Two years ago, Jim bought 100 shares of IBM stock at $50 per share, and just sold them for $65 per share after receiving dividends worth $3 per share over the two year holding period. Mary, bought 5 ounces of gold at $800 per ounce, three months ago, and just sold it for $1000 per ounce. Calculate each investor's HPR, APR, and EAR and comment on your findings.

 

The answer is as follows:

Step-by-step explanation

JIM:

HPR = (Selling Price + Dividends - Purchase Price)/Purchase Price = (65 +3 - 50) / 50 = 18 / 50 = 36%

APR = HPR / Number of years = 36% / 2 = 18%

EAR = (1 + 36%)^(1/2) - 1 = 16.62%

Hence:

Jim's HPR = 36%

Jim's APR = 18%

Jim's EAR = 16.62%

MARY:

HPR = (Selling Price - Purchase Price)/Purchase Price = (1000 - 800) / 800 = 200 / 800 = 25%

APR = 25%/ (1/4) = 100%

EAR = (1 + 25%)^4 - 1 = 144.14%

As such:

Mary's HPR = 100%

Mary's APR = 100%

Mary's EAR = 144.14%

COMMENT:

From above we observe that Mary has much higher APR and EAR as compared to Jim's APR and EAR.

Mary's HPR of 25% is from holding period of 3 months as against Jim's HPR of 36% over two years.

As such overall Mary has better returns as compared Jim's return.

However, Mary's return appears exceptional and is unrealistic in normal circumstances.