# Actuarial Science Profit Testing

**Profit testing **is a technique of assessment of the probability of an insurance contract before it is sold. Paying mortality claims, expenses etc. out of premium every year and the last amount left at the end of the year; its evaluation is called profit testing.

Profit testing is applied to two types of contracts:

**Conventional / Traditional / Non-Unit Linked Contract**

- It is the traditional life insurance policy on which benefit is fixed and known at the start of the policy.
- Example: Whole Life Assurance, Term Insurance, Pure endowment, Endowment assurance, etc.

**Unit Linked Contract**

- In Unit linked contract minimum sum assured is guaranteed on death and no sum assured is guaranteed at maturity.
- The unit Linked contract comprises two types of funds: Unit fund and Non-unit fund. The unit fund is managed by the company on behalf of the policyholder and is the part of the policy that is visible to the policyholder. The non-unit fund is the insurance company’s money and this fund is not visible to the policyholder.

Proﬁt is assured by taking a margin on the basis of the main assumptions- interest rates and mortality. Firstly **Profit Vector**, i.e. profits per policy in force at the start of each year is determined. Then the **Profit Signature**, i.e. profits per policy in force at inception and **Net Present Value (NPV)** is calculated. Finally, we get the **PROFIT MARGIN** which is the expected NPV of the profit signature expressed as a percentage of the expected NPV of the premium income.

**PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS
**If you have already studied CT5, you must have done profit testing on paper. But the new curriculum requires us to do it on spreadsheets. So, if you are appearing for CM1 – Actuarial Mathematics, you should be aware of how to do it in Excel. Not to worry more, this article will teach us how to do it.

The aim of this article is to demonstrate the profit test models in life assurance using excel. This article presents an example of a conventional contract and a unit-linked contract.

The profit testing technique starts with the calculation of the __premiums__. The premiums charged by a life insurance company are calculated in such a way that the present value of the premiums should be equal to or exceed the present value of the future benefits and expenses. In this article, we will work through basic problems of Profit Testing. Hence, we will calculate premiums __using the equation of value__.

Let us first start with a unit-linked policy as the first example.

**EXAMPLE 1**

**Formulas used are as follows**

- Cost of allocation= Premium allocated (1- B/O Spread).
- Premium allocation = Premium received x allocation percentage.
- FV before growth = Bid value at end + Cost of allocation.
- FV after growth = FV before growth (1+ UF growth rate).
- Management charges = FV after growth x Mng. Charges.
- Bid value at end = FV after growth – Mng. Charges.

Now let’s have a look at an example of a conventional policy.

**EXAMPLE 2**

Every business needs to know if the products it is selling are proﬁtable. However, it is very hard to determine the profitability of a business. Hence some technique is required to assess the proﬁtability before writing the business and profit testing is widely used as a process of determining the profitability of an insurance contract in advance. Nevertheless, the actual experience may not be the same as the expected experience. But profit testing gives us results which are almost similar to the actual result.

Profit testing is a very important and high scoring topic of CT5 (New Curriculum CM1). I hope this article helped you understand how to incorporate profit testing models in Excel. That’s all from our side.

Read more about Actuarial Science New Curriculum **Click**

Thank you!