Problem 1. I wish to discount a stream of revenue,Rt; that grows at a constant rate, g. Thus the stream of revenue from time period 1 to n is:
R1;R2 =R1(1+g);:::;Rn =R1(1+g)n1
the discount rate is d.
a. Derive a formula to calculated the discounted present value of this revenue stream, V . (2pts)
b. Suppose R1 = $1M il; g = 5% and d = 2%. Use the formula you derived in part a to calculate the discounted present value of the revenue stream, V , over a 5 year period.(1pt)
c. Under what conditions will the series be convergent? In answering use DíAlembertís test of convergence (1pt) Is the series convergent when g = 5% and d = 2%?(2pt)
d. Suppose I want the V = $5Mil. All else equal what growth rate, g, would be required? (1pt)