Question

Last year company X issued a 10-year, 12% semi-annual coupon bond at its par value of $1000. Currently, the bond can be called in 4 years at a price of $ 1,060 and it sells for $ 1,100. What are the bond’s nominal YTM and nominal YTC ? Would the investor more likely be earning YTM or YTC ?

(b) Three bonds were issues at par value of $1000 and YTM of 8 %. Evaluate the price of below: • 10-year, 10% annual coupon • 10 year zero • $100 perpetuity

Answer 1

Part a)
Computation of YTM:
Coupon per 6months = 1000*12%/2 = 60, Remaining maturity periods (n) = 9years*2=18, Price(p)=1100, Maturity value (MV)=1000
YTM = {Coupon+[(MV-p)/n]}/[(MV+p)/2] = {60+[(1000-1100)/18]}/[(1000+1100)/2] = {60-(100/18)}/(2100/2) = (60-5.56)/1050 = 54.44/1050 = 5.19%

Computation of YTC:
Coupon per 6months = 1000*12%/2 = 60, Remaining call periods (n) = 4years*2=8, Price(p)=1100, Call value (CV)=1060
YTC = {Coupon+[(CV-p)/n]}/[(CV+p)/2] = {60+[(1060-1100)/8]}/[(1060+1100)/2] = {60-(40/8)}/(2160/2) = (60-5)/1080 = 55/1080 = 5.09%
The investor more likely to earn YTM than YTC, because YTM is greater than YTC.

Part b i)

Year	Type	Cashflow	PVF @ 8%	DCF @ 8% (Cashflow*PVF @ 8%)
1	Coupon	100	1/1.08 = 0.9259	92.59
2	Coupon	100	0.9259/1.08 = 0.8573	85.73
3	Coupon	100	0.8573/1.08 = 0.7938	79.38
4	Coupon	100	0.7938/1.08 = 0.7350	73.50
5	Coupon	100	0.7350/1.08 = 0.6806	68.06
6	Coupon	100	0.6806/1.08 = 0.6302	63.02
7	Coupon	100	0.6302/1.08 = 0.5835	58.35
8	Coupon	100	0.5835/1.08 = 0.5403	54.03
9	Coupon	100	0.5403/1.08 = 0.5003	50.03
10	Coupon+Maturity	1,100	0.5003/1.08 = 0.4632	509.52
	Price of the bond			1,134.21

Part b ii)
Price of zero coupon bond = Maturity value/[(1+YTM)^life of bond] = 1000/[(1+0.08)^10] = 1000/(1.08^10) = 1000/2.1589 = $463.19

Part b iii)
Price of perpetuity bond = Perpetual cashflow/YTM = $100/8% = $1,250