Question

A 20-year XXX bond has a coupon rate of 8 percent and sells at a yield to maturity of 10 percent.

1. Assuming annual coupon payments, at what price does the bond sell?

2. If XXX wants to issue a new 20-year bond at face value, what coupon rate must the bond offer?

Answer 1

Par/Face value	1000
Annual Coupon rate	0.08
Annual coupon	80
Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 10% and t is the time period in years.
price of the bond = sum of present values of future cash flows
r	0.1
t	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
future cash flow	80	80	80	80	80	80	80	80	80	80	80	80	80	80	80	80	80	80	80	1080
present value	72.72727	66.1157	60.10518	54.64108	49.67371	45.15791	41.05265	37.32059	33.92781	30.84346	28.03951	25.49047	23.17315	21.0665	19.15136	17.41033	15.82757	14.3887	13.08064	160.5351
sum of present values	829.73
1) The bond sells at $829.73.
2) If the company wants to issue new 20 year bonds at face value, then the coupon rate
must equal the yield to maturity.
In other words, the coupon rate should equal 10%.