Immediate Vesting Versus Cliff Vesting

Why Vesting Rules Change Expected Benefit Cost

A benefit formula determines what a member could receive after a stated period of service. A vesting rule determines how much of that benefit the member is entitled to keep after leaving employment. These are separate parts of a valuation: the benefit may grow with service, while the vesting fraction determines how much is payable when a particular exit occurs.

The distinction matters when withdrawal competes with death or another exit. A member who withdraws after one year may receive a different fraction of the accrued benefit under immediate, graded, and cliff vesting. The probability of reaching that year also depends on earlier exits. This tutorial compares the expected present value (EPV) of the benefits under each rule, using annual decrement probabilities conditional on being active at the start of the year.

Definition: Let $B_t$ be the benefit accrued after $t$ completed years of service, and let $g(t)$ be the vesting fraction applicable to a withdrawal at the end of year $t$. The withdrawal benefit is $g(t)B_t$. Under immediate vesting, $g(t)=1$ for every $t$. Under graded vesting, $g(t)$ increases with service according to the plan’s schedule. Under a cliff at $m$ completed years, $g(t)=0$ for $t<m$ and $g(t)=1$ for $t\ge m$.

These definitions describe the withdrawal benefit only. A plan may specify separate vesting treatment for death benefits, disability benefits, or benefits payable at retirement. Do not apply a withdrawal vesting fraction to those benefits unless the plan terms say to do so. In each valuation, the benefit schedule and the event that triggers payment must be stated explicitly.

Competing Exits and the Expected Present Value

Suppose a member is active at the start of year $t$. Let $q_{w,t}$ and $q_{d,t}$ be the conditional probabilities of withdrawal and death, respectively, during that year. Assume these exits are mutually exclusive, and that there are no other exits in the model. The conditional probability of remaining active through the year is $1-q_{w,t}-q_{d,t}$. Define $p_0=1$, and let $p_t$ be the probability of being active at the start of year $t+1$. Then

p_t=p_{t-1}(1-q_{w,t}-q_{d,t}).

Thus, the probability of withdrawal during year $t$, measured from the original starting population, is $p_{t-1}q_{w,t}$. If the effective annual interest rate is $i$, use $v=1/(1+i)$ to discount a payment at the end of year $t$. The product of the event probability, the benefit payable on that event, and $v^t$ gives that event’s contribution to EPV.

Theorem: If withdrawals and deaths can occur in years $1,\ldots,T-1$, and every member still active after year $T-1$ retires at the end of year $T$, then $$ \operatorname{EPV} =\sum_{t=1}^{T-1}v^t p_{t-1} \left(q_{w,t}g(t)B_t+q_{d,t}D_t\right) +v^T p_{T-1}R_T, $$ where $D_t$ is the death benefit payable at the end of year $t$, and $R_T$ is the retirement benefit payable at the end of year $T$. The formula assumes that $D_t$ is not subject to the withdrawal vesting fraction. If it is subject to a separate vesting rule, use that rule in the death-benefit term. The retirement term applies to those active after year $T-1$; it does not include an additional year-$T$ survival factor.

The formula follows by partitioning outcomes according to the first exit. For each $t<T$, the member must first reach the start of year $t$, with probability $p_{t-1}$, and then withdraw or die during that year. Those events are disjoint, so their expected discounted payments add. Members still active after year $T-1$ have probability $p_{T-1}$ and receive the retirement benefit at time $T$. This argument also explains why survival probabilities must be applied only through the periods that must actually be survived.

Worked Example: Comparing Three Vesting Rules With Competing Exits

A hypothetical plan has a 5% effective annual interest rate. In each of years 1 and 2, conditional on being active at the start of the year, a member has withdrawal probability 0.20 and death probability 0.05. Members still active after year 2 retire at the end of year 3. The accrued withdrawal benefit is $B_t=\$10{,}000t$ after $t$ completed years. A death benefit of $\$4{,}000$ is paid at the end of the year of death and is not subject to vesting. The retirement benefit is $\$30{,}000$, payable to every member who reaches retirement. Find the total EPV under immediate vesting, graded vesting of 25% after year 1 and 50% after year 2, and a three-year cliff.

Method and event probabilities. The probability of remaining active through either year 1 or year 2, conditional on being active at its start, is $1-0.20-0.05=0.75$. Therefore $p_0=1$, $p_1=0.75$, and $p_2=0.75(0.75)=0.5625$. The unconditional withdrawal probabilities are $1(0.20)=0.20$ in year 1 and $0.75(0.20)=0.15$ in year 2. The corresponding death probabilities are 0.05 and $0.75(0.05)=0.0375$. The probability of reaching retirement is 0.5625.

Discount factors. Here $v=1/1.05$, so $v=0.952380952$, $v^2=0.907029478$, and $v^3=0.863837599$. The calculations below retain the unrounded discount factors; dollar amounts are rounded to cents at the end.

