Fixed and Variable Underwriting Expenses

Why Expense Behavior Matters

Underwriting expenses help an insurer acquire and service policies. Their behavior matters because the total cost of writing business can respond differently to a change in premium than to a change in the number of policies. A commission tied to premium, for example, may rise when premium rises even if policy count is unchanged. A per-policy processing charge instead responds to policy count.

The classification is about how a cost behaves as an activity measure changes, not simply what the expense is called. The same kind of expense can behave differently under different arrangements: compensation might be a fixed salary, a commission, or a combination. This tutorial focuses on classifying expense behavior with respect to premium or policy volume; it does not calculate rate provisions.

Definition: Over a stated time period and within a relevant range of activity, a fixed expense has a total amount that does not change as the specified activity measure changes. A variable expense changes with that activity measure; in the common proportional model, its total equals a constant rate per unit of activity times the activity amount. A mixed expense has both a fixed component and a component that changes with activity.

State the Cost Driver Before Classifying

An activity measure, or cost driver, is the quantity a cost responds to. For underwriting expenses, common drivers include written premium and the number of policies processed or serviced. A classification is incomplete unless it identifies the driver. “Variable” should therefore be read as “variable with respect to a stated driver,” not as “changes for any reason.”

For example, a commission defined as a percentage of premium is variable with respect to premium. A processing charge of a fixed dollar amount per policy is variable with respect to policy count. If premium per policy changes while policy count stays constant, the commission may change while the processing charge does not.

A useful simple model for a set of expenses over one period is:

$$ E = F + bN + cP $$

Here $E$ is total expense, $F$ is the fixed amount for the period, $N$ is the number of policies, $b$ is a variable cost per policy, $P$ is premium, and $c$ is a variable expense rate per dollar of premium. A separate mixed expense can be written as a fixed base plus its own activity-sensitive component. This is a simplified linear model, not a claim that every actual expense follows a straight line.

Model condition: Treat an expense as fixed only for the stated period and within the stated range of activity. A lease may be fixed as policy count changes over a year, but could change at renewal or when additional space is needed. A per-policy charge is variable in total with policy count even if its dollar amount per policy is constant.

A Short Justification From the Cost Model

The model explains why two expenses can respond differently to the same change in business. Suppose a commission is $cP$, and a per-policy service charge is $bN$. Between two periods, their changes are:

\Delta E_{\text{commission}}=c(P_2-P_1), \qquad \Delta E_{\text{policy}}=b(N_2-N_1)

These relationships follow by subtracting the first-period amount from the second-period amount. For the commission, $cP_2-cP_1=c(P_2-P_1)$; for the policy charge, $bN_2-bN_1=b(N_2-N_1)$. Thus a premium change affects the commission through $P$, while a policy-count change affects the service charge through $N$. If only one driver changes, the other expense does not change under this model.

Worked Classifications and Expense Changes

The table gives common patterns, not universal classifications. The arrangement and cost driver in the particular scenario determine the answer.

Expense arrangement	Typical classification	Relevant driver
Commission stated as a percentage of premium	Variable	Premium
Processing charge stated as dollars per policy	Variable	Policy count
Office lease fixed for the period	Fixed within the relevant range	Neither premium nor policy count within that range
Service contract with a base fee plus a charge per policy	Mixed	Policy count for the changing component

Worked Example: Classifying an Expense Schedule

A hypothetical insurer processes 12,000 policies in a quarter and records $18,000,000 of premium. For that quarter, it pays $90,000 for office space, a 12% commission on premium, $4 per policy for issuance, and a software charge of $24,000 plus $0.75 per policy. Classify each expense by driver and calculate each amount and the total.

Method: identify the driver, then calculate the amount. The office payment is fixed with respect to both premium and policy count for this quarter, so its amount is $90,000.

The commission is variable with respect to premium. Its amount is $0.12 \times \$18,000,000=\$2,160,000$.

The issuance charge is variable with respect to policy count. Its amount is $12,000 \times \$4=\$48,000$.

The software charge is mixed: it has a fixed base of $24,000 and a variable charge of $12,000 \times \$0.75=\$9,000$. Its total is $\$24,000+\$9,000=\$33,000$.

The total is $\$90,000+\$2,160,000+\$48,000+\$33,000=\$2,331,000$. The component amounts sum to the total, which checks the arithmetic. The common mistake is to treat the $4 issuance charge as a fixed $4 expense. It is $4 per policy, so the quarterly total is $48,000 and changes if policy count changes.

Worked Example: Separating Premium and Policy-Count Effects

A hypothetical insurer compares two months. In month 1 it writes 10,000 policies and $15,000,000 of premium; in month 2 it writes 12,500 policies and $18,000,000 of premium. Monthly underwriting expenses are salaries of $160,000, commission of 8% of premium, an administrative charge of $6 per policy, and postage of $20,000 plus $0.40 per policy. Calculate the expense total in each month and explain the change.

Method: calculate each account from its stated driver in each month. Salaries are fixed for the two-month comparison, so they are $160,000 in each month.

Month 1 commission is $0.08 \times \$15,000,000=\$1,200,000$. The administrative charge is $10,000 \times \$6=\$60,000$. Postage is mixed: $\$20,000+(10,000 \times \$0.40)=\$24,000$. The total is $\$160,000+\$1,200,000+\$60,000+\$24,000=\$1,444,000$.

