause applies.
The average clause penalizes under-insurance by making the insured bear a proportionate share of any partial loss.
2
Apply the Average Clause formula for Underwriter Alpha
Compensation from Alpha=(Sum Insured with AlphaActual Property Value)×Actual Loss\text{Compensation from Alpha} = \left(\frac{\text{Sum Insured with Alpha}}{\text{Actual Property Value}}\right) \times \text{Actual Loss}
When an average clause is present, each insurer pays in proportion to the total value of the subject matter, not just the total sum insured.
3
Calculate the exact monetary payout
Compensation from Alpha=(N6,000,000N15,000,000)×N4,500,000=0.4×N4,500,000=N1,800,000\text{Compensation from Alpha} = \left(\frac{\text{N}6,000,000}{\text{N}15,000,000}\right) \times \text{N}4,500,000 = 0.4 \times \text{N}4,500,000 = \text{N}1,800,000
Evaluating the mathematical expression yields the final compensation figure.

Key Concept

Average Clause and Under-insurance in Indemnity Policies
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Topics

Insurance: Principles and Types

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