Discount Rate
Definition and Overview
A discount rate refers to the interest rate that a central bank, like the Federal Reserve System in the United States, charges financial institutions for loans obtained through its discount window lending facility. It is a critical tool in monetary policy and is used to control the supply of money in the economy.
The discount rate also has other applications in finance, such as in the calculation of present value of future cash flows, and in the Capital Asset Pricing Model (CAPM) to determine the cost of equity.
Central Bank Discount Rate
The central bank discount rate is a tool used by central banks to influence monetary policy. By adjusting the discount rate, the central bank can control the cost of borrowing for financial institutions, which in turn affects the interest rates those institutions charge their customers.
When the central bank raises the discount rate, it makes borrowing more expensive for financial institutions, which can lead to a decrease in the money supply as banks lend less. Conversely, lowering the discount rate makes borrowing cheaper, potentially increasing the money supply as banks are more willing to lend.
Discount Rate in Present Value Calculation
In finance, the discount rate is used to determine the present value of future cash flows. This is based on the concept of time value of money, which states that a dollar today is worth more than a dollar in the future due to the potential earning capacity of the money.
The formula for calculating the present value (PV) of a future cash flow (FV) is:
PV = FV / (1 + r)^n
where: - r is the discount rate - n is the number of periods
Discount Rate in Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is a financial model that determines the expected return on an investment given its risk. The discount rate in CAPM is used to calculate the cost of equity, which is the return required by an investor to hold a particular stock.
The formula for CAPM is:
E(Ri) = Rf + βi * (E(Rm) - Rf)
where: - E(Ri) is the expected return on the investment - Rf is the risk-free rate - βi is the beta of the investment - E(Rm) is the expected return of the market
The term (E(Rm) - Rf) is known as the market risk premium, and it represents the excess return that an investor requires for taking on the additional risk of investing in the market over a risk-free asset.
Conclusion
The discount rate plays a crucial role in various aspects of finance, from central banking to investment analysis. Understanding how it works can provide valuable insights into the workings of financial markets and the economy as a whole.
See Also
- Federal Reserve System - Present Value - Capital Asset Pricing Model - Time Value of Money - Risk-Free Rate - Market Risk Premium