Question

1.You own a 10-year, 3% semi-annual coupon bond with $100 face value. If its yield to maturity is 5.3%, what percentage of its value comes from coupon payments?

Answer 1

Answer: 3.64%

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First compute the value of bond.

Computing bond from bond formula and financial calculator (both):

Using financial calculator BA II Plus - Input details:	#
I/Y = R = Rate or yield / frequency of coupon in a year = 5.3/2 =	2.650000
PMT = Coupon rate x FV / frequency = 3%/2*100 =	-$1.50
N = Number of years remaining x frequency = 10 x 2 =	20.00
FV = Future Value =	-$100.00
CPT > PV = Present value of bond = Price of Bond = Current value of bond =	$82.32
Formula for bond value: PV = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N) =
PV = (1.5* ((1-(1+0.0265)^-20)/0.0265) + 100/(1+0.0265)^20)	$82.32

Now,

Current yield gives the percentage of value comes from coupon payments:

Current yield = Coupon paid x Frequency of coupon / Value of bond

Current yield = 1.5 x 2 / 82.32

Current yield = 3.64%

This means 3.64% comes from coupon payments of total value of bond.