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)?
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20.34%, 40.68%, 44.82% |
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14.17%, 28.34%, 30.35% |
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20.34%, 40.68%, 9.70% |
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19.62%, 39.24%, 43.09% |
Solution:
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 %
Thus the solution is Option 4 : 19.62 %, 39.24 %, 43.09 %
Lila purchased Hampton Industries Inc. stock for $18.35 and sold it 6 months later for $21.45...
Amber 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)? a) 19.62% ; 39.24% ; 43.09% b) 20.34% ; 40.68% ; 9.7% c) 14.17% ; 28.34% ; 30.35% d) 20.34% ; 40.68% ; 44.82%