Time value of money

The time value of money ( English time value of money , TVM ) is a central component of the financing - and capital budgeting as well as financial mathematics and is based on the return of the money and means that money you have today is worth more than money one will own in the future. In other words: "One euro today is better than one euro in a year." If you give the bank an amount of money today, this amount will be repaid in one year plus interest. However, if you only receive the same amount in a year, you have to forego the interest.Economically , this relationship is known as opportunity costs .

This preference results largely from the uncertainty about future payments that arise from bankruptcy and inflation : money we have today is safe, while it is not certain that we will get the money back in the future or how much we can buy with it. The fair value concept is the basis for the identification of cash and end values .

Future value of money (final capital)

To find out how much 100 euros will be worth today in six years with an interest rate of 5% pa, use the following formula:

${\displaystyle K_{n}=K_{0}(1+i)^{n}=100(1+0{,}05)^{6}=134{,}01}$

Present value of future earnings (present value)

To find out how much 100 euros will be worth today in six years at an interest rate of 5%, use the following formula:

${\displaystyle K_{0}={\frac {K_{n}}{(1+i)^{n}}}={\frac {100}{(1+0{,}05)^{6}}}=74{,}62}$

This means that at this point in time you would have to invest the amount of € 74.62 at an interest rate of 5% to get to € 100 final value (final capital) in 6 years.

Investment calculation

The meaning of this concept becomes particularly clear in the investment calculation. With the static method, the current value is completely ignored, which means that only incomplete statements can be made about the value of an investment and thus lead to economically wrong decisions.

This relationship can be illustrated using a simple example by comparing the amortization calculation (static method) and the net present value method (dynamic method). Let us assume that the following two projects are available for selection, whereby they have the same risk and the opportunity costs of capital ( discount rate ) are a uniform 10%:

Project	${\displaystyle C_{0}}$	${\displaystyle C_{1}}$	${\displaystyle C_{2}}$	Payback period	NPV at 10%
A.	−4,000	+1,000	+3,600	2	−116
B.	−4,000	+3,600	+1,000	2	+99

Both projects have the same payback period, i.e. H. The capital employed is amortized ( paid back) in the same time for both investments . So they make sense straight away, as it doesn't matter at what point in time and in what amount the repayments are made as long as the entire return flow occurs in the same time. However, if the time value of money is included (the earlier the payment, the better) it becomes clear that project B makes more economic sense, as it has the higher net present value (today's value of the discounted cash flows). From the point of view of the net present value method, project A must be completely rejected due to the negative value.

application

The time value as a universal concept for evaluating payment flows is the basis for all modern finance, including all state finances as well as banking and insurance transactions . It is used in commodity and securities trading as well as in simple interest calculation problems , project cost accounting using the discounted cash flow method and countless more.

literature

• Pamela Peterson Drake, Frank J. Fabozzi: Foundations and Applications of the Time Value of Money. Wiley, 2009, ISBN 9780470526002

Individual evidence

1. ↑ Timothy J. Gallagher, Joseph D. Andrew Financial Management; Principles and Practice. 4th edition, ISBN 1930789025 , pp. 190 ff.
2. ^ LC Posthumus, N. Basson, P. Olivier: Principles of Financial Management. 3rd edition, Juta Academic, ISBN 9780702152788 , p. 18 ff.