## Approaches to Calculating the Cost of Capital

This section discusses how to price risky securities to determine if a business should undertake an investment. Why is this important? When you finish this section, you should understand unsystematic risk, systematic risk, and beta.

### The Capital Asset Pricing Model

The capital asset pricing model (CAPM) allows us to price risky securities in order to determine if an investment should be undertaken.

#### LEARNING OBJECTIVE

• Calculate a company's expected rateof return using the Capital Asset Pricing Model (CAPM)

#### KEY POINTS

• CAPM determines the expected rate of return of an asset.
• The model takes into account the asset's sensitivity to systematic risk (beta), the expected return of the market, and the expected return of a risk-free asset.
• CAPM states that investors are only rewarded for bearing systematic risk.
• CAPM states that if the expected return is not greater than or equal to our required return the investment should not be made.

#### TERMS

• Unsystematic risk

Risk peculiar to an asset, which can be eliminated through diversification.

• systematic risk

The risk associated with an asset that is correlated with the risk of asset markets generally, often measured as its beta.

• beta

Average sensitivity of a security's price to overall securities market prices.

#### EXAMPLE

• The current risk-free rate is 5%. The market is expected to return 12% next year. The beta of the security is 1.9. Expected return = 5% + 1.9*(12% - 5%). Expected return = 18.3%. If 18.3% is greater than or equal to the return we require, the investment should be undertaken.

#### The Capital Asset Pricing Model (CAPM)

The capital asset pricing model is a financial model, used to price risky securities, that describes the relationship between risk and expected return. It determines what the rate of return of an asset will be, assuming it is to be added to an already well-diversified portfolio, given that asset's systematic risk. The model takes into account the asset's sensitivity to market fluctuations, often represented by the quantity beta (β), as well as the expected return of the market and the expected return of a theoretical risk-free asset .

$E(R_i) = R_f + \beta_i (E(R_m) - (R_f)$

CAPM Equation: The expected rate of return = the rate of return for a risk-free asset + beta* (the rate of return of the market - the risk-free rate). The return of the market minus the risk-free rate is also known as the risk premium.

CAPM assumes that every asset is correctly priced. In real world applications, it enables us to determine whether or not a security is a worthwhile investment by comparing the expected rate of return of the security, given by the CAPM equation, with the actual rate of return. If the actual return is greater than or equal to what we expect from CAPM, then the investment should be undertaken.

#### Assumptions of CAPM

All investors:

1. Aim to maximize economic utilities.
2. Are rational and risk-averse.
3. Are broadly diversified across a range of investments.
4. Are price takers, i.e., they cannot influence prices.
5. Can lend and borrow unlimited amounts under the risk-free rate of interest.
6. Trade without transaction or taxation costs.
7. Deal with securities that are all highly divisible into small parcels.
8. Assume all information is available at the same time to all investors.

Further, the model assumes that past returns will effectively predict the future risk associated with a given security.

#### Systematic vs. Unsystematic Risk

Systematic risk - also called market risk or non-diversifiable risk - represents the risk present in a security in relation to the economy as a whole. Unsystematic risk - also called idiosyncratic risk or diversifiable risk - represents the risk present in a security that is specific to that investment and unrelated to the overall risk of the market .

Systematic vs. Unsystematic Risk: As the number of stocks in a portfolio increase, the amount of unsystematic risk approaches zero. However, it is impossible to remove systematic risk, as it concerns the economy in general.

CAPM states that in market equilibrium, investors are only rewarded for bearing systematic risk - the type of risk that cannot be diversiﬁed away. Investors should not be rewarded for bearing unsystematic risk, since this uncertainty can be mitigated through appropriate diversiﬁcation.

Source: Boundless