Question

Peter purchased a 10-year corporate bond with an 8% annual coupon and the yield-to-maturity (YTM) was 10% three years ago. Today, Peter just received the third coupon payment. Due to a financial emergency, Peter is forced to sell the bond today at a price of $1,100.

(a) Determine the annual rate of return (APR) Peter can earn if he held the bond to maturity.

(b) At what price should Peter buy the bond? [Round your final answer to 2 d.p.]

(c) What is Peter’s rate of return after selling his investment? [Hint: You have to consider all the cash flow Peter received and perform a trial-and-error estimation in the calculation]

(d) As compared with your answer computed in part (c), did Peter earn the return of 10% (i.e. YTM of the bond when he purchased) in this investment? Why or why not?

Answer 1

a]	APR = YTM =	10.00%
b]	Price for buying = 1000/1.1^10+80*(1.1^10-1)/(0.1*1.1^10) =	$          877.11
c]	The rate of return is the IRR of the cash flows, which is to be found out by trial and errror.
	Year	Cash flow	PVIF at 16%	PV at 16%	PVIF at 17%	PV at 17%
	0	$        -877.11	1	$       -877.11	1	$     -877.11
	1	$ 80.00	0.86207	$ 68.97	0.85470	$ 68.38
	2	$ 80.00	0.74316	$ 59.45	0.73051	$ 58.44
	3	$      1,180.00	0.64066	$        755.98	0.62437	$ 736.76
				$ 7.29		$ -13.53
	The rate of return lies between 16% and 17%.
	By simple interpolation rate of return = 16%+1%*7.29/(7.29+13.53) =			16.35%
d]	Yes, Peter earned more than 10%. The rate of return earned by him is 16.35%.
	The reason is that the market interest rates decreased which resulted in the sale price of the bond becoming $1,100.