Question

Ryan sold his one stock for TLC, Inc at a price of $550. He purchased the stock 6 years ago. If his Arithmetic Average Return on the stock was 3.36% and his Geometric Average Return was 3.28%, what was his original purchase price? Assume no dividends paid and the AAR and GAR are based on annual rate of returns. (round to the nearest $1 and show your answer like this $394)

Answer:

Answer 1

Per our financial and mathematical concept, arithmetic and geometric averages serve different purposes and only geometric averages will accurately reflect compounded investment returns.

Since, the geometric average considers compounding, which forms the basis of our time value of money. We would use that.

Now, we will turn this into a Time value of Money Question,

PV = Share price 6 years ago,

FV = 550

T = 6 Years

Rate = 3.28%

Hence, PV = FV/(1+Rate)^T

PV = 550/(1+3.28%)^6

= 550/1.214

= 453.17

Hence, 453 was the price of purchase for Ryan