FIN 300 Fundamentals of Finance Time Value of Money Perpetuities Chapters 5 & 6 1 FIN 300 - TVM Perpetuities
Perpetuities •What happens if there is an asset or investment that pays an infinite stream of identical payments? –We start off assuming that all of these payments are at the end of the period –The payments occur at t=1, t=2, t=3, etc. –We are calculating a value/price/PV, etc. today (or, at t=0) FIN 300 - TVM Perpetuities 2
Perpetual Stream of Cash •Let’s go back to build a basic formula –All payments = C,are identical –i= discount rate/period –All payments at period end –PVis calculated at t=0 –PVis of a sum of an infinite number of lump-sums 𝑃𝑃=𝐶1+𝑖1+𝐶1+𝑖2+𝐶1+𝑖3+𝐶1+𝑖4+…….(to infinity) FIN 300 - TVM Perpetuities 3
Perpetuity Formula •Or more formally…. PV of perpetuity = ∑𝐶1+𝑖𝑛∞𝑛=1(an infinite sum of the PV’s of identical cash flows) •Thank goodness, there is a much more compact form!