Immediate vesting. The year 1 withdrawal contribution is $0.20(1.00)(\$10{,}000)v=\$1{,}904.761905$. The year 2 contribution is $0.15(1.00)(\$20{,}000)v^2=\$2{,}721.088435$. The withdrawal component is therefore $\$1{,}904.761905+\$2{,}721.088435=\$4{,}625.850340$.

Graded vesting. The year 1 withdrawal contribution is $0.20(0.25)(\$10{,}000)v=\$476.190476$. The year 2 contribution is $0.15(0.50)(\$20{,}000)v^2=\$1{,}360.544218$. The withdrawal component is $\$476.190476+\$1{,}360.544218=\$1{,}836.734694$.

Three-year cliff. A withdrawal at the end of year 1 or year 2 occurs before the three-year service threshold, so neither withdrawal earns a vested benefit. The withdrawal component is $\$0$.

Common death and retirement components. The death component under each rule is $0.05(\$4{,}000)v+0.0375(\$4{,}000)v^2=\$190.476190+\$136.054422=\$326.530612$. The retirement component is $0.5625(\$30{,}000)v^3=\$14{,}577.259442$. These benefits are the same under all three vesting rules because the problem specifies that they are not affected by withdrawal vesting.

Totals and check. Immediate vesting gives $\$4{,}625.850340+\$326.530612+\$14{,}577.259442=\$19{,}529.64$. Graded vesting gives $\$1{,}836.734694+\$326.530612+\$14{,}577.259442=\$16{,}740.52$. The three-year cliff gives $\$0+\$326.530612+\$14{,}577.259442=\$14{,}903.79$. The common components agree across all three totals, and the withdrawal components are ordered immediate, graded, then cliff, as expected for these vesting schedules. The calculation avoids treating a year-2 withdrawal probability as unconditional: it is $p_1q_{w,2}=0.75(0.20)=0.15$.

A Shorter Cliff Comparison

The next example isolates the effect of a two-year cliff. Death is included as a competing exit because it reduces the number of members who can withdraw in year 2, but the plan specifies no death payment in this example. The comparison is therefore limited to withdrawal benefits.

Worked Example: Immediate, Graded, and Two-Year Cliff Vesting

A hypothetical plan uses a 4% effective annual interest rate. In year 1, conditional withdrawal and death probabilities are 0.10 and 0.05. For members active at the start of year 2, the corresponding probabilities are 0.25 and 0.05. Withdrawal benefits are $\$10{,}000$ after year 1 and $\$20{,}000$ after year 2. Compare immediate vesting, graded vesting of 50% after year 1 and 75% after year 2, and a two-year cliff.

Reach and exit probabilities. The probability of reaching the start of year 2 is $p_1=1-0.10-0.05=0.85$. The unconditional probability of withdrawing in year 1 is 0.10, and in year 2 it is $0.85(0.25)=0.2125$. The year-2 probability includes the requirement to remain active through year 1.

Discounting. The factors are $v=1/1.04=0.961538462$ and $v^2=1/1.04^2=0.924556213$.

Immediate vesting. The withdrawal EPV is $0.10(\$10{,}000)v+0.2125(\$20{,}000)v^2$. The first term is $\$1{,}000/1.04=\$961.538462$; the second is $\$4{,}250/1.0816=\$3{,}929.363906$. The total is $\$4{,}890.902368$, or \$4,890.90.

Graded vesting. The year-1 contribution is $0.10(0.50)(\$10{,}000)v=\$500/1.04=\$480.769231$. The year-2 contribution is $0.2125(0.75)(\$20{,}000)v^2=\$3{,}187.50/1.0816=\$2{,}947.022929$. The total is $\$3{,}427.792160$, or \$3,427.79.

Two-year cliff. The year-1 withdrawal has zero vesting. A withdrawal at the end of year 2 has completed two years of service and is fully vested. Its EPV is $0.2125(\$20{,}000)v^2=\$4{,}250/1.0816=\$3{,}929.363906$, or \$3,929.36. The cliff cost is below the immediate-vesting cost because it excludes the year-1 benefit, but above the graded cost because the year-2 cliff pays the full benefit rather than 75%.

Different Vesting Schedules Can Change the Ordering

Immediate vesting cannot produce a smaller withdrawal benefit than a schedule that vests less than 100% at the same service duration, assuming the accrued benefit and exit probabilities are unchanged. But graded vesting and cliff vesting need not have a fixed ordering. A graded schedule may pay something for early departures, while a cliff schedule may pay more once its threshold is reached. Their relative EPVs depend on how likely members are to leave at each duration and on the benefit amounts at those durations.

Worked Example: Graded Vesting Versus a Two-Year Cliff

A hypothetical plan has a 5% effective annual interest rate. In year 1, conditional withdrawal and death probabilities are 0.20 and 0.10. In year 2, conditional on being active at the start of the year, withdrawal and death probabilities are 0.30 and 0.10. Withdrawal benefits are $\$10{,}000$ after year 1 and $\$15{,}000$ after year 2. Graded vesting is 40% after year 1 and 80% after year 2. Compare its withdrawal-benefit EPV with immediate vesting and a two-year cliff.

Event probabilities. The probability of reaching year 2 is $p_1=1-0.20-0.10=0.70$. Thus the unconditional withdrawal probabilities are 0.20 in year 1 and $0.70(0.30)=0.21$ in year 2. The discount factors are $v=1/1.05=0.952380952$ and $v^2=1/1.1025=0.907029478$.

Immediate vesting. The year-1 contribution is $0.20(\$10{,}000)v=\$2{,}000/1.05=\$1{,}904.761905$. The year-2 contribution is $0.21(\$15{,}000)v^2=\$3{,}150/1.1025=\$2{,}857.142857$. The total is $\$4{,}761.904762$, or \$4,761.90.

Graded vesting. The year-1 contribution is $0.20(0.40)(\$10{,}000)v=\$800/1.05=\$761.904762$. The year-2 contribution is $0.21(0.80)(\$15{,}000)v^2=\$2{,}520/1.1025=\$2{,}285.714286$. The total is $\$3{,}047.619048$, or \$3,047.62.

Two-year cliff. The year-1 withdrawal receives no benefit, while the year-2 withdrawal receives the full benefit. The EPV is $0.21(\$15{,}000)v^2=\$3{,}150/1.1025=\$2{,}857.142857$, or \$2,857.14. The graded EPV exceeds the cliff EPV because its year-1 payments more than offset the difference between 80% and 100% vesting on year-2 withdrawals. This comparison is specific to the stated exit probabilities and benefit amounts.

Common Exam Traps

The main calculation errors arise from mixing conditional probabilities, service eligibility, and payment timing. In particular, the probability of an exit during a year is not generally the conditional decrement probability alone; it must include the probability of reaching the start of that year.

Using an annual conditional probability as an unconditional probability. In the second worked example, the year-2 withdrawal probability is $0.85(0.25)=0.2125$, not 0.25. The member must first survive the competing year-1 exits.
Applying survival twice. If $p_{T-1}$ already means the probability of being active at the start of year $T$, then a retirement payment made to those members at the end of year $T$ has probability $p_{T-1}$, not $p_{T-1}$ multiplied again by a survival factor. An extra factor is appropriate only if eligibility explicitly requires surviving competing exits during year $T$.
Applying vesting at the wrong service duration. For a two-year cliff, a withdrawal at the end of year 2 has completed two years and is vested. A withdrawal during year 2, before two full years are completed, may have a different result; payment timing and the plan’s definition of completed service must be clear.
Applying the withdrawal schedule to every benefit. A death or retirement benefit may have its own eligibility and vesting provisions. Keep its cash flow separate unless the stated terms explicitly apply the same vesting fraction.
Discounting to the wrong date. A benefit paid at the end of year $t$ is discounted by $v^t$. Do not use $v^{t-1}$ just because the decrement probability is conditional at the start of the year.

Key takeaway: For each possible exit, identify the probability of reaching the exit year, the conditional probability of that exit, the service-based benefit payable, and the payment date. Multiply these components and discount each cash flow separately. Comparing those event-by-event EPVs is the reliable way to evaluate immediate, graded, and cliff vesting, aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.

Check Your Understanding

For each problem, treat the stated decrement probabilities as conditional on being active at the start of the year. Round monetary answers to the nearest cent.

A hypothetical plan has a 5% effective annual interest rate and a 0.12 withdrawal probability during year 1. An immediately vested benefit of $\$8{,}000$ is paid at the end of the year if withdrawal occurs. Find its EPV. (Answer: $\$914.29$)
A hypothetical plan has a 4% effective annual interest rate. In year 1, withdrawal and death probabilities are 0.10 and 0.05. In year 2, the conditional withdrawal probability is 0.20. A $\$18{,}000$ withdrawal benefit is fully vested only after completing two years of service. Find the EPV under a two-year cliff. (Answer: $\$2{,}829.14$)
A hypothetical plan has a 5% effective annual interest rate. In year 1, withdrawal and death probabilities are 0.15 and 0.05; in year 2, the conditional withdrawal probability is 0.20. Benefits are $\$12{,}000$ and $\$24{,}000$ after years 1 and 2, with graded vesting fractions 25% and 75%. Find the withdrawal-benefit EPV. (Answer: $\$3{,}040.82$)
A hypothetical plan has a 4% effective annual interest rate. Year-1 withdrawal and death probabilities are 0.08 and 0.02; the conditional year-2 withdrawal probability is 0.25. Withdrawal benefits are $\$9{,}000$ after year 1 and $\$24{,}000$ after year 2. Find the difference between the immediate-vesting and two-year-cliff withdrawal EPVs. (Answer: $\$692.31$)
A hypothetical plan has a 5% effective annual interest rate. Year-1 withdrawal and death probabilities are 0.10 and 0.10; the conditional year-2 withdrawal probability is 0.20. Benefits are $\$10{,}000$ and $\$20{,}000$, with graded vesting fractions 30% and 60%. Find the graded EPV and compare it with the two-year-cliff EPV. (Answer: Graded $\$2{,}027.21$; two-year cliff $\$2{,}902.49$)

What You'll Learn