Delayed Perpetuity: Meaning, Examples, Calculations

Julia Kagan is a financial/consumer journalist and former senior editor, personal finance, of Investopedia.

Michael Boyle is an experienced financial professional with more than 10 years working with financial planning, derivatives, equities, fixed income, project management, and analytics.

What Is Delayed Perpetuity?

Perpetuity is a series of fixed payments that last an infinite period. Delayed or deferred perpetuity is a perpetual stream of cash flows that begins at a predetermined date in the future.

Fixed dividend-paying preferred shares are often valued using a perpetuity formula. If the dividends originate in five years, rather than next year, the stream of cash flows would be considered delayed perpetuity.

Understanding Delayed Perpetuity

In financial terms, perpetuity refers to a constant series of payments received over time with no ending date. Rather than disbursements in the present, a financial instrument with delayed perpetuity has payments that begin at a determined point in the future. Delayed perpetuity is also referred to as deferred perpetuity.

Key Takeaways

• Perpetuity refers to a fixed set of payments that continue without an ending date.
• Delayed or deferred perpetuity is a term that refers to payments that begin on a future start date.
• A deferred annuity, where retirement benefits are paid at a later date with fixed payments for life, employs the delayed perpetuity concept.

It is possible to calculate the present value of a financial instrument that relies on delayed perpetuity. Such an example involves a version of the perpetuity formula, but one that factors in the discounted value of the delayed income.

It is important to remember that the net present value, or NPV, of delayed perpetuity, is less than ordinary perpetuity. This is because of the time value of money principles, which hold that money available in the present moment is worth more than the same sum of money available in the future.

Money in the present moment is worth more because of its potential ability to earn interest, as well as other opportunity costs associated with money received on a delayed basis. In calculating the present value of delayed perpetuity payments, the payments have to be discounted to account for the delay.

Examples of Delayed Perpetuity

Fixed dividend shares, also known as preferred stock shares, can be structured as delayed perpetual payments if the payments are scheduled to begin at a future date rather than right away.

Retirement products are often structured using the concept of delayed perpetuity because they are designed to make fixed periodic payments in an unknown life span of the retiree. They allow retirees or prospective retirees to invest money now to later fund their daily expenses in retirement.

The terminal value of a project or a company can be considered an example of delayed perpetuity. Terminal value (TV) is the value of an asset, business, or project beyond the forecasted period when future cash flows can be estimated and produce a fixed cash flow indefinitely.

A deferred annuity is a financial instrument that relies on delayed perpetuity. Investors in a deferred annuity receive a consecutive stream of fixed payments in perpetuity beginning at a future date. For example, a deferred annuity may provide $10,000 payments annually for life, with the first payment delayed until the end of the sixth year.

How Does an Investor Calculate the Present Value of a Delayed Perpetuity?

The formula for calculating the present value of delayed perpetuity is:

• PV = ( CF / r ) * ( 1 / ( 1 + r ) ( n – 1 ) )

• CF = Annual cash flow
• r = discount rate
• n = Number of periods of deferral

What Is the Difference Between Perpetuity an Delayed Perpetuity?

While both represent an infinite stream of cash flows, perpetuity begins immediately with the first cash flow. Deferred perpetuity is a stream of cash flows that begins after a specified period, such as a dividend that starts after five years of the inception of a new business.

Why Is Calculating Perpetuity or Delayed Perpetuity Important?

The perpetuity formula makes it possible for financial experts to assign a present and future value to stocks, estates, land, and additional investments.

The Bottom Line

Delayed perpetuity is a perpetual stream of cash flows that begins at a predetermined date in the future. Financial instruments that use delayed perpetuity include retirement investments and annuities. Delayed perpetuity is also referred to as deferred perpetuity.

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A war bond is is a form of government debt that seeks to raise capital from the public to fund war efforts.

A payment-in-kind bond is a type of bond that pays interest in additional bonds rather than in cash. PIK bonds are typically issued by companies facing financial distress.

A variable rate demand note is a debt instrument that represents funds that are payable on demand and accrue interest based on the money market rate.

Industrial revenue bonds are municipal debt securities issued by a government agency on behalf of a private sector company and intended to build or acquire factories or tools.

An agency bond is a debt security issued by a federal government department or by a government-sponsored enterprise such as Freddie Mac or Fannie Mae.

The present value of an annuity is the current value of future payments from that annuity, given a specified rate of return or discount rate.

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