Question

Suppose there is a 3-year bond with a $1000 face value, 12% coupon payments and a 6% yield to maturity.

a) Without any calculation, briefly explain whether this bond will be selling a premium or a discount

b) Calculate the price of this bond.

c) Calculate the duration of this bond. d) If someone buys this bond and holds it for three years, what is their rate of return? e) Suppose after one year, interest rates in the economy fall by 2%. If the person that bought this bond sells it at that time, what would be their rate of return? (Hint: First think about what the fall in interest rates will do to the bond’s price and then think about the rate of return.)

Answer 1

(a)	Here YTM is lower then the coupon rate, therefore the bond is selling at premium.
	(As the bond provides higher returns then the market it is selling at more then par value).
(b)	Year	Cash flow	PVF @ YTM	PV of cash flows
	1	120	0.943396	113.2075
	2	120	0.889996	106.7996
	3	1120	0.839619	940.3736
				1160.381
	Price of bond =			1160.381
(c )	Year	Cash flow	PVF @ YTM	PV of cash flows
	x			w
	1	120	0.943396	113.2075	113.2075
	2	120	0.889996	106.7996	213.5991
	3	1120	0.839619	940.3736	2821.121
				1160.381	3147.927
	Duration =	Sum WX/Sum W=		3147.927/1160.381
				2.71284
(d)	Rate of return =		(Change in price + Intermediate cash flows)/ Price
	Total interest return =			120 x 3 =	360
	Price Appreciation =			(1000 - 1160.381 )	-160.381
					199.6193
	Rate of return =			199.6193/1160.381
				0.172029
				17.203%
(e)	Holding period =		1 year
	Price at the end of year 1 =
	Year	Cash flow	PVF @ 4%	PV of cash flows
	1	120	0.961538	115.3846
	2	1120	0.924556	1035.503
				1150.888
	(alternatively we can calculate bond price using modified duration)
	Interest received =			120 x 2 =	240
	Change in price =		(1150.888 - 1160.381) =		-9.49314
					230.5069
	Rate of return =			230.5069/1160.381
				0.198648
				19.865%
	Please provide feedback…. Thanks in advance…. :-)