Discount element - Simple Quick Loan
Discount element - Simple Quick Loan
Discount element
The discount factor, DF(T), may be the factor by which the next cash flow must
be multiplied to be able to obtain the present worth. For a zero-rate (also
known as spot rate) r, obtained from a yield curve, along with a time to cash circulation T
(in years), the actual discount factor is:
DF(T) = \frac1 (1+rT)
In case where the only discount rate you've is not a zero-rate
(neither obtained from a zero-coupon bond nor converted from the swap rate to the
zero-rate through bootstrapping) however an annually-compounded rate (for
example in case your benchmark is a ALL OF US Treasury bond with annual coupons and also you
only have its deliver to maturity, you might use an annually-compounded
low cost factor:
DF(T) = \frac1 (1+r)^T
Nevertheless, when operating in the bank, where the amount the financial institution can lend (and
therefore get interest) is from the value of its property (including
accrued interest), investors usually use daily compounding in order to discount cash
flows. Certainly, even if the interest from the bonds it holds (for example) is actually
paid semi-annually, the value of it's book of bond increases daily,
thanks to built up interest being accounted with regard to, and therefore the financial institution will
be able in order to re-invest these daily built up interest (by lending extra
money or buying much more financial products). In which case, the discount element
is then (if the typical money market day count convention for that currency is
ACT/360, in the event of currencies such as Usa dollar, euro, Japanese
yen), with r the zero-rate and T time to cash flow within years:
DF(T) = \frac1 ( 1 + \fracr360 )^ 360T
or even, in case the market convention for that currency being discounted is actually
ACT/365 (AUD, CAD, GBP):
DF(T) = \frac1 ( 1 + \fracr365 )^ 365T
Occasionally, for manual calculation, the actual continuously-compounded hypothesis
is a close-enough approximation from the daily-compounding hypothesis, and
makes calculation easier (even though it doesn't have any real software
as no financial device is continuously compounded). If so, the
discount factor is actually:
DF(T) = e^-rT
Additional discounts
For discounts within marketing, see discounts as well as allowances, sales promotion,
as well as pricing. The article on discounted income provides an example regarding
discounting and risks in property investments.
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Discount element
The discount factor, DF(T), may be the factor by which the next cash flow must
be multiplied to be able to obtain the present worth. For a zero-rate (also
known as spot rate) r, obtained from a yield curve, along with a time to cash circulation T
(in years), the actual discount factor is:
DF(T) = \frac1 (1+rT)
In case where the only discount rate you've is not a zero-rate
(neither obtained from a zero-coupon bond nor converted from the swap rate to the
zero-rate through bootstrapping) however an annually-compounded rate (for
example in case your benchmark is a ALL OF US Treasury bond with annual coupons and also you
only have its deliver to maturity, you might use an annually-compounded
low cost factor:
DF(T) = \frac1 (1+r)^T
Nevertheless, when operating in the bank, where the amount the financial institution can lend (and
therefore get interest) is from the value of its property (including
accrued interest), investors usually use daily compounding in order to discount cash
flows. Certainly, even if the interest from the bonds it holds (for example) is actually
paid semi-annually, the value of it's book of bond increases daily,
thanks to built up interest being accounted with regard to, and therefore the financial institution will
be able in order to re-invest these daily built up interest (by lending extra
money or buying much more financial products). In which case, the discount element
is then (if the typical money market day count convention for that currency is
ACT/360, in the event of currencies such as Usa dollar, euro, Japanese
yen), with r the zero-rate and T time to cash flow within years:
DF(T) = \frac1 ( 1 + \fracr360 )^ 360T
or even, in case the market convention for that currency being discounted is actually
ACT/365 (AUD, CAD, GBP):
DF(T) = \frac1 ( 1 + \fracr365 )^ 365T
Occasionally, for manual calculation, the actual continuously-compounded hypothesis
is a close-enough approximation from the daily-compounding hypothesis, and
makes calculation easier (even though it doesn't have any real software
as no financial device is continuously compounded). If so, the
discount factor is actually:
DF(T) = e^-rT
Additional discounts
For discounts within marketing, see discounts as well as allowances, sales promotion,
as well as pricing. The article on discounted income provides an example regarding
discounting and risks in property investments.
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