Question

1. Suppose that you bought a five year coupon bond with $20,000 face value, 7% coupon rate and 7% yield to maturity. After holding it for a year and collecting the first coupon payment you decide to sell it. Calculate the return (in %) on this investment if the interest rate has increased to 9% while selling the bond.

Answer 1

Calculate the price of the bond the year you sell it that is
one year after you buy it. Then calculate the return.
Present Value = Future value/ ((1+r)^t)
where r is the interest rate and t is the time period
Price of bond = sum of present values of future cash flows.
Par/Face value	20000
Coupon rate	7%
Annual coupon	1400
r	0.07
Year	1	2	3	4	5
future cash flow	1400	1400	1400	1400	21400
present value	1308.41	1222.81	1142.82	1068.05	15257.90
Price of bond	20000
When the interest rate changes to 9% one year after you buy it.
r	0.09
Year	1	2	3	4
future cash flow	1400	1400	1400	21400
present value	1284.40	1178.35	1081.06	15160.30
Price of bond	18704.11
When the interest rate rises to 9% from 7% one year after you buy it, the price of the
bond will be $18704.11.
Selling price = $18704.11
Initial price = $20000
Return in % = (18704.11 - 20000)/ (20000)
Return in % = -1295.89/20000
The return is -6.48% on this investment if the interest
rate has increased to 9% while selling it.