Discount

Quick Summary of Discount

Discount. In a bond trade, discount is the difference between face value and the market price.

1. The amount by which a bond’s par exceeds its market price.
2. The amount by which the Net Asset Value per share of a closed-end fund’s holdings exceeds its market price.
3. Anything selling below its normal price. opposite of premium.
4. In the case of a convertible security, the difference between the gross proceeds received on sale and the convertible’s price. This difference occurs whenever the market expects that the convertible security will be redeemed before the next coupon date, and so investors will receive the accrued interest.

A discount is a difference between the price paid for an asset and the specified list price of a good or face value of an instrument. For instance, a bank holding a defaulted mortgage may settle the obligation at a significant discount by accepting less than the principal owed from an investor who is buying the property. The discount may be acceptable to the bank when it avoids the legal expenses and time that would be involved in foreclosure proceedings. This particular type of discount is often called a haircut. A bond is said to trade at a discount to its face value at maturity, and in this context, the discount rate is the interest rate used to determine the present value of future cash flows. The word discount can be used not only as a noun but also as a verb. A seller is said to discount an asset by lowering the price.

In finance, discounting is the process of finding the current value of an amount of cash at some future date, and along with compounding cash form the basis of time value of money calculations. The discounted value of a cash flow is determined by reducing its value by the appropriate discount rate for each unit of time between the time when the cash flow is to be valued to the time of the cash flow. Most often the discount rate is expressed as an annual rate.

To calculate the net present value of a single cash flow, it is divided by one plus the interest rate for each period of time that will pass. This is expressed mathematically as raising the divisor to the power of the number of units of time.

Example

For example: You want to find the net present value of $100 that will be received in five years’ time. What is it worth now? What amount of money, if you let it grow at the discount rate, would equal $100 in five years?
We will assume a 12% per year discount rate.

NPV = 100 dollars divided by 1 plus 12% (0.12) divided by 1 plus 12% (0.12), etc.

:{\rm NPV}=\frac{100}{(1+0.12)^5}.

Since 1.125 is about 1.762, the net present value is about $56.74.

Discount rate

The discount rate used in financial calculations is usually chosen to be equal to the cost of capital. Some adjustment may be made to the discount rate to take account of risks associated with uncertain cash flows.

Discount factor

The discount factor’, P(T), is the number by which a future cash flow to be received at time T must be multiplied in order to obtain the current present value. Thus for a fixed annually compounded discount rate r we have
: P(T) = \frac{1}{(1+r)^T}

For a fixed continuously compounded discout rate r we have

: P(T) = e^{-rT}

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