Question

What is the present value of a stream of cash flows expected to grow at a 10 percent rate per year for 5 years and then remain constant thereafter until the final payment in 30 years. The payment at the end of the first year is $1,000 and the discount rate is 5.00 percent.

Answer 1

The first stream is a growing annuity. The PV of a growing
annuity is given by the formula:
PVGA = [P/(r-g)]*[1-((1+g)/(1+r))^n]
Where
P = First payment
r = rate per period
g = growth rate
n = number of periods
Substituting values, the PV of the first 5 year's cash flow = ((1000/(0.05-0.10))*((1-(1.1/1.05)^5)) =	$    5,237.53
PV of the cash flows from 6th year = 1000*1.1^5*(1.05^25-1)/(0.05*1.05^25*1.05^5) =	$ 17,784.82
PV of the cash flows for 30 years	$ 23,022.36