Commission

Similar to expense, commission can also be divided into 2 parts: initial commission and renewal commission.

Initial commission is typically higher than renewal commission. Unlike expense, the formula for commission is much simpler.

\begin{equation}
\begin{split}
INIT\_COMM\_PP & = INIT\_COMM\_PC × PREM\_INC\_PP _t \\
REN\_COMM\_PP _t & = REN\_COMM\_PC _t × PREM\_INC\_PP _t
\end{split}
\end{equation}

In addition to commission, there is a special type of commission called "commission override". Agents have managers / supervisors. They will receive an additional fee on top of the commissions earned by those agents (his / her down-line). That additional fee is called "commission override".

Commission override is typically only payable at the first year. It is also a percentage of premium income.

\[COMM\_OR\_PP _t = COMM\_OR\_PC _t × PREM\_INC\_PP _t \]

The commission outgo is calculated by its per policy amount multiplied by the number of policies inforce start of period. Note that commission is a start of period cashflow.

\begin{equation}
\begin{split}
INIT\_COMM & = INIT\_COMM\_PP _t × NOP\_IFSM _t  \\
REN\_COMM _t & = REN\_COMM\_PP _t × NOP\_IFSM _t \\
COMM\_OR _t & = COMM\_OR\_PP _t × NOP\_IFSM _t
\end{split}
\end{equation}

And the total commission is therefore:

\[TOT\_COMM _t = INIT\_COMM + COMM\_OR _t + REN\_COMM _t \]

Some companies may have commission clawback. We skipped this topic first.

Let's go through a practical example below:

We use the same model as in previous chapters. And the following commission related information is given:

 

Year 1

COMM_OR_PP = COMM_OR_PC * PREM_INC_PP = 10% * 100 = 10

COMM_OR = COMM_OR_PP * NOP_IFSM = 10 * 1 = 10

INIT_COMM_PP = INIT_COMM_PC * PREM_INC_PP = 30% * 100 = 30

INIT_COMM = INIT_COMM_PP * NOP_IFSM = 30 * 1 = 30

TOT_COMM = COMM_OR + INIT_COMM + REN_COMM = 10 + 30 +  0 = 40

Year 2

REN_COMM_PP = REN_COMM_PC * PREM_INC_PP = 2% * 100 = 2

REN_COMM = REN_COMM_PP * NOP_IFSM = 2 * 0.899835 = 1.80

TOT_COMM = COMM_OR + INIT_COMM + REN_COMM = 0 + 0 + 1.80 = 1.80

Year 3

REN_COMM_PP = REN_COMM_PC * PREM_INC_PP = 1% * 100 = 1

REN_COMM = REN_COMM_PP * NOP_IFSM = 1 * 0.854540 = 0.85

TOT_COMM = COMM_OR + INIT_COMM + REN_COMM = 0 + 0 + 0.85 = 0.85

...

Year 10

REN_COMM_PP = REN_COMM_PC * PREM_INC_PP = 1% * 0 = 0

REN_COMM = REN_COMM_PP * NOP_IFSM = 0 * 0.785212 = 0

TOT_COMM = COMM_OR + INIT_COMM + REN_COMM = 0 + 0 + 0 = 0

A demonstration spreadsheet showing the calculation above can be downloaded here:

https://drive.google.com/file/d/0B4OirwHLcmE1N05aNmVGa0pRZlU/view?usp=sharing