# Discount Rate Formula

The Discount rate is an interest rate a Central Bank charges depository institutions that borrow reserves from it. Discount rate is calculated on the basis of future cash flow. We will also depict the mathematical expression of discount rate.

In the United States of America, the commercial banks are charged at the discount rate on their loans provided by the Federal Reserve Bank. The Fed offers discount rate through several channels like, secondary credit, seasonal credit and primary credit. Under primary credit, loans are usually extended for a short span of time for those depository institutions that has been maintaining a sound financial growth whereas; secondary credit is provided to the small institutions.

The discount rate used is generally the appropriate Weighted Average Cost of Capital (WACC), which reflects the risk of the cash flows. The discount rate reflects two things:

1. The time value of money (risk-free rate) – According to the theory of time preference, investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay.
2. A risk premium – It reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all.

An alternative to including the risk in the discount rate is to use the risk free rate, but multiply the future cash flows by the estimated probability that they will occur (the success rate). This method, widely used in drug development, is referred to as rNPV (risk-adjusted NPV), and similar methods are used to incorporate credit risk in the probability model of CDS valuation.

## Discount Rate Formula:

Discount rate (d) can be mathematically depicted as follows:

d = i / (1 + i)

where i = interest rate.
This formula is used to calculate “Principal Future Value” and, how much future value is will be taken as interest.

In other way it can be calculated as:

d = (F*n – P) / F*n
where F = future value of cash flow,
n = no. of years,
P = Present value of cash flow
Here, the divisor is the resultant future value of cash flow.