532 Chapter 13 Insurance and Risk Management
simply listing different rates for difference coverage levels, or by providing multipliers
similar to the ones used in previous examples for underwriting classifications. The follow-
ing examples will serve to illustrate:Example 13.1.11 The rates for an umbrella liability policy based on the coverage
limits are given in the table below:GLOBAL RISK MUTUAL LIABILITY INSURANCE COMPANY
UMBRELLA LIABILITY COVERAGE ANNUAL PREMIUMSBasic $1,000,000 $195.00
Each additional $1,000,000 (up to $5 million) $125.00
Each additional $1,000,000 ($5 million to $10 million) $105.00(a) Determine the premium for a $3,000,000 policy.(b) Determine the premium for a $10,000,000 policy.(a) The fi rst $1,000,000 costs $195.00. We need $2,000,000 beyond that to get to the
desired total. So the total cost will be $195.00 2($125.00) $445.00.(b) $195.00 4($125.00) 5($105.00) $1,220.00.Note that the premium rates per million go down as the coverage limit goes up. This may seem
surprising at first. The reason for this is that even though a higher limit policy does expose the
insurer to a higher limit on each claim, most claims fall nowhere near the coverage limit.Example 13.1.12 Right now, Dave has a 50/100 motor vehicle liability policy,
and a $200 deductible collision policy. His liability premium is $273.50 and his
collision premium is $255.00, for a total of $528.50. He is considering changing
these coverages. His insurance agent provides him with a table of adjustment
multipliers.New Liability
Coverage MultiplierNew Collision
Deductible Multiplier
25/50 0.925 $50 1.355
75/200 1.055 $300 0.925
100/300 1.125 $500 0.845
250/500 1.235 $1,000 0.725Calculate Dave’s total premium for these coverages if (a) he changes his liability
limit to 100/300 and his deductible to $50 and (b) if he increases his liability limit to
250/500 and his deductible to $1,000.(a) The multiplier for his liability coverage is 1.125. So his new liability premium would be
(1.125)($273.50) $307.69. For his collision deductible, the multiplier would be 1.355, so
his new collision premium would be (1.355)($255.00) $345.53. The total for these cover-
ages would be $307.69 $345.53 $653.22.(b) His new liability premium would be (1.235)($273.50) $337.77. His new collision
premium would be (0.725)($255.00) $184.88. The total is $337.77 $184.88
$522.65.When buying insurance, consumers are often more focused on deductibles than on cover-
age limits. It is often a good idea, though, to focus more on coverage limits than deduct-
ibles. In part (b) of this example, Dave could actually lower his overall premiums while
raising his coverage limits dramatically if he is willing to accept a higher deductible. Dave
may want to consider the adjustments. Any significant accident could far exceed his cur-
rent coverage limits and wipe him out financially, so higher coverage limits would provide
him with greater protection. An increase in the deductible would be unpleasant should he
have a claim, but it would not be financially disastrous.