There are multiple sites that post a formula for the present value (PV) of a perpetual EQUAL periodic payment:
PV = a / ((1 + i)^t - 1)
where a (in $) is the value of the periodic payment, and t (in years) is the period. In other words, the instrument generates a payment of $a every t years. i is the discount interest rate (as a decimal fraction).
My current task differs slightly. The payment is generated periodically (every t years), but the payment amount grows at an annual growth rate (g). For the avoidance of doubt, the growth rate g is ANNUAL.
Unfortunately, I do not have the math skills to construct a formula for my case. My guess would be that the annual growth rate g can be subtracted from the discount rate i. Hence:
PV = a / ((1 + i - g)^t - 1)
Is this correct? Thank you very much.