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Discount
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A "Discount" is a "Charge" that is paid to obtain the right to delay a payment. Essentially, the payer purchases the right to make a given payment in the future instead of in the Present. The "Discount", or "Charge" that must be paid to delay the payment, is simply the difference between what the payment amount would be if it were paid in the present and what the payment amount would be paid if it were paid in the future.
Since a person can earn a return on money by investing it, most economic models assume the "Discount Rate" is the same as the rate of return the person could receive on invested money.
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Encyclopedia
A "Discount" is a "Charge" that is paid to obtain the right to delay a payment. Essentially, the payer purchases the right to make a given payment in the future instead of in the Present. The "Discount", or "Charge" that must be paid to delay the payment, is simply the difference between what the payment amount would be if it were paid in the present and what the payment amount would be paid if it were paid in the future.
Since a person can earn a return on money by investing it, most economic models assume the "Discount Rate" is the same as the rate of return the person could receive on invested money. The person delaying payment must actually compensate the person who should be paid for the lost revenue that could be earned from an investment during the time period covered by the delay. Since an investor earns a return not only on the original principle investment, but also on the earnings made from the original investment, earnings are compounded as time moves forward into the future. Therefore, this is usually the justification for having the growth of the "Discount" compounded over the time period the payment is delayed. The “Discount Rate” is the rate growth of the “Discount”.
We are essentially using compounding from the basic time value of money calculations to assess the future value of money that could be obtained in the present, and using this assessment to determine the “Discount” associated with delaying the payment until the said future date. As a result, the “Discount” that must be paid for delaying the payment of $P for t periods is:
- Discount = $P * (1 + r)t - $P
- where $P * (1 + r)t is the future value of the payment since invested today at an r rate of return.
This is similar to the process of finding the present value of an amount of cash at some future date by using compounding from the basic time value of money calculations. Of course, the present value of a future payment may be also called the “discounted value” of the future payment since it is arrived at by removing the “Discount” from the future payment. The value of the future payment is reduced its by the appropriate discount rate for each unit of time the person must wait before the payment is received. Hence, the “Discounted Value” of receiving $F t periods in the future is
- ”Discounted Value” = $F / (1 + r)t
Example
To calculate the 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.
Consider the task to find the present value PV of $100 that will be received in five years. Or equivalently, which amount of money today will grow to $100 in five years when subject to a constant discount rate?
Assuming a 12% per year interest rate it follows
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Discount rate
The discount rate which is 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 cashflows, with other developments.
The discount rates typically applied to different types of companies show significant differences:
- Startups seeking money: 50 – 100 %
- Early Startups: 40 – 60 %
- Late Startups: 30 – 50%
- Mature Companies: 10 – 25%
Reason for high discount rates for startups:
- Reduced marketability of ownerships because stocks are not traded publicly.
- Limited number of investors willing to invest.
- Startups face high risks.
- Over optimistic forecasts by enthusiastic founders.
One method that looks into a correct discount rate is the capital asset pricing model.
This model takes in account three variables that make up the discount rate:
1. Risk Free Rate: The percentage of return generated by investing in risk free securities such as government bonds.
2. Beta: The measurement of how a company’s stock price reacts to a change in the market. A beta higher than 1 means that a change in share price is exaggerated compared to the rest of shares in the same market. A beta less than 1 means that the share is stable and not very responsive to changes in the market. Less than 0 means that a share is moving in the opposite of the market change.
3. Equity Market Risk Premium: The return on investment that investors require above the risk free rate.
Discount rate= risk free rate + beta*(equity market risk premium)
Discount factor
The discount factor, P(T), is the number which a future cash flow, to be received at time T, must be multiplied by in order to obtain the current present value. Thus, a fixed annually compounded discount rate is
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For fixed continuously compounded discount rate we have
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Other discounts
For discounts in marketing, see discounts and allowances, sales promotion, and pricing.
External links
See also
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