# Actuarial Present Value APV

Actuarial present value is the present value of a series of future payments or obligations, as calculated by an actuary. It is used to determine the current value of a liability or asset, taking into account factors such as the time value of money and the likelihood of future payments being made.

To calculate the actuarial present value, an actuary will use a variety of techniques, including discounted cash flow analysis, stochastic modeling, and risk assessment. The actuary will consider factors such as the expected future cash flows, the time period over which the cash flows are expected to occur, and the appropriate discount rate to apply.

Actuarial present value is commonly used in the insurance industry to determine the value of liabilities, such as policy claims and benefits. It is also used in other industries, such as finance and healthcare, to evaluate the value of assets or liabilities.

By calculating the actuarial present value, an actuary can provide a company with an accurate and reliable estimate of the current value of a liability or asset, which can be used to inform business decisions and risk management strategies.

Imagine that a life insurance company has issued a policy that pays out a benefit of \$100,000 to the policyholder’s beneficiary upon the policyholder’s death. The policy has a term of 20 years, and the insurer expects to pay out the benefit in 20 years’ time.

To determine the actuarial present value of this liability, the actuary might consider the following factors:

The expected future cash flow: In this case, the actuary expects to pay out a benefit of \$100,000 in 20 years’ time.

The time period over which the cash flow is expected to occur: The actuary expects the cash flow to occur in 20 years’ time.

The appropriate discount rate: The actuary will apply a discount rate to the expected cash flow to account for the time value of money. For example, if the discount rate is 5%, the actuary will consider the fact that \$100,000 received in 20 years’ time is worth less than \$100,000 received today.

Using these factors, the actuary can calculate the actuarial present value of the liability as follows:

Actuarial present value = \$100,000 / (1 + 0.05)^20
= \$43,622.06

This means that the actuarial present value of the liability is \$43,622.06.