Introduction
When a policyholder surrenders an equity-linked contract, the amount payable is not necessarily the policy fund shown immediately before surrender. The contract may apply a surrender penalty, a market-value adjustment, or both. A correct calculation starts by identifying which fund value is being used and then applying each exit deduction in the order specified by the contract.
The distinction between ongoing charges and exit deductions is essential. Ongoing charges are normally reflected in the policy fund as they are deducted during the contract. Exit deductions are applied because the policy is surrendered. Subtracting an ongoing charge again from a fund that is already net of that charge understates the surrender benefit.
Separating Fund Value from Exit Deductions
A useful calculation begins with the fund value at the surrender date. If the fund has been projected through premiums, investment returns, unit cancellations, and ongoing charges, use the resulting fund as \(F\). Do not reconstruct or subtract those charges again unless the stated fund is explicitly before them.
For example, suppose the contract specifies a fixed deduction \(D\), followed by a percentage surrender penalty \(c\) applied to the remainder, followed by an MVA multiplier \(M\). Under that exact order, the surrender benefit \(B\) is
This is not a universal contract formula: it is the result for the stated order. If the percentage penalty is applied before the fixed deduction, or the MVA is applied to a different amount, the calculation changes. If the MVA is defined as a dollar adjustment rather than a multiplier, its contract definition must be used instead.
| Item | When it affects the calculation | Typical treatment |
|---|---|---|
| Ongoing policy charge | During the period the policy remains in force | Deducted in projecting the fund; do not deduct again if already reflected in \(F\) |
| Fixed surrender deduction | When the policy is surrendered, if applicable | Subtract from the specified base |
| Percentage surrender penalty | When the policy is surrendered, if applicable | Apply to the base specified in the contract |
| Market-value adjustment | When the contract’s MVA terms apply | Apply the stated multiplier or dollar adjustment to its specified base |
Market-Value Adjustments
An MVA adjusts a surrender value to reflect a change in market rates under a contract-specific formula. One common multiplier form is
where \(j\) is the annual effective rate used in the contract’s original accumulation basis, \(k\) is the comparison annual effective market rate at surrender, and \(n\) is the stated remaining term in years. This form is only appropriate when the contract specifies this rate-and-term relationship. Contract formulas can differ.
The direction of the adjustment follows from the ratio. If \(k>j\), then \(M<1\) and this multiplier reduces the amount to which it applies. If \(k<j\), then \(M>1\), so the multiplier increases that amount. An MVA is therefore not automatically a penalty, even though it may reduce the surrender benefit in a particular scenario.
Calculating the Surrender Benefit
Use a consistent sequence. Confirm the surrender date and the fund value at that date; establish whether ongoing charges are already reflected; identify each exit deduction’s base; apply deductions in the stated order; and round only the final payable amount. In the examples below, the policyholder is alive and elects to surrender at the stated date, so no death-contingent payment is being calculated. The investment rates are deterministic assumptions for the hypothetical scenarios, not descriptions of actual products.
Use the fund after any ongoing charges due by that time, unless the problem explicitly gives a pre-charge value.
Identify fixed deductions, percentage penalties, MVA terms, applicability conditions, bases, and order.
Follow the specified sequence without repeating charges already allowed for in the fund.
Confirm the benefit is consistent with the deductions and adjustment direction, then round as required.
Worked Example: Ongoing Charge Followed by a Surrender Penalty
A hypothetical equity-linked policy has a fund of $24,000 at the start of a year. It earns a deterministic effective annual investment return of 5%. A $600 ongoing charge is deducted at year-end after the investment return is credited. The policyholder, alive at year-end, surrenders immediately after the charge is deducted. The contract applies a 4% surrender penalty to the fund after that charge. There are no premiums or other cash flows during the year. Calculate the surrender benefit. No mortality assumption is needed for this calculation because it is conditional on the policyholder being alive and choosing to surrender at year-end.
Method. Project the fund through the year, allow for the year-end ongoing charge, and then apply the exit penalty to the resulting fund.
The fund after the investment return but before the charge is \(24{,}000(1.05)=\$25{,}200\). After the ongoing charge, the surrender-date fund is \(\$25{,}200-\$600=\$24{,}600\).
The penalty is \(0.04(24{,}600)=\$984\). Therefore the surrender benefit is \(\$24{,}600-\$984=\$23{,}616\).
Check and common mistake avoided. The benefit is $984 below the post-charge fund, exactly the 4% penalty. Deducting the $600 charge again would incorrectly use a fund of $24,000 and produce a benefit of $23,040. The charge has already been allowed for in the stated surrender-date fund.
Worked Example: Comparing Two Contract-Specified MVA Multipliers
Consider two separate hypothetical policies, each surrendered while the policyholder is alive. In each case the stated fund is immediately before the MVA, all ongoing charges have already been reflected, and no other exit deduction applies. The MVA formula uses annual effective rates and the remaining term stated below. Calculate each adjusted benefit and its reduction from the fund. There is no additional mortality or investment projection in these surrender-date calculations.
Case A. The fund is $36,000, the original-basis rate is \(j=2\%\), the comparison market rate is \(k=4\%\), and \(n=3\) years. The contract specifies \(M=(1.02/1.04)^3\). Thus
The adjusted benefit is \(36{,}000(132651/140608)=\$33{,}962.7617\ldots\), or $33,962.76 to the nearest cent. The reduction is \(\$36{,}000-\$33{,}962.7617\ldots=\$2{,}037.2382\ldots\), or $2,037.24.
Case B. A second fund is $50,000. Its original-basis rate is \(j=3\%\), its comparison market rate is \(k=5\%\), and the remaining term is \(n=4\) years. The contract specifies \(M=(1.03/1.05)^4\), so
The adjusted benefit is \(50{,}000(112550881/121550625)=\$46{,}297.944169\ldots\), or $46,297.94 to the nearest cent. The reduction is \(\$50{,}000-\$46{,}297.944169\ldots=\$3{,}702.055831\ldots\), or $3,702.06.
Check and common mistake avoided. In both cases \(k>j\), so the multiplier is less than 1 and the adjusted benefit is below the fund. Keep sufficient precision through the multiplication and round only the final amounts; rounding an intermediate multiplier can change the answer by a cent.
Worked Example: Applying Several Exit Terms in the Stated Order
A hypothetical policy is surrendered while its policyholder is alive. Its fund immediately before exit deductions is $50,000, after all ongoing charges. The contract first subtracts a fixed $500 exit deduction, then applies a 3% surrender penalty to the remainder, and finally applies an MVA multiplier of \((1.03/1.05)^2\). The MVA rates are annual effective rates and the stated term is two years. Assume no further investment return, premiums, or mortality-contingent payment between the fund valuation and surrender. Calculate the benefit to the nearest cent.
Method. Follow the contract order: fixed deduction, percentage penalty, then MVA.
After the fixed deduction, the amount is \(\$50{,}000-\$500=\$49{,}500\). After the 3% penalty, it is \(\$49{,}500(0.97)=\$48{,}015\). The MVA multiplier is \((1.03/1.05)^2=1.0609/1.1025\). Hence
The surrender benefit is $46,203.28 to the nearest cent.
Check and common mistake avoided. The final amount is below the fund, consistent with the fixed deduction, penalty, and multiplier below 1. Applying the percentage penalty to the original $50,000 rather than to the post-fixed-deduction amount would contradict the stated order. In this contract, the penalty base is $49,500.
Common Traps and Practical Checks
Surrender calculations are often short, but small interpretation errors can change the result. In an exam-style problem, state the amount to which each term applies before doing arithmetic.
- Subtracting ongoing charges twice. If the given fund is after regular charges, start with that fund. Only subtract an ongoing charge again if the problem explicitly gives a value before it is due.
- Using the wrong penalty base. A percentage of the original fund is not the same as a percentage of the fund after a fixed deduction. Follow the contract’s stated order.
- Treating every MVA as a reduction. For the multiplier form shown here, whether the factor is above or below 1 depends on the comparison rates. Other contract formulas may behave differently.
- Assuming an MVA formula without evidence. The rate-and-term expression is valid only when the contract or problem specifies it. Do not infer an MVA solely from the fact that the product is equity-linked.
- Rounding too early. Retain the exact ratio or adequate precision through the calculation, then round the final dollar amount to cents.
The distinction matters because the policy fund and the surrender benefit answer different questions. The fund measures the value remaining in the policy account under the specified projection and charge treatment. The surrender benefit is the amount payable after the surrender provisions are applied. Keeping those quantities separate supports accurate benefit calculations and clear communication of the contract’s exit terms. This treatment is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.
Check Your Understanding
For each hypothetical scenario, use the stated timing and contract order. Round dollar answers to the nearest cent where needed.
- A policy fund is $28,000 immediately before surrender deductions and already reflects all ongoing charges. The contract deducts a 5% surrender penalty from that fund. Calculate the surrender benefit. (Answer: $26,600.00)
- A surrender-date fund of $41,500 is subject to a fixed $250 exit deduction followed by a 2% penalty on the remainder. No MVA applies. Calculate the benefit. (Answer: $40,425.00)
- A fund of $24,000 is subject only to the specified MVA multiplier \((1.01/1.03)^2\), with annual effective rates and a two-year term. Calculate the adjusted benefit. (Answer: $23,077.01)
- A fund of $18,000 is after all ongoing charges. The contract first deducts $300, then applies a 4% penalty to the remainder, and then applies an MVA multiplier of \((1.03/1.04)^2\). Calculate the benefit. (Answer: $16,666.80)
- A fund of $30,000 already reflects a $600 ongoing charge. At surrender, a 5% penalty applies to the fund, with no other deduction. What is payable, and should the $600 be deducted again? (Answer: $28,500.00; no, the $600 charge is already reflected in the fund.)