Month 2 commission is $0.08 \times \$18,000,000=\$1,440,000$. The administrative charge is $12,500 \times \$6=\$75,000$. Postage is $\$20,000+(12,500 \times \$0.40)=\$25,000$. The total is $\$160,000+\$1,440,000+\$75,000+\$25,000=\$1,700,000$.

Total expense increases by $\$1,700,000-\$1,444,000=\$256,000$. The increase is also checked by driver: commission rises by $240,000, the administrative charge by $15,000, and postage by $1,000; salaries and the fixed postage base do not change. The increases sum to $256,000. The common mistake is to attribute the entire change to policy count: the commission changes with premium, not directly with policy count.

Worked Example: A Volume Increase With Stable Average Premium

A hypothetical specialty insurer has 8,000 policies and $12,000,000 of premium. Its expenses are fixed payroll of $240,000, commission of 9% of premium, issuance cost of $3.50 per policy, and technology support costing $30,000 plus $1.25 per policy. In a later period, policy count increases to 9,000 and average premium per policy is unchanged. Find the expense total in each period and classify the accounts.

Method: calculate premium from the stated volume relationship, then apply each expense formula. Average premium is initially $\$12,000,000/8,000=\$1,500$ per policy. With 9,000 policies at the same average, later premium is $9,000 \times \$1,500=\$13,500,000$.

Initially, payroll is $240,000 and commission is $0.09 \times \$12,000,000=\$1,080,000$. Issuance costs $8,000 \times \$3.50=\$28,000$. Technology support is $\$30,000+(8,000 \times \$1.25)=\$40,000$. The initial total is $\$240,000+\$1,080,000+\$28,000+\$40,000=\$1,388,000$.

Later, payroll remains $240,000. Commission is $0.09 \times \$13,500,000=\$1,215,000$; issuance costs $9,000 \times \$3.50=\$31,500$; and technology support is $\$30,000+(9,000 \times \$1.25)=\$41,250$. The later total is $\$240,000+\$1,215,000+\$31,500+\$41,250=\$1,527,750$.

The increase is $\$1,527,750-\$1,388,000=\$139,750$. Checking by account gives $135,000 more commission, $3,500 more issuance cost, and $1,250 more technology cost, with payroll and the technology base unchanged; these changes sum to $139,750. The common mistake is to leave commission unchanged because its percentage is unchanged. The percentage is constant, but premium rises, so the commission amount increases.

Common Classification Traps

Confusing a unit cost with a total cost. A charge of $5 per policy is constant per policy but variable in total with policy count.
Using the wrong driver. A percentage-of-premium commission responds to premium. It does not automatically respond to policy count if premium is held constant.
Calling a mixed cost entirely fixed or entirely variable. Identify the base amount and the activity-sensitive component separately.
Ignoring the time period and relevant range. A cost can be fixed for a quarter but change in a later period, or remain fixed only until business volume requires additional capacity.
Assuming an expense category determines behavior. Salaries are often fixed over a short period, but compensation arrangements can include variable components. Classify the actual contract or payment rule.

Expense classification matters because premium and policy volume need not move together. A rate change can increase premium without increasing the number of policies, while growth in policy count can increase per-policy servicing costs. Clear driver-based classification helps an analyst describe which costs change and why, before any later calculation uses those expenses.

Key takeaway: State the period and cost driver, write the expense rule, and then classify the total as fixed, variable, or mixed. A fixed amount per policy is not a fixed total expense; a constant percentage of premium is not a constant dollar expense.

Check Your Understanding

For each situation, identify the relevant cost driver and classify or calculate the expense as requested.

A hypothetical carrier has 6,000 policies and $9,000,000 of premium. Its expenses are $42,000 for a fixed office lease, commission of 5% of premium, $2.25 per policy for records processing, and a service contract of $8,000 plus $0.50 per policy. Classify each account and find total expense. (Answer: Lease fixed, $42,000; commission variable with premium, $450,000; processing variable with policy count, $13,500; service contract mixed, $11,000; total $516,500.)
A hypothetical insurer increases from 4,000 policies and $6,000,000 premium to 5,000 policies and $7,500,000 premium. Salaries are fixed at $75,000, commission is 7% of premium, and processing costs $4 per policy. By how much does total expense increase? (Answer: $109,000.)
A hypothetical insurer retains 3,200 policies while premium rises from $4,800,000 to $5,280,000. It pays $90,000 in fixed salaries, commission of 11% of premium, and software cost of $12,000 plus $1.50 per policy. Find total expense in each period and the increase. (Answer: $634,800 initially, $687,600 later, an increase of $52,800.)
A service contract costs $18,000 per month plus $0.80 for each policy serviced. Find the monthly amount at 10,000 policies and at 12,500 policies, and identify the change. (Answer: Mixed expense; $26,000 and $28,000, an increase of $2,000.)
A hypothetical book keeps 8,000 policies while average premium per policy rises from $1,200 to $1,320. Commission is 10% of premium, a per-policy administration charge is $2.50, and fixed payroll is $100,000. Find the change in total expense, assuming these terms are unchanged. (Answer: Premium rises from $9,600,000 to $10,560,000; commission rises by $96,000; policy charge and payroll do not change, so total expense increases by $96,000.)

What You'll Learn