Answer:
The holding period yield is 11.87%
Explanation:
First, we need to determine the interest income received in the holding period
Interest income = Face value x Coupon rate x Holding period
Where
Face value = $1,000
Coupon rate = 9% per anum
Holding period = 3 years
Placing values in the formula
Interest income = $1,000 x 9% x 3 years = $270
Now calculate the price of the bond after 3 years as follow
Use the following formula to calculate the price of the bond
Price of the bond = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Where
F = Face value = $1,000
C = Periodic coupon payment = $1,000 x 9% = $90
r = Periodic interest rate = 7%
n = Numbers of periods = 12 years - 3 year = 9 years
Placing values in the formula
Price of the bond = [ $90 x ( 1 - ( 1 + 7% )^-9 ) / 7% ] + [ $1,000 / ( 1 + 7% )^3 ]
Price of the bond = $586.37 + $543.93
Price of the bond = $1,130.30
Now determine the holding period return
Holding period return = Interest income + Price appreciation
Holding period return = Interest income + ( Price after 3 years - Purchase price )
Where
Interest income = $270
Price after 3 years = $1,130.30
Purchase price = $1,000
Placing values in the formula
Holding period return = $270 + ( $1,130.30 - $1,000 ) = $270 + $130.30 = $400,.30
Now calculate the holding period return rate
Holding period return rate = Holding period return / Initial investment = $400.30 / $1,000 = 0.40 = 40%
Annualise the rate of return as follow
Annual rate of return = ( ( ( 1 + rate of return )^(1/n) ) - 1 ) x 100
Annual rate of return = ( ( ( 1 + 40% )^(1/3) ) - 1 ) x 100
Annual rate of return = 0.1187 x 100
Annual rate of return = 11.87%
