Question

Assume that today you have purchased a 5-year coupon bond with a coupon interest rate of 12 percent at a price of $1,000 which also happens to be its face value.  Assume further that you hold it for one year, pocket the coupon payment you receive at the end of that year and then sell it.  Also, at that time the market interest rate has fallen to 5 percent.  Find your rate of return. Please answer in mathematical way, not Excel.

Answer 1

Let us calculate the worth of bond at the end of year 1

Coupon per year=12% of face value=1000*12%=$120

No. of years left for maturity =n=4

Face Value of bond=FV=$1000

Rate of interest=i=5%

Coupon's worth will be equal to the present value of future cash flows

Coupon's worth=120(P/A,5%,4)+1000(P/F,5%,4)

P/A,n,i) can be calculated as

(P/F,5%,4)=1/(1+0.05)⁴=0.822702

Coupon's worth after 1 year=120*3.545951+1000*0.822702=1248.22

Coupon's price after 1 year=P1=Coupon's worth after one year=1248.22

Coupon amount received in one year=C=120

Investor's return=(P1-Po+C)/Po=(1248.22-1000+120)/1000=36.82%