Question

	Bond 2
Coupon rate	6.8%
Annual coupon frequency	2
Par	$1,000
Time to maturity (years)	5

c) the realized compound yield for Bond 2 if the current price is $1000 and the semi-annual coupons are reinvested at an annual rate of 2% until the bond matures.

d) the realized compound yield for Bond 2 if the current price is $1000 and the semi-annual coupons are reinvested at an annual rate of 2% until the bond is sold in 3 years for $1,050.

e) Suppose the yield to maturity for Bond 2 changes from 5% to 4.75%. Compute the bond’s price at each YTM. What is the percentage difference in price? Compute the percentage as the (price when YTM is 4.75% - price when YTM is 5%) / price when YTM is 5%.

Answer 1

c.

Step -1
Period	Event	Cashflow	Maturity Value	Amount
1	Coupon	$          34.00	1.01	$      34.34
2	Coupon	$          34.00	1.02	$      34.68
3	Coupon	$          34.00	1.03	$      35.03
4	Coupon	$          34.00	1.04	$      35.38
5	Coupon	$          34.00	1.05	$      35.73
6	Coupon	$          34.00	1.06	$      36.09
7	Coupon	$          34.00	1.07	$      36.45
8	Coupon	$          34.00	1.08	$      36.82
9	Coupon	$          34.00	1.09	$      37.19
10	Coupon	$          34.00	1.10	$      37.56
10	Redemption	$     1,000.00	1.00	$1,000.00
			Total	$1,359.27
Step-2
	Year	Cashflow
	0	$   -1,000.00
	10	$     1,359.27
Step-3
	Calculation of Realized YTM
	FV      =