How do you calculate the cost of equity?

In general I would take the minimum rate of return, which is a relativly risk free security, which might be bonds issued from stable souvereigns. To this minimum rate of return I would add the premium you might expect for taking the risk of your investment (difference between risk-free rate and market rate) adjusted by the beta coefficient reflecting the specifics of your industry/investment (Beta). In case you are not sure if your investment would deviate from other comparable investments you can set Beta =1. However, this strongly depends on your investment. You can check on public available database to see some comparables for the Beta. To reflect the different weight of different aspects of equities, I would take weighted average cost of equity. This depends on the capital structure of your company. From an islamic point of view, one might argue it can be an issue to take an interest driven risk free security as a bases for your calculation as you would not be allowed to invest in such securities. (Typically bonds are used). However, if you would follow such argumentation, you would find Sukuks with sufficient history to reflect a proper rate of return and show a relativly strong stability.

The formula is:

Cost of equity (re) = Risk free rate (rf) + β x Market risk premium (rm-rf )

• Risk free rate: The risk free rate should theoretically reflect yield to maturity of a default-free government bonds of equivalent maturity to the duration of each cash flows being discounted. In practice, lack of liquidity in long term bonds have made the current yield on10-year U.S. Treasury bonds as the preferred proxy for the risk-free rate for US companies.
• Market risk premium: The market risk premium (rm-rf) represents the excess returns of investing in stocks over the risk free rate. Practitioners often use the historical excess returns method, and compare historical spreads between S&P500 returns and the yield on10 year treasury bonds.

• Beta (β): Beta provides a method to estimate the degree of an asset’s systematic (non-diversifiable) risk. Beta equals the covariance between expected returns on the asset and on the stock market, divided by the variance of expected returns on the stock market. A company whose equity has a beta of1.0 is “as risky” as the overall stock market and should therefore be expected to provide returns to investors that rise and fall as fast as the stock market. A company with an equity beta of2.0 should see returns on its equity rise twice as fast or drop twice as fast as the overall market.