**DISCOUNT RATES IN APPRAISAL WORK: THE CAPM**

DISCOUNT RATES IN THE APPRAISAL ACTIVITY: THE CAPM

One of the specific and most interesting activities of the Chartered Accountant and Statutory Auditor profession is certainly the one related to the **drafting of appraisals**: the professional is called upon to carry out **appraisals** of different types, depending on the purpose required, for example, having tax purposes, in connection with arbitrations or civil proceedings in the presence of disputes related to the transfer price, fairness opinions and professional assignments of other nature, in conjunction with extraordinary finance transactions such as transformations, transfers, mergers, demergers, quotations and so on.

Depending on the objective set, there are **different valuation methodologies** that therefore involve different parameter estimates: however, it always turns out to be a **key component** to calculate and choose the **discount rate** to be used in the valuation.

THE DISCOUNT RATE

The discount rate is equal to the rate of interest to be used to transfer to time zero, i.e., to today, a financial principal or cash flow that is due exclusively at a specified future date, so that the discounted principal or flow, due today, and the one due in the near future are financially equivalent.

The determination of the **discount rate** usually relates to **two parameters**:

- the
**pure interest rate**, that is, the rate paid for the use of capital in investments with zero risk; - the
**markup for the assumed business risk**, that is, the risk of incurring losses and not profits from the capital investment made.

THE CAPM

The most widely used model for said calculation is the **CAPM**: an acronym for "**Capital Asset Pricing Model**", it is an equilibrium model of financial markets proposed by W.Sharpe, which earned him along with M.Miller and H.Markowitz the Nobel Prize in economics in 1990.

According to CAPM theory, the cost of equity capital, Ke, equivalent to the rate of expected return on business activity Ri, is regarded as the **rate of return on equity** or **the minimum rate of return** that a firm must offer to its partners or shareholders in order to **remunerate** **the funds** received and invested by them. Since it is a **return** to the shareholder, it is **linked to the risk** to which the shareholder is exposed, namely **systemic** and **typical****investment** risk.

The CAPM is derived by estimating the following parameters:

CAPM = Ke = Ri = Rf + β x (Rm - Rf) = Rf + β x (ERP),

where,

- Ke, is the cost of equity capital or minimum rate of return;
- Ri is the expected return on the business activity;
- Rf is the risk-free rate of the investment. This rate
**does not conceptually incorporate risk**: it is usually taken to be equal to the rate of return on a**nation's**medium- to long-term**government bonds**, because of the**remote possibility of default**; normally, for Italy, the average rate of ten-year BTPs is chosen and implies that the**investment**in the business**must at least return that return**. The choice of the time horizon of benchmark government bonds is in derivation of the presumption that a nation has no real chance of default, however, too much uncertainty is dumped on the 30-year curve, which is why 10-year rates are usually used in practice; - β x (Rm - Rf) or also β x (ERP) is the equity risk premium, i.e., the
**extra yield of the reference market in excess of the risk-free yield**. The**β**expresses the**correlation between returns**, acting as a risk-weighting factor; the ERP is affected by a variety of factors, however, it can be easily stated that it is**country specific**, since it depends on the reference country and varies depending on the market being analyzed: very often, to achieve extreme model accuracy usually the value of inflation is subtracted from the ERP.

IMPLICATIONS IN PARAMETER ESTIMATION

The following should be taken into account when estimating the discount rate through the CAPM model:

- the risk-free rate contains country risk since it is based on government bonds, and although they are defined as risk-free, they actually incorporate the remote risk of individual country default that generates differences in the yields of such bonds. Consequently, since the equity risk premium is to be measured as the difference between market yield and risk-free yield, it necessarily depends on the "country" of reference: while this effect is unavoidable, it is therefore important that the
**rate used in the calculation of the equity risk premium**be the**same**as the**risk-free rate**, since the country risk must be the same in the two addends, and consequently refer to the same country; - once the equity risk premium for the given market is determined, it is necessary to weight the risk
**using****β**; in fact, the risk profiles of different firms do not coincide, and the equity risk premium must therefore be adjusted to be translated and referred to the risk of the specific firm being evaluated.

β can be **estimated** in several complicated ways, however, by considering a certain time interval, the return of the stock being evaluated can be determined and compared with the market return. In general, as mentioned above, **β** expresses the correlation between returns and explains how the company under consideration behaves relative to the general market performance, **in terms of risk**:

- a β = 1 implies that the firm has the
**same risk profile**as the market, Ke = Rm; - a β < 1 implies that the firm has
**less market risk**, Ke < Rm; - a β > 1 implies that the firm has
**greater market risk**, Ke > Rm.

The estimation of β can lead to the following problems in its determination:

- the correct estimation of the period of measurement and frequency of data, as the readings may be daily, weekly, monthly;
- the correct calculation of the yield, since, for example, it may be based on a share price that does or does not include the dividend;
- the exact reference index, since beta is a correlation index that can be calculated with reference to the market index or the specific segment, in which the stock is listed.

Consequently, in light of the considerations so far, it is stated that, given the complexity of estimating the various parameters, in order to have the best weighting of the discount rate estimated by means of the CAPM, the parameters estimated by the best reference institutes, one above all the Stern School of Business at New York University, headed by Professor Aswath Damodaran, a true guru of "corporate finance and valuation," are usually used in the equation above.

Edited by: *Luigi Alfredo Carunchio, Chartered Accountant and Statutory Auditor*

You can download the article in PDF here

For more information:

luigicarunchio@valoreassociati.it

*The firm fully supports clients in the preparation of appraisal reports*

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