Cash flow

Cash flow is in the business a current magnitude that payment transactions between payers and payees describes.

General

The cash flow is the monetary performance or consideration from a transaction or unilateral performance without consideration ( gift ). It can be made as a cash payment or by transferring book money as part of payment transactions . This can be a single deposit or withdrawal or a sequence of several payments at different times (e.g. from a continuing obligation ).

species

In general, a distinction must be made between positive and negative cash flows. Positive payment flows ( English cash inflow ) are incoming payments from the perspective of the payee, negative payment flows ( English cash outflow ) are outgoing payments from the perspective of the debtor . Positive ones improve liquidity accordingly , negative cash flows burden them. A negative cash flow requires self-financing via equity or debt financing via outside capital , while a positive cash flow creates opportunities for internal financing . Avoided payouts are shown as a positive cash flow (deposit). Long-term negative cash flows will lead to a consumption of assets or an increase in debts .

For example, from the company's point of view , the expansion investment initially triggers negative cash flows in the form of payments for the payment of capital goods , while positive cash flows result from the sales process after the investment phase has been completed . An investment has paid off if the positive cash flows are higher than the negative. Conversely solves the credit disbursement from the perspective of the borrower initially a positive cash flow, while the subsequent debt service ( loan interest and repayment ) has negative cash flows result.

Cash flows in the economy

The economic cycle of an economy consists of the money cycle , to which the payment flows belong, and the goods cycle consisting of goods and services . In the case of the cash flow, there is an exchange of means of payment between the debtor and the recipient.

The most typical example is the financial contract , in which there is a mutual exchange of cash flows and underlying assets . For companies in Germany, cash flow is officially referred to as “payment flow ”. In contrast to the balance sheet, a cash flow statement does not focus on inventory values , but on payment flows.

A financial risk arises when positive cash flows that are definitely expected do not materialize ( loan repayments from the point of view of the lender ) or unexpected negative cash flows occur ( cost of defects from incorrect production in companies).

Cash flows in financial mathematics

Cash flows in the financial mathematics , the flow of payments from securities , foreign exchange , varieties , derivatives , other financial contracts or investments during their term of result. The point in time of the individual payments is decisive because from a valuation point of view it makes a big difference whether payments are made in the near or distant future.

In financial mathematics, cash flows are the most important information relevant to valuation about a financial instrument . Two securities that have the same cash flow have the same value in a model world , even if both securities are legally constructed differently. The aim of financial mathematics is therefore to find a function that assigns a cash value to a cash flow. ${\ displaystyle P}$ ${\ displaystyle Z}$

Properties of cash flows

In the case of securities, payments are generally exclusively positive in nature, while cash flows, particularly in the case of derivatives, contracts or investments, can consist of both positive and negative payments. For example, investments often begin with negative payments that later turn into positive payments. Contracts such as swaps or futures are concluded in such a way that their current value is zero and there is no exchange of payments. You can have both positive and negative payments for this in the future.

As a rule, one looks at payment flows in which payments are made at regular intervals, such as annually, half-yearly or quarterly. Then you can represent a payment stream as a sequence of payments:

{\ displaystyle Z = (z_ {t_ {i}}) _ {i \ in \ {1,2, \ ldots, n \}}}

.

In some academic models, however, one also falls back on continuous payment flows, for example a fictitious bond that pays between the points in time and the amount , whereby the amount of the continuous coupon is. Steady cash flows are used in many models, but are not found in reality. ${\ displaystyle t_ {1}}$ ${\ displaystyle t_ {2}}$ ${\ displaystyle \ int _ {t_ {1}} ^ {t_ {2}} \, c \, dt}$ ${\ displaystyle c}$

A rough distinction can be made between secure and insecure payment flows. In practice, secure cash flows are found in bonds with a fixed coupon without credit risk, while bonds with credit risk, bonds with variable coupons, stocks and derivatives typically show uncertain cash flows.

Cash flows can be multiplied by a scalar value and added component-wise. For example, a portfolio with two securities of the same type has a cash flow that has twice the payments of the original cash flows. A portfolio of two different securities has a cash flow in which the payments result from the sum of the payments of the two original cash flows. From a mathematical point of view, the set of payment flows has the structure of a vector space .

Assessment of secure payment flows

With a secure flow of payments, the times of the individual payments must be explicitly included. This is important because for most investors, today's consumption is valued higher than consumption later. So it is better to have a certain amount of money available today than at some point in the future. This reduced benefit from future payments is offset by an investor receiving interest on his invested capital.

Personal preference for use is not decisive, however, if funds can be invested and borrowed in a functioning capital market . With the help of the capital market, payments can then be transformed through time. In the model world, the same interest rate is often assumed for the term for both invested and borrowed money. The interest rates for the individual maturities form a yield curve . ${\ displaystyle r (t)}$ ${\ displaystyle t}$ ${\ displaystyle t_ {1}, t_ {2}, \ ldots, t_ {n}}$

The present value of a cash flow is then ${\ displaystyle Z}$ ${\ displaystyle Z}$

{\ displaystyle P (Z) = \ sum _ {i = 1} ^ {n} \, {\ frac {1} {\ left (1 + r (t_ {i}) \ right) ^ {t_ {i} }}} \ cdot z_ {t_ {i}}}

.

The present value changes when the interest rates change. With stochastic interest rates, even a secure cash flow can have a stochastic present value. ${\ displaystyle r (t_ {i})}$

Evaluation of uncertain cash flows

In the case of uncertain payment flows, the risk of the payment flow must be explicitly assessed. Typical risks are credit risks , market risks and liquidity risks . There are two different ways to determine the present value.

A common method is to charge a premium ( spread ) on the risk-free interest rate for the risk assumed . The present value is then ${\ displaystyle s}$ ${\ displaystyle r}$

{\ displaystyle P (Z) = \ sum _ {i = 1} ^ {n} \, {\ frac {1} {\ left (1 + r (t_ {i}) + s (t_ {i}) \ right) ^ {t_ {i}}}} \ cdot z_ {t_ {i}}}

.

The surcharge of a system with a comparable risk can often be used as a first approximation. In the case of risk aversion , the premium is negative. ${\ displaystyle s}$

The second option is to determine a security equivalent for each payment . This is understood to be a secure payment that brings the recipient the same benefit as the insecure payment. In the case of risk aversion, the security equivalent is lower than the expected value of the insecure payment. The safety equivalent is often expressed with the help of the expected value under risk-neutral probabilities : ${\ displaystyle z (t_ {i})}$

{\ displaystyle P (Z) = \ sum _ {i = 1} ^ {n} \, {\ frac {1} {\ left (1 + r (t_ {i}) \ right) ^ {t_ {i} }}} \ cdot E ^ {Q} [z_ {t_ {i}}]}

.

The former method has proven itself in practice, while the latter is much more abstract and can mainly be found in academic models.

Cash flows in capital market theory

In capital market theory , especially in financial engineering, payment flows play a prominent role. To value derivatives, a possibility is being sought to duplicate the cash flows of a new security using a portfolio of existing instruments . The common argument in financial engineering is that in a market without arbitrage the derivative must have the same present value as the duplication portfolio. The duplication portfolio is also known as a hedge . A duplication portfolio does not have to be static, but can be dynamically adapted to market developments using a hedge strategy , especially with options .

A model capital market fulfills the spanning condition if all cash flows can be duplicated through existing capital market instruments or through portfolios from such instruments.

Individual evidence

↑ Klaus Schredelseker, Fundamentals of Finance , 2013, p. 17
↑ IDW Standard S1, 2008, Section 4.4.1.1
↑ Florian Böhmdorfer / Peter Kralicek / Günther Kralicek, key figures for managing directors , 2009, o. P.

[1] Klaus Schredelseker, Fundamentals of Finance , 2013, p. 17

[2] IDW Standard S1, 2008, Section 4.4.1.1

[3] Florian Böhmdorfer / Peter Kralicek / Günther Kralicek, key figures for managing directors , 2009, o. P.