Full scale method

The terminal value method is a decision-making process of the classic dynamic investment calculation, in which in the end the alternative action that brings the highest (asset) terminal value is preferred .

The final value of an investment is the sum of the final values ​​of the individual excess payments of the investment being examined. To determine these final values of each individual payment surplus is applied to the end of life is unwound , being made between a total calculation and a difference calculation differs (s u..): While in the former, the end values of the investment and of their expediency determined (alternative without this investment) and compared, is in the latter case (only) the additional final value of the investment is determined.

example

First, the final values ​​for the company with the investment ( EW ^M ) and without the investment ( EW ^O ) are to be calculated. The following applies to EW ^M :

• ${\displaystyle EW^{M}=-FK_{0}\cdot q^{n}+\sum _{t=1}^{n}{d_{t}\cdot q^{n-t}}}$

For the final value of the opportunity (i.e. alternative without investment), however, the following applies:

• ${\displaystyle EW^{O}=EK_{0}\cdot q^{n}}$

Are there

• n - useful life n of the investment object in years
• i - discount rate and ${\displaystyle q=1+i}$
• FK ₀ - Borrowing at the beginning of the investment (t = 0)
• EK ₀ - Capital employed at the beginning of the investment (t = 0)

Payment surplus (possibly negative) in period t

• ${\displaystyle d_{t}=(EK_{0}+FK_{0})-a_{t}=a_{0}-a_{t}}$

Are there

• ${\displaystyle a_{0}}$ - Rate at the beginning of the year
• ${\displaystyle a_{t}}$ - rate at the end of the year

Final value factor (EWF)

also called final pension value factor (REF)

• ${\displaystyle EWF=((i+1)^{n}-1)/\ i}$

An investment is to be assessed positively if it has a higher final value than the final value of its opportunity, for example investing one's own funds in the capital market or using it for another project. The return on the opportunity is determined with the discount rate i , so that an investment based on the total calculation of the terminal value method is advantageous if . ${\displaystyle EW^{M}>EW^{O}}$

Difference consideration

The additional final value ΔEW ( Delta EW ) of an investment results from the difference between the final value with the investment and the final value without the investment:

• ${\displaystyle \Delta EW=EW^{M}-EW^{O}}$

Are there

• EK ₀ - equity at the beginning of the investment (t = 0)
• FK ₀ - Borrowing at the beginning of the investment (t = 0)

Purchase payment a ₀

• ${\displaystyle a_{0}=EK_{0}+FK_{0}}$

Therefore, a formula for ΔEW can be given directly by inserting it into the equation and transforming it:

• ${\displaystyle \Delta EW=-a_{0}\cdot q^{n}+\sum _{t=1}^{n}{d_{t}\cdot q^{n-t}}}$

According to the difference calculation of the end value method, an investment is advantageous if the additional end value ΔEW is positive.

The additional final value can also be determined by adding interest to the capital value (additional initial value) of the investment by multiplying it with at the end of the investment. ${\displaystyle (1+i)^{n}}$

See also

• Pension present value factor