Question

Bonds of RCY Corporation with a face value of $1000 sells for $960, mature in 5 years, and have a 7% coupon rate paid semiannually. Calculate the investor's RCY by assuming the following: - Bond sold to yield at 7% and the end of the 3-year holding period. - Reinvestment rate 6% APR during this holding period. - PS: state what assumption(s) you need to make in calculating this RCY.

Answer 1

Current selling price = $960, Years to maturity = 5 years, Coupon rate = 7% paid semi annually, Par value = $1000

As coupons are paid semi annually therefore,

Semi annual Coupon payment = (Coupon rate x par value) / 2 = (7% x 1000) / 2 = 70 / 2 = $35

As it is known that Semi- annual coupon payment are reinvested at APR = 6% over 3 year holding period

Semi annual reinvestment rate = APR / 2 = 6% / 2 = 3%, Holding period in half years = 2 x holding period in years = 2 x 3 = 6 half years

Now we will find the future value of reinvested coupons over 3 years

Future value of reinvested coupons = 35(1+3%)⁵ + 35(1+3%)⁴ + 35(1+3%)³ +35(1+3%)² +35(1+3%)¹ + 35

Future value of reinvested coupons can be found out by finding out future value of ordinary annuity with each payment equal to $35. We can find the future value by using FV function in excel

Formula to be used in excel: =FV(rate,nper,-pmt)

Using FV function in excel, we get Future value of reinvested coupons = $226.39

Now we will calculate the selling price of bond after 3 years

No of years to maturity after 3 years = 2 ,

No of half years to maturity after 3 years = 2 x No of years to maturity after 3 years = 2 x 2 = 4 half years

Yield to maturity after 3 years = 7%, Semi annual yield to maturity after 3 years = 7%/2 = 3.5%

We can find the selling price of bond after 3 years using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt,-fv)

Using PV function in excel, we get Price of bond after 3 years = $1000

No we know that

Price of bond after 3 years + Future value of reinvested coupons = Current selling price of bond x (1+ Semi annual RCY)ⁿ

Semi annual RCY = [(Price of bond after 3 years + Future value of reinvested coupons) / Current price of bond]^1/n - 1

Semi annual RCY = [(1000 + 226.39) / 960]^1/6 - 1 = [1226.39 / 960]^1/6 - 1 = (1.2774895)^1/6 - 1 = 1.041660 - 1 = 0.041660 = 4.1660%

RCY = 2 x semi annual RCY = 2 x 4.1660% = 8.332% = 8.33% (rounded to two decimal places)

Investor's RCY during holding period = 8.33%