From a Modification Change to a Premium Change
An experience modification is a factor applied to a specified premium base. A change in the factor therefore changes premium in dollars according to the size of that base. The calculation is direct, but it is easy to get the wrong answer by applying the factor to total billed premium when some charges are not subject to modification, or by comparing the factors without considering the premium base.
The key comparison holds the eligible premium base constant: calculate premium using the old modification, calculate it again using the new modification, and subtract old premium from new premium. This isolates the premium effect of the modification change rather than mixing it with changes in exposure, rates, coverage, or other policy terms. The calculation is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
The eligible base is the premium amount specified by the rating plan as subject to the modification. It is not automatically the entire invoice or total policy premium. Any component represented by \(C\) in the definition remains outside this comparison only if it is in fact unchanged by the modification. Identify the applicable base and components from the stated plan terms before calculating.
The Basic Calculation and Its Derivation
With the base held constant, old modified premium is \(BM_{\text{old}}\), and new modified premium is \(BM_{\text{new}}\). Subtracting the old amount from the new amount gives the dollar change. If fixed charges are included in total premium, they appear in both calculations and cancel in the subtraction.
This derivation explains why the same eligible base must be used twice: the difference is intended to isolate the effect of changing \(M\). If the base also changes, the subtraction reflects both the factor change and the base change, so it no longer measures the modification change alone. When the question asks for a percentage change in total premium, the denominator is the old total premium, including any unchanged charges.
A Reliable Calculation Sequence
Use this sequence to keep the premium base, direction of change, and reporting convention clear. The modification values are factors, not percentages to add to the premium base.
Confirm the premium amount to which the modification applies and the policy period it represents. Separate any unchanged components.
Multiply the same eligible base by each modification. Add unchanged components to both totals if the question asks for total premium.
Use new minus old for the premium impact. State whether the result is an increase or decrease.
For percentage change in total premium, divide the dollar impact by old total premium. Round only the final result as instructed.
Worked Applications
Worked Example: Direct Dollar and Percentage Impact
A hypothetical commercial policy has an eligible premium base of $84,600. Its modification changes from 0.92 to 1.07. Assume there are no other premium components. Calculate the old premium, the new premium, the dollar change, and the percentage change relative to old premium.
Method. Apply each factor to the same $84,600 base. This isolates the effect of the factor change.
Old premium.
New premium.
Dollar impact. New minus old is \(\$90{,}522.00-\$77{,}832.00=\$12{,}690.00\), an increase. As a check, the factor difference is \(1.07-0.92=0.15\), and \(\$84{,}600(0.15)=\$12{,}690.00\).
Percentage change. Divide the increase by old premium: \(\$12{,}690/\$77{,}832=0.1630\), or 16.30% to two decimal places. This is the premium percentage change, not the factor difference of 0.15 expressed as 15% of the old premium.
Common mistake avoided. Treating the factor difference of 0.15 as the percentage change in the old premium would give 15%. The change is 15% of the eligible base; relative to the old premium, it is \(0.15/0.92=16.30\%\).
Worked Example: Separating Modifiable Premium from Fixed Charges
A hypothetical policy has $126,000 of eligible premium and $18,000 of policy charges that do not change when the experience modification changes. The modification decreases from 1.14 to 0.96. Find old and new total premium, the dollar impact, and the percentage change in total premium.
Method. Apply each factor only to the $126,000 eligible base, then add the $18,000 unchanged charges to each total.
Old total premium. The modified eligible portion is \(\$126{,}000(1.14)=\$143{,}640.00\). Adding fixed charges gives \(\$143{,}640.00+\$18{,}000.00=\$161{,}640.00\).
New total premium. The modified eligible portion is \(\$126{,}000(0.96)=\$120{,}960.00\). Adding the same charges gives \(\$120{,}960.00+\$18{,}000.00=\$138{,}960.00\).
Dollar impact. New minus old is \(\$138{,}960.00-\$161{,}640.00=-\$22{,}680.00\), a decrease. The direct check is \(\$126{,}000(0.96-1.14)=\$126{,}000(-0.18)=-\$22{,}680.00\).
Percentage change in total premium. Divide by old total premium, not by the eligible base: \(-\$22{,}680/\$161{,}640=-0.1403\). Total premium decreases by 14.03% to two decimal places. The fixed charges cancel from the dollar difference, but they remain part of the old total used in this percentage calculation.
Common mistake avoided. Applying the factors to $144,000, the invoice amount before modification, would incorrectly modify the $18,000 of fixed charges. The stated eligible base is $126,000.
Worked Example: Applying the Factor to a Policy-Term Base
A hypothetical insured is quoted an annual eligible premium base of $72,000, but the policy term is nine months. Assume premium is prorated uniformly by months, with no other adjustments. The modification changes from 0.95 to 1.08. Calculate the term base, old and new modified term premiums, and the dollar impact.
Method. First convert the annual base to the nine-month eligible base. Then apply both factors to that same term base.
The term fraction is \(9/12=0.75\). Thus the eligible term base is \(\$72{,}000(0.75)=\$54{,}000.00\).
Old modified term premium. \(\$54{,}000(0.95)=\$51{,}300.00\).
New modified term premium. \(\$54{,}000(1.08)=\$58{,}320.00\).
Dollar impact. \(\$58{,}320.00-\$51{,}300.00=\$7{,}020.00\), an increase. Checking directly, \(\$54{,}000(1.08-0.95)=\$54{,}000(0.13)=\$7{,}020.00\).
Common mistake avoided. Applying the factor difference to the full annual base would produce \(\$72{,}000(0.13)=\$9{,}360.00\), which is not the impact for this nine-month term. The factor change must be applied to the eligible base for the period being rated.
Common Errors and Practical Checks
The basic equation is short, but a sound answer depends on choosing the right base and reporting the requested change. The following checks catch many calculation errors.
- Reversing the subtraction. For the convention new minus old, \(M_{\text{new}}>M_{\text{old}}\) implies a positive dollar impact when \(B>0\). If the factors rise but the calculated impact is negative, recheck the order of subtraction.
- Using total premium as the base without checking eligibility. Apply the factor to the premium amount specified as eligible, not automatically to fees, taxes, assessments, or other charges. Their treatment depends on the stated plan or problem.
- Using different bases for old and new. That comparison combines a change in premium base with the change in modification. To isolate the factor impact, keep \(B\) fixed.
- Confusing the factor difference with the percentage change in premium. The dollar impact is the factor difference times the eligible base. The percentage change in total premium uses old total premium as its denominator.
- Ignoring the policy term. If the supplied eligible base is annual but the question concerns a shorter term, determine the applicable term base before applying the factor, using only the proration assumption provided.
A useful final check is to calculate the impact in two ways: subtract the two modified premiums, and multiply the eligible base by the difference in factors. The results must agree when the base is the same and no other premium components change. If they do not, a base, arithmetic, or sign error is present.
Check Your Understanding
For each problem, identify the eligible base before applying the modification. Unless stated otherwise, report dollar amounts to the cent and percentage changes to two decimal places.
- A hypothetical policy has an eligible premium base of $58,000. The modification changes from 0.91 to 1.04. Find the dollar impact and state whether it is an increase or decrease. (Answer: $7,540.00 increase)
- A policy has $96,000 of eligible premium and $4,800 of unchanged charges. The modification changes from 1.12 to 0.99. Find the change in total premium and the percentage change relative to old total premium. (Answer: $12,480.00 decrease; 11.11% decrease)
- A hypothetical account has two eligible premium components, $48,000 and $32,000, both subject to the same modification. The factor changes from 0.78 to 0.93. Find the old modified premium, new modified premium, and dollar impact. (Answer: $62,400.00 old; $74,400.00 new; $12,000.00 increase)
- An annual eligible premium base is $120,000. A six-month term is priced by uniform monthly proration, and the modification changes from 0.89 to 1.02. Find the term premium impact. (Answer: $7,800.00 increase)
- A policy has $75,000 of eligible premium and $5,000 in unchanged charges. The modification changes from 0.80 to 0.92. Find the dollar impact and percentage change in total premium relative to old total premium. (Answer: $9,000.00 increase; 13.85% increase)