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# Discount rate

The term discount rate is used in several different contexts: mathematical discount rate, monetary policy, and project valuation.

### Mathematical Discount Rate

Discount rate normally refers to the interest rate, though in fact a discount rate is slightly different from the interest rate, in terms of how it is calculated. This is because the discount rate is based on the future cash flow in lieu of the present value of the cash flow.

Assume I have $80, and I buy a government bond that pays me$100 in a year's time. The discount rate represents the discount on the future cash flow:

(100–80)/100= 20%

The interest rate on the cash flow is calculated using 80 as its base:

(100–80)/80= 25%

It should become apparent that for every interest rate, there is a corresponding discount rate, given by the following formula:

d= i/(1+i)

Again when referring to a cash flow being discounted, it will likely refer to the interest rate and not the proper mathematical discount rate. However, the two are separate concepts in financial mathematics.

### Monetary Policy

The discount rate is the interest rate that an eligible depository institution (such as a bank) is charged to borrow short term funds directly from the central bank through the discount window. This is also known as the base rate, as a profit-making bank will need to charge rates higher than this to its customers.

### Project Valuation

The discount rate is the value used in accounting procedures to determine the present value of future cash flows arising from a project, ie the discounted value of all future cashflows.

[itex]\mbox{PV} = \frac{C_1}{(1+r_1)^t_1} + \frac{C_2}{(1+r_2)^t_2} + ... + \frac{C_n}{(1+r_n)^t_n}[itex]

Typically, the discount rate is arrived at by beginning with the appropriate interest rate for the length of time in question, then adding an additional sum to account for risk. For example, some companies add 15% to term-specific risk-free rates.

As such, the discount rate used will almost always vary from project to project, and will likely vary for cash flows of different maturities when valuing the same project.

The concept of a discount rate is an old one – the future is uncertain, and having something now is worth more than (maybe) having it later. This is reflected in the saying "A bird in the hand is worth two in the bush."