Question

Consider the following information of Petronas Bond

Description	Petronas Bond
Face value	RM 1000

Maturity	5 YEARS
Coupon rate	9.00% per annum
Compounding (m)	Semiannually

a) Assuming annual interest rate is 6.00% on the bond, calculate the value of the bond.
b) Illustrate the discounting cash flows using the Macaulay Duration Schedule.

c) Compute

i. Modified duration.
ii. Convexity
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Answer 1

a. Value of the bond=

(PV of semi-annual coupon cash flows+ PV of FV to be recd.at maturity)both discounted at the semi-annual interest rate

ie. ((1000*0.045)*(1-1.03^-10)/0.03)+(1000/1.03^10)

1127.95

b.Calculation of Macaulay Duration
Coupon	9%/2=4.5%	Yield	6%/2=3%
Period	Semi-annual Cash flows	PV of $1 at 3%	PV of C/fs	Period*CF	PV of (Period*CF)
1	2	3=1/1.03^n	4=2*3	5=1*2	6=5*3
1	45	0.97087	43.69	45	43.69
2	45	0.94260	42.42	90	84.83
3	45	0.91514	41.18	135	123.54
4	45	0.88849	39.98	180	159.93
5	45	0.86261	38.82	225	194.09
6	45	0.83748	37.69	270	226.12
7	45	0.81309	36.59	315	256.12
8	45	0.78941	35.52	360	284.19
9	45	0.76642	34.49	405	310.40
10	1045	0.74409	777.58	10450	7775.78
Total	Current price=		1127.95		9458.69
				PV of time Wt.ed C/fs.
Macaulay duration =
PV of Time weighted coupon cash flows/Current market price of the bond
(PV of (Period*CF))/Current Bond price
ie.9458.69/1127.95=
8.39
Semi annual periods
ie.8.39/2=4.20.yrs.
Modified Duration
Macaulay duration/(1+YTM/n)
where, YTM is the annual effective interest rate & n= no.of coupons/yr.
8.39/(1+(6%/2))=
8.15
Semi annual periods
ie.8.15/2=4.075 yrs.

Convexity
Period (t)	Semi-annual Cash flows	PV of $1 at Ytm 3%	PV of C/fs	Wt.=PV of cash flow/Price,ie.1127.95	Convexity=t*(t+1)*Wt*1/(1+ytm)^2
1	2	3=1/1.03^n	4=2*3	5=4/1127.95	6=1*(1+1)*5/(1+0.03)^2
1	45	0.97087	43.69	3.87%	0.0730
2	45	0.94260	42.42	3.76%	0.2127
3	45	0.91514	41.18	3.65%	0.4130
4	45	0.88849	39.98	3.54%	0.6682
5	45	0.86261	38.82	3.44%	0.9732
6	45	0.83748	37.69	3.34%	1.3227
7	45	0.81309	36.59	3.24%	1.7123
8	45	0.78941	35.52	3.15%	2.1374
9	45	0.76642	34.49	3.06%	2.5939
10	1045	0.74409	777.58	68.94%	71.4780
Total			1127.95		81.5844
Semi-annual convexity=81.5844
Annual convexity=81.5844/4=
20.40