Lila purchased Hampton Industries Inc. stock for $18.35 and sold it 6 months later for $21.45 after receiving a $0.50 dividend. What was her holding period return (HPR), Annual Percentage Rate (APR), and Effective Annual Rate (EAR)?

HPR = 19.62 %

APR = 39.24 %

EAR = 43.09 %

Explanation:

a.Calculation of Holding Period Return :

The formula for calculating the holding period Return is

= ( Sale price + Dividend earned during the holding period – Purchase Price ) / Purchase Price

As per the information given in the question is

Purchase Price : $ 18.35

Sale price : $ 21.45

Dividend per share = $ 0.50

Applying the above values in the formula we have

= ( 21.45 + 0.50 – 18.35 ) / 18.35

= 3.60 / 18.35

= 0.196185 = 19.6185 %

= 19.62 % ( when rounded off to two decimal places )

Thus the HPY i.e., Holding period return is 19.62 %

b.Calculation of Annual Percentage Rate :

The formula for calculating the Annual Percentage Rate = Holding period return / n

Where n = Period of Investment / 12 months

We know that the period of Investment = 6 months

Thus n = 6 / 12 = 0.50

Holding Period Return = 19.62 %

Applying the above values in the formula we have

Annual Percentage Rate = 19.62 % / 0.50

= 39.24 %

Thus the Annual Percentage Rate = 39.24 %

c. Calculation of Effective Annual Return :

The formula for calculating the Effective annual rate = ( 1 + Return ) ( 1/n ) - 1

Where Return = Holding period return = 19.62 % = 0.1962

N = No. of years = ( 6 / 12 ) years = 0.5 years

Applying the above values in the formula we have

= ( 1 + 0.1962 ) ( 1 / 0.5 ) - 1

= ( 1.1962 ) 2 - 1

= 1.430894 – 1

= 0.430894 = 43.0891 %

= 43.09 % ( when rounded off to two decimal places )

Thus the Effective annual rate = 43.09 %

NOTE : The value of ( 1.1962 )2   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.1962,2) = 1.430894

Thus we have :

HPR = 19.62 %   ; APR = 39.24 %   ; EAR = 43.09 %

a) both were commissioned explorers