Question

A perpetuity with the first annual cash flow paid at the beginning of year 4 is equivalent to receiving $103,000 in 15 years’ time. Assume that the perpetuity and the lump sum are of equivalent risk and that j12 = 14.32% pa is the appropriate interest rate. How much is the annual cash flow associated with the perpetuity?

Answer 1

A perpetuity with the first annual cash flow paid at the beginning of year 4 is equivalent to receiving $103,000 in 15 years’ time. Assume that the perpetuity and the lump sum are of equivalent risk and that j12 = 14.32% pa is the appropriate interest rate. How much is the annual cash flow associated with the perpetuity?

Answer 2

i = (1+j12/12)12 -1
= 11.3509
Compare the two different options at the same point in time e.g. both at t = 2 or both at t = 0.
Here we are using t = 2

The Perpetuity
PV2 = CF3/i = CF/.113509
Lump Sum
PV2 = 108000/(1.113509)16 = $19,334

These are same so CF/0.113509= 19,334
Reordering we get CF = 19,334*0.113509 = $ 2195