Question

1. (12 points) A bondholder owns one corporate bond that pays semi-annual coupons, has 6 percent coupon rate, and a face value of $1000. The bond has 5 years to maturity, and it currently traded at par. (1) Based on the information that the bond is traded at par, what is the YTM of the bond currently? (2) If the YTM of the bond rises to 7 percent one year later, what is the new price of the bond? (3) What is the holding period return (in percentage) for the bondholder in this one-year holding period?

Answer 1

(1): Here as the bond is trading at par its YTM = coupon rate. Thus YTM = 6%.

You can also compute the YTM using the ‘rate’ function in excel. Here nper = 5*2 = 10, pmt = 6%/2*1000 = 30, pv = -1000 and fv = 1000. Thus YTM = [rate(10,30,-1000, 1000)]*2 = 6%

(2): Here after 1 year means the period after 2 payouts i.e. 2 periods of 6 months each. So we will consider semi-annual periods 3 to 10 i.e. years 2 to 5. Also the rate will now be 7%/2 = 3.5%. Thus new price of the bond = present value of cash flows for the next 8 periods (i.e. 4 years) discounted at 3.5% (i.e. 7%/2). Thus new price = $901.43

Semi-annual period	Cash flow	1+r	PV
3	30	1.035	27.06
4	30		26.14
5	30		25.26
6	30		24.41
7	30		23.58
8	30		22.78
9	30		22.01
10	1030		730.19
		Total	901.43

(3): Holding period return = [Income + (ending value - initial value)]/initial value

Income = 30+30 = 60. Ending value = 901.43 and initial value = 1000

Thus return = [60+(901.43-1000)]/1000

= -3.86%