Formula for continuous discounting
To discount continuously, we rearrange the continuous compounding formula and use present value (PV) in the place of principal (P). Solving for PV, we arrive at the continuous discounting formula.
PV = FVT[ 1 / (eRT)
PV = Present value of the investment (value today)
FVT = Future value of the investment at time T
e = Base of the natural logarithm (2.718282)
T = Time in years until maturity
R = Annual discount rate (opportunity cost of money)
As you can see, the present value interest factor for continuous
discounting 1 / (eRT) is the reciprocal of the future value interest factor
for continuous compounding eRT
. A more common notation for this present value interest factor is e-RT ; the formula is:
PV = FVT[e-RT]
As an example, let's calculate the present value of a $1,500 cash flow to be received in 4 years, discounted continually at an annual rate of 10%.
PV = FVT[ e-RT]
PV = $1,500 [ 2.718282-0.10 x 4]
PV = $1,500 [ 0.6703200]
PV = $1,005.48
Use the the formula for discrete discounting ( PV = FVT[1/(1 + R)T]) or continuous discounting (PV = FVT[ e-RT]) or your financial calculator to solve the discounting problems in the Practice Exercise that follows.
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