# Investment calculation

Discounting (sample overview)

The investment calculation comprises all procedures that enable a rational assessment of the calculable aspects of an investment . For this purpose, the financial consequences of an investment should be quantified and summarized in order to give a decision recommendation.

The investment calculation is the most important aid for investment decisions (> 50%). It is important for pre-selection and recalculation and is independent of the investment decision.

In addition to the investment calculation, other factors play a role in actually making an investment - as in many decision-making processes. These are of a technical, legal and economic nature or are shaped by personal preferences .

The investment term used is decisive for the various investment calculation methods:

• From the accounting point of view, an investment is the transfer of means of payment into tangible and financial assets. All static methods are based on this view.
• Within modern investment theory , an investment is viewed as a cash flow of all deposits and withdrawals . The dynamic procedures are based on this view.

## Classic procedures

### Static process

Static methods use performance indicators from cost and revenue accounting. This is to keep the data collection effort low and the computing effort limited. Instead of using the individual data from the net payments and the initial payment, average values ​​are formed. In the case of very different payment structures, an average analysis can only provide approximate values.

### Dynamic process

In the dynamic process, several periods are considered from the point of view of economic efficiency . The cash value spent on the investment is compared with the cash value of the income in a plan drawn up over several accounting periods. Obtaining the data is time-consuming due to the time difference, but it weights the time the payment flows occur by means of compounding or discounting. If the cash value of the income exceeds the investment, the investment is considered economical. Mathematical models are used to plan, implement and control investment decisions. The models are based on the payments from previous periods. The principle applies: "The money available today is worth more than what will be in the future."

## Risk assessment

With the classic methods of investment calculation and the complete financial plan, only an inadequate analysis of the individual risks is carried out. They are only included via discount rates. In order to make a meaningful business decision, it is essential to aggregate the individual risks associated with an investment.

In general, the risk and return are usually proportional, which means that the more uncertain an investment is, the higher the possible return. The relationship between these two key figures can be shown in a diagram (risk-return diagram), which makes decision-making easier, for example in the case of several investment projects. It should be noted that risk can be seen as an opportunity or a danger.

### Performance measures

Based on the positioning of an investment within the risk-return diagram, its performance measure can be derived. This results from the combination of the expected value (e.g. profit) with an associated risk measure such as standard deviation or value at risk: ${\ displaystyle E (X)}$${\ displaystyle R (X)}$

${\ displaystyle p ^ {ea} (X) = f (E (X), R (X))}$

An example of such a performance measure is the RAVA (Risk Adjusted Value Added), which, in contrast to the common EVA (Economic Value Added), records aggregated earnings risks in a planning-consistent and adequate manner.

${\ displaystyle RAVA = E (X) -r_ {f} \ cdot CE- \ lambda _ {1-p} \ cdot EKB_ {1-p}}$

The RAVA reduces the expected profit minus risk-free interest on the capital employed by a risk discount. The most commonly used measure of risk is the equity requirement.

### Effect of Risks

In the context of the investment calculation, risks affect two sizes. On the one hand on the expected value and on the other hand on the risk discount or discount rate . The expected value assumes the most likely value for repayment and assigns a probability of occurrence. The same is done for a minimum and maximum expectation ( triangular distribution ). The expected repayment results from the summation of the values ​​multiplied by their probability of occurrence. Expected values ​​are always a preferable alternative to plan values ​​and form a calculation basis for determining further parameters. For example for the net present value :

${\ displaystyle {\ text {net present value}} = - {\ text {investment}} + {\ frac {\ text {expected repayment}} {(1 + {\ text {discount rate}})}}}$

If the result is> 0, the investment is considered economical and should be carried out.

The risk discount can also be determined using the expected value . This is namely the difference between the expected value and the safety equivalent . Risk discounts are characterized by risk-averse behavior. The higher the risk aversion of the decision maker and the higher the risk, the greater the discount. In this case, risk premiums have to be created to compensate the decision maker.

An alternative to valuing investments, in addition to the risk discount, is risk-based discounting . For this purpose, a risk-adjusted discount rate is determined with which the investment is discounted. This interest rate is calculated as follows:

${\ displaystyle k = r_ {f} \ cdot \ lambda \ cdot V \ cdot d}$

With

${\ displaystyle \ lambda = {\ frac {r_ {m} ^ {e} -r_ {f}} {\ sigma _ {r_ {m}}}}}$ and ${\ displaystyle V = {\ frac {\ sigma ({\ tilde {Z}})} {E ({\ tilde {Z}})}}}$

${\ displaystyle r_ {f}}$is the risk-free rate. is the “market price of risk” and expresses risk aversion. It can be derived from the risk-return profile (risk-return diagram) of the alternative investment opportunities. is the so-called risk diversification factor, which shows what proportion of the risks of a project the owner has to bear (taking into account risk diversification effects). Finally, the coefficient of variation . This takes into account the fluctuation range of a yield over the standard deviation . The value of the discount rate corresponds to a return appropriate to the scope of the risk . ${\ displaystyle \ lambda}$${\ displaystyle d}$${\ displaystyle V}$

In practice, the cost of capital is often a valuation basis for investment projects. Business activity is namely valued according to whether the expected return is sufficient to cover the capital costs required. This is precisely why these should be recorded in accordance with the risk. This is done by adding a premium to the cost of capital in the amount of the risk-free cost of capital, a so-called risk premium. This increase creates a direct comparison between the uncertain and the safe investment alternative (safe alternative = investment at the risk-free market interest rate). How high the risk premium is depends on the risk assessment of the evaluator and the respective evaluation approach. In practice, flat-rate risk premiums are often added to the risk-free interest rate . The problem here lies in the subjectivity of the determination of flat-rate risk premiums, which appear arbitrary due to a lack of theoretical justification.

### CAPM

The Capital Asset Pricing Model (CAPM) was originally only used to calculate stock returns. Due to the lack of alternatives and the simplicity of the model, it was expanded and used, for example, to assess investment projects. For this purpose, however, it is irrelevant in practice, since the imperfection of the capital market is not taken into account (“assumption of the perfect capital market”). Risk is recorded in the CAPM using the so-called β-factor, which represents a measure of the risk of individual stocks in relation to the risk of the market.

If the traditional approach of the CAPM still wants to be used, the risk reduction or security equivalent variant of the CAPM should be used. The information relevant to the valuation about the risks of insecure payment is condensed to a suitable risk level and taken into account in the value calculation.

### Replication approach

An alternative to CAPM, without its restrictions, is the derivation of evaluation equations by means of replication . To determine the value of an insecure payment, a periodic model, an unbiased and risk-adequate duplication (replication) is carried out. There should be two investment options for this, the market portfolio with an uncertain return and a risk-free investment with interest . Other alternative investments can also be considered. ${\ displaystyle r_ {f}}$

If the same assumptions are made in the replication as in CAPM and the risk measure contains the same information as the standard deviation and the β-factor, then there is no contrast between the two.

An extension to multi-period payments is also possible. The payment then not only models returns from operational transactions in the current operating period, but also includes the value of the company at the end of the period (assuming that plant A can be sold at the end of the period).

### Risk coverage approach

In contrast to the classic WACC approach ( Weighted Average Cost of Capital , based on CAPM ), the risk coverage approach is not based on the assumption of a perfect market. The equity required to cover the risks is used as a measure of risk. This means that possible fluctuations in a market price of the investment project can be neglected. The capital costs are determined individually via the financing costs of the capital. As an alternative measure of risk , the standard deviation of profits or free cash flow can also be used here instead of the equity requirement ( VaR ) . Since this approach expresses the extent of possible deviations from the expected value, it is to be used specifically for the valuation of entire companies or, in principle, more salable assets.

### Monte Carlo simulation

In general, risks cannot be added together and simple analytical formulas are only suitable for calculating the total risk in a few realistic special cases. The reasons for this are various interactions between the risks. In order to nevertheless determine the overall risk aggregation, an iterative procedure, the Monte Carlo simulation , is used.

The main advantage of the Monte Carlo simulation is that the often difficult estimation of statistical dependencies between the risky planning variables of the income statement is considerably simplified. After the model has been developed, the simulation can start and the possible future scenarios are calculated. After the end of the runs, risk-adequate expected values ​​(or frequency distribution of the overall risk) result with which further calculations are possible

## Individual evidence

1. ^ AG Coenenberg , Thomas M. Fischer, Thomas Günther: Cost accounting and cost analysis. 6th edition. Schäffer-Poeschel, Stuttgart 2007, ISBN 978-3-7910-2491-2 , p. 16.
2. Werner Gleißner : Risk-based assessment and management decisions . S. 7 .
3. a b Werner Gleißner: Risk assessment for investments: Determination of risk-appropriate financing structures and return requirements through simulations . Ed .: Gleich, R. / Klein, A. Band 30 , p. 226 .
4. Werner Gleißner: Fundamentals of Risk Management . 3. Edition. S. 32 .
5. Robert Gillenkirch: risk discount. Retrieved December 3, 2017 .
6. Werner Gleißner: Fundamentals of Risk Management . S. 43 .
7. Werner Gleißner: Fundamentals of Risk Management . S. 44 .
8. Ulrich Schacht: Practical Guide Company Valuation . 2nd Edition. Springer, S. 109 .
9. Ulrich Schacht: Practical Guide Company Valuation . 2nd Edition. Springer, S. 109 .
10. Boris Nöll: Investment calculation under uncertainty . S. 216 .
11. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 346 .
12. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 346 .
13. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 347 .
14. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 347 .
15. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 349 .
16. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 349 .
17. Werner Gleißner: Risk assessment for investments: determination of risk-appropriate financing structures and return requirements through simulations . Ed .: Gleich R. / Klein, A. S. 216 .
18. Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . S. 348 .