PV of a Perpetuity (6.2 Schweser Notes, pg 78-79); 6.3 Quiz #1

CFA Level I Quant
#1

This may be very straight forward for you guys, but I just started Quant and I’m having issues understanding the 1st question from the 6.3 Quiz:

An analyst estimates that XYZ’s earnings will grow from $3.00 a share to $4.50 per share over the next 8 years. The rate of growth in XYZ’s earning is closest to:

A. 4.9%
B. 5.2%
C. 6.7%

From what I’ve read, dividend/rate of growth = share price. With only 2 share prices and the term, I’m having trouble calculating. I’m sure it’s simple. Please advise. Thanks!

#2

This is not a perpetuity problem - you are considering what happens over the course of 8 years.
This is a simple compounding problem. You start with a share worth $3.00, and after 8 years, it will be worth $4.50.
4.50 = 3.00 (1+i)^8
where i is the annual effective rate of growth
all you have to do is solve for i.

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