Question

Today, you pay $1043.76 to buy a $1000 face value 6% coupon bond (semi-annual coupon payments) bond that matures in 5 years.

a.) what is the yield to maturity of this bond?

b.) If you reinvest the coupon payments at 2% per year (1% per 6 monhs), what is the value of the reinvested coupons after 5 years?

c.) what is yout nominal realized compound yield if hold the bond to maturity but reinvest the coupons at a rate of 2% per year (2% per six months)

Answer 1

PV of Bond = $1043.76

Face value = $1000

semi-annual coupon rate = 6%

Maturity = 5 years

a.) Coupon is paid semi-annually and the bond matures in 5 years. Hence, there will be 10 coupon payments. Below is the formula to calculate the present value of bonds

PV = CF₁/(1+YTM)¹ + CF₂/(1+YTM)²+.......+CF_n/(1+YTM)ⁿ+FV/(1+YTM)ⁿ

where n is the total number of coupon payments and CF_n is the Cash Flow in the n^th coupon payment. In this case n = 10. Substituting values in the above equation (using scientific calculator) we get,

1043.76 = 60/(1+YTM) + 60/(1+YTM)² +.......+ 60/(1+YTM)¹⁰ + 1000/(1+YTM)¹⁰

YTM = 5.421%

b.) coupons are invested at 2% per year, value of reinvested coupons after 5 years. For this we will be calcualationf the future value of the coupons.

Period	1	2	3	4	5	6	7	8	9	10
Coupons	60	60	60	60	60	60	60	60	60	60
FV of coupons	65.59217	64.94593	64.30605	63.67248	63.04515	62.424	61.80897	61.2	60.59703	60

FV of first coupon (period 1) = 60*(1+0.02)^4.5

FV of second coupon (period 2) = 60*(1+0.02)^4

Similarly, FV of the last coupon (period 10) = 60*(1+0.02)^0

therefore, the total value of reinvested coupons after 5 years = sum of all the FV of coupons = 65.59217+64.94593+.....+60 = $627.5918