IAI Actuarial Core Principles · Actuarial Mathematics for Modelling

Projecting Expected Future Cashflows and Profit Testing for CM1

Profit testing projects the expected cashflows of a policy year by year, using assumptions for interest, mortality, expenses and reserves. You turn these into a profit vector, then a profit signature, then measures such as NPV and IRR at the risk discount rate. You use the results to price the product.

What this chapter covers

This chapter shows how an insurer tests whether a product makes money. You build a table of expected cashflows for one policy: premiums, expenses, interest, claims and the change in reserves. The result is the profit emerging at the end of each policy year.

From that profit you build a profit vector, then a profit signature that allows for the chance the policy has already ended. You then discount at the risk discount rate to get the net present value (NPV), and compare measures such as profit margin, IRR and discounted payback period. Reserves and capital strain affect when profit emerges, so zeroisation and the cost of capital matter.

The chapter pulls together much of the rest of CM1. You need interest theory and equations of value for discounting. You need life tables and decrement models for survival and claim probabilities. You need reserving ideas for the policy values. Pricing and reserving carries a large weighting in the 2026 CM1 syllabus, so this chapter rewards solid work. Expect both Paper A written questions and Paper B computer-based work, where you build the projection in a spreadsheet or code.

Profit testing is a standard long-answer topic because one question can test many skills at once: setting out cashflows, handling reserves, discounting, interpreting results and commenting on assumptions. The method is mechanical, so well-prepared students can collect most of the marks. It also suits Paper B, where a clean, correctly structured projection is worth marks even if one input is wrong. Pricing and reserving has the largest weighting in the 2026 CM1 syllabus, and this chapter sits inside it. Time spent here also strengthens your reserving and multiple-decrement work.

Projecting expected future cashflows and profit testing: topics in the order to study them

1Profit Testing Basics and Cashflow ProjectionStart here because every later idea depends on being able to lay out premiums, expenses, interest, claims and reserves year by year.
2Profit Vector, Profit Signature and Discounted ProfitNext turn the cashflow table into profit per policy in force and per policy issued, which is the input to every profit measure.
3Profit Measures: NPV, Profit Margin, IRR and PaybackOnce you have the profit signature, learn how to summarise it into numbers that decision makers use.
4Reserves in Profit Testing and ZeroisationReserves change the timing of profit, so study them after you can run a basic projection and see their effect.
5Risk Discount Rate and Cost of CapitalNow you can see why the discount rate and the cost of holding capital change NPV and the choice of reserves.
6Pricing Using Profit Tests and Sensitivity AnalysisUse the full toolkit to set premiums to hit a profit target and to test how results move when assumptions change.
7Unit-Linked and Multiple-State Profit TestsFinish with the extensions, which reuse the same framework with more complex cashflows and states.

How to prepare Projecting expected future cashflows and profit testing

Treat this chapter as a method you practise until it is automatic. Reading alone will not build the speed you need for Paper A or the accuracy you need for Paper B.

Learn the layout first. Write the standard columns in order: premium, expenses, interest, claims, change in reserve, profit. Use the same order every time.
Do one full projection by hand for a simple term assurance or endowment over three to five years. Check each column before moving on.
Convert the profit vector to the profit signature by multiplying by the probability of being in force at the start of each year. Then compute NPV, and practise stating clearly what each measure means.
Add reserves and capital. Redo the same product with different reserve bases and with zeroisation, and compare when profit emerges.
Practise pricing. Find the premium that gives a target profit margin or NPV, and run sensitivity changes to mortality, interest and expenses. Write one sentence of comment on each result.
Rebuild the projection in a spreadsheet or R for Paper B. Make assumptions into inputs so you can change one and see the result.
Finish with timed past-paper questions. Check that you state assumptions, show the working and interpret the answer.

Common mistakes in Projecting expected future cashflows and profit testing

Using the profit vector as if it were the profit signature when discounting.
Fix: Always ask whether the figure is per policy in force or per policy issued. Discount the profit signature to get the NPV.
Getting the timing of premiums, expenses and interest wrong.
Fix: Mark each cashflow as start of year or end of year in a column heading and apply interest only to the start-of-year items.
Forgetting the reserve in the profit calculation, or using the wrong reserve for survivors and for exits.
Fix: Include the reserve brought forward and the reserve carried forward as explicit rows, and check that the year-end reserve is for those still in force.
Mixing up the discount rate used for the profit test with the interest rate used for the reserve basis.
Fix: Label them separately: the rate earned on assets, the rate in the reserve basis and the risk discount rate. Use each only where it belongs.
Giving a number for NPV, IRR or margin with no interpretation.
Fix: Add a short comment on whether the result meets the profit target, and which assumptions it is most sensitive to.
In Paper B, hard-coding assumptions inside formulas.
Fix: Put each assumption in its own input cell or variable. This makes sensitivity tests quick and reduces errors.

Last-day revision: Projecting expected future cashflows and profit testing

Profit vector: expected profit at each year end per policy in force at the start of that year.
Profit signature: profit vector weighted by the probability the policy is in force at the start of each year, so it is per policy issued.
NPV: the profit signature discounted at the risk discount rate.
Profit margin: NPV of profit divided by the present value of premiums, using the same discount rate and basis.
IRR: the discount rate at which the NPV of the profit signature is zero.
Discounted payback period: the earliest policy year end at which the accumulated present value of profits, at the risk discount rate, is positive.
Interest in the projection is earned on the start-of-year reserve plus premium less expenses at the start of the year.
Profit at the year end per policy in force: Profit_t = (tV + P − e)(1 + i) − q(S + E) − p·(t+1)V, where p = 1 − q. Here p·(t+1)V means p multiplied by (t+1)V. The reserve at the start of the year is held for all policies in force. The death claim q(S + E) is paid at the year end and is not offset by any reserve release. The year-end reserve is needed only for survivors.
Zeroisation: reserves are set, working backwards from the end of the term, so that any negative profit in years after the first is made zero. It does not set every later profit to zero. Any new-business strain in the first year remains and is still financed from the insurer's capital.
A higher risk discount rate reduces the present value of positive profits. For the usual pattern of initial strain followed by positive profits, NPV therefore falls.
Always state your assumptions on mortality, interest, expenses, lapses and reserve basis.
Comment on every result: what it means for the insurer and what could change it.

Projecting expected future cashflows and profit testing practice questions

Projecting expected future cashflows and profit testing in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Projecting expected future cashflows and profit testing: frequently asked questions

What is the difference between a profit vector and a profit signature?

The profit vector gives expected profit at each year end for a policy that is in force at the start of that year. The profit signature multiplies each element by the probability the policy is still in force at the start of that year, so it is expected profit per policy issued.

Do I need to build profit tests in Paper B?

You should be ready to. Paper B is computer-based and a projection is a natural task for a spreadsheet or R. Practise setting assumptions as inputs and checking totals, as well as the hand method for Paper A.

Why does zeroisation matter?

Zeroisation sets reserves, working backwards, so that any negative profit in years after the first is made zero. It does not set every later profit to zero. Any new-business strain in the first year remains and must still be funded from the insurer's capital. It changes the profit signature, so measures calculated from it, such as NPV and IRR, will differ from those without zeroisation.

Which topics in this chapter should I study first?

Begin with the cashflow projection, then the profit vector and signature, then the profit measures. Reserves, discount rate and pricing come after, and unit-linked and multiple-state tests come last because they extend the same method.