Question

On October 1st, 2015, Ellie Jackson purchased a newly issued 30-year bond from Wal-mart for $1,000. The bond pays a 5.25% annual coupon with a $1,000 face value. Today, on October 1st, 2018, Ellie decides to sell the bond. Currently, Wal-mart bonds have a yield to maturity of 5.27%. Calculate the realized yield or annual return for Ellie’s investment.

Answer 1

Price today, P₀ = $ 1,000

Price three years later, P₃ = - PV (Rate, Period, PMT, FV)

Rate = YTM = 5.27%

Period = Balance years to maturity = 30 - 3 = 27

PMT = payment per year = annual coupon = 5.25% x 1,000 = 52.50

FV = future value = par value = face value = 1000

Hence, P₃ = - PV (Rate, Period, PMT, FV) = - PV (5.27%, 27, 52.50, 1000) = $  997.15

Coupons received during the holding period of 3 years = 3 x 52.50 = 157.50

Hence, Holding period return = HPR = (P₃ + Intermediate coupons - P₀) / P₀ = (997.15 + 157.50 - 1,000) / 1,000 = 15.47%

Hence, average annual return = 15.47% / 3 = 5.16%