Why is this one counting 3 years instead of 4 years for PV? it says 4 years from now…
Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.
Graphically is easier to explain, but will try in words.
When you calculate the present value of an annuity, lets say it start paying at the end of year 1, end of year 2, etc, the PV is set on year 0 (value today).
The question says it start paying 4 years from now, so when we calculate PV, that present value is on 3 years from now. Being 3 years from now, you should discount only 3 years.
Hope this helps
A perpetuity immediate will have the PV calculated as of 1 year before the first payment: this is why in your example the PV is discounted by 3 years. On the other hand, a perpetuity due will have the PV calculated as of the first payment date, in which case you would discount by 4 years.
PV perpetuity immediate = payment / i
PV perpetuity due = (1 +i ) * payment / i
Thank you all!
When you calculate the PV of this perpituity using the formula Payment/ i (its PV Perpituity Immediate formula), you would get the PV at 3.
Now you have to discount it 3 years back.