Suppose that you bought a five year coupon bond with $20,000 face value, 7% coupon rate...

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.

Solutions

Expert Solution

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.

Rahul Sunny answered 1 year ago

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