Capitalized value of a flow (Kapitalwert)

Level 2 · Foundations

German termKapitalwert

Read firstPresent value (PV) · Capitalization factor (~200–300×)

Don't confuse withPresent value of an annuity

The capitalized value of a flow is the lump sum today that a recurring, indefinite cash flow is worth, once converted using an assumed rate of return. Divide the periodic amount by the rate (or multiply by a capitalization factor) to get a single euro figure — the capital that, earning that rate forever, would produce the same flow without ever running out.

Why it matters

Spending decisions often pit a one-time price against an ongoing amount: a lifetime buyout versus a monthly fee, a lump-sum settlement versus a recurring payment, an upfront purchase versus a subscription kept indefinitely. Comparing them directly is comparing different units — capitalizing the flow converts it into the same unit as the lump sum, a single euro figure, so the two can sit side by side.

The concept builds directly on present value (discounting a single future sum) and the capitalization factor (the 12/rate shortcut for monthly amounts): capitalized value is what results from applying that factor, or the equivalent annual division, to a flow assumed to continue without end.

Worked examples

1. Capitalizing an annual income flow. A relative offers to buy out a private annuity contract that otherwise pays an illustrative €2,000 a year for as long as it stays in force, with no planned end date. At an illustrative 5% assumed annual return, the capitalized value is €2,000 / 0.05 = €40,000. That is the sum which, invested at 5% a year, would throw off €2,000 annually forever without touching the principal — the figure to weigh against any buyout offer.

2. Deciding on a lifetime buyout — rate sensitivity. A household pays an illustrative €180 a month for a private Rechtsschutzversicherung (legal expense insurance) rider it plans to keep indefinitely, and the insurer offers a one-time lifetime buyout at €50,000. Using the capitalization factor 12 / rate:

Assumed annual rate	Capitalization factor	Capitalized value of €180/month	Versus €50,000 buyout
4%	300	€54,000	flow capitalizes higher
5%	240	€43,200	buyout is higher
6%	200	€36,000	buyout is higher

At a conservative 4% rate assumption, the ongoing flow capitalizes to more than the €50,000 buyout; at 5% or 6%, the buyout price exceeds the flow's capitalized value. The comparison flips entirely on which rate is assumed — the arithmetic doesn't settle which rate is realistic, only how the answer moves as the assumption changes.

Don't confuse with

Present value of an annuity assumes the flow runs for a fixed, finite number of periods and discounts each individual payment back to today before summing them. Capitalized value of a flow assumes the amount continues indefinitely — a perpetuity — with no end date in the calculation at all. As the number of periods in an annuity grows very large, its present value approaches the capitalized value of the same flow, but for a bounded commitment (a five-year lease, a three-year contract), using the perpetuity formula overstates the value, because it credits payments that were never going to happen.

Check yourself

A contract pays an illustrative €1,500 a year indefinitely, with no planned end date. Using an assumed annual return of 5%, what is the capitalized value in euros? (Capitalized value = flow / rate.)

A monthly cost of €200 is kept indefinitely. As the assumed annual rate of return rises from 4% to 6%, what happens to its capitalized value?

It rises, because a higher rate means the flow is worth more.It falls — from €60,000 at 4% to €40,000 at 6%.It stays the same, since the capitalized value depends only on the flow amount, not the rate.

A contract pays a fixed €500 a month for exactly 8 more years, then stops for good. Which figure correctly represents its value today at a 5% discount rate?

Its capitalized value — €500 x (12/0.05), treating the payments as indefinite.The present value of an annuity over 8 years, which discounts only the 8 years of actual payments.Both approaches give the same euro figure for an 8-year, fixed-end flow.

Which statements about the capitalized value of a flow are correct? (Select all that apply.)

It assumes the recurring flow continues without a planned end date.As the number of periods in a present-value-of-annuity calculation grows very large, that annuity's present value approaches the capitalized value of the same flow.The capitalized value depends only on the size of the flow, never on an assumed rate of return.Applying the capitalized-value formula to a cost or income with a known, fixed end date overstates its true present value.