When firms consider issuing equity, or 'stock', which is a share in theownership in the firm,the cost can be estimated by using a number of approaches. The most frequently used today is the capital asset pricing model (CAPM). This model says that the market-required return on any capital asset (equity or stock being examples of 'capital assets') can be estimated by considering the risk-free rate of return, because investing means that consumption must be delayed, plus an adjustment factor which considers how variable the asset's return is relative to the market portfolio of all risky assets, because investors generally require a higher return when higher variability and risk are present. If the asset's returns vary exactly with the market, the adjustment factor will be the number one (1), and the required return will be equal to the market return. The adjustment factor will be greater than one when the asset returns are more variable than the market, and generally in the same direction with the market. The adjustment factor will be between zero and one when the asset returns are less volatile than the market, and again in the same direction. If the asset's returns generally vary in the opposite direction from the market returns, the adjustment factor will be negative. This adjustment factor is referred to as 'Beta' or .The estimated cost of equity (also the investors' required return) is then calculated with the formula Ra = Rrf + (MRP x a), where:

Ra = Market's required return on Firm A's stock

Rrf= Risk-free rate, usually estimated by the yield on 10-year US treasury notes

MRP = Market Risk Premium,estimated by the difference between the return of the market (Rm) and the risk-free rate (Rrf)

Rm = The return of the market, often estimated by the return on the S&P 500

a = Beta = The adjustment factor considering Firm A's variability of returns relative to the market

It is important to note that, generally speaking, a firm faces two types of risk, firm-specific risk and market risk. Firm-specific risks are those events that only affect the firm, such as a new CEO, a new patent or a labor dispute. Market risks are those that affect all participants in the economic system, such as growth in Gross Domestic Product, unemployment and inflation. Beta only measures the firm's sensitivity to market risks. Firm-specific risks are not considered because investors can neutralize those risks by holding a diversified portfolio of investments.

Also, please note that Beta is not stable over time. A firm's composition of projects that are in progress and products that are being sold are constantly changing, and each of those projects and products conceptually have their own Betas, with the firm's Beta being the weighted average of all the project and product Betas. As projects and products with different Betas come and go, it's logical that the firm Beta would change over time.

1. So if the current market conditions are such that the risk-free rate is 2%, the market risk premium is 10% and Firm A's Beta is 1.25, what would be the investors' required return on an investment in firm A's stock?
2. If Firm B is less volatile than the market, and has a Beta of 0.5, what would be its required return in the same market conditions as listed above?
3. If Firm B had a pressing need to increase its financial returns, so invested in several larger higher-risk projects, what would you think would happen to its Beta over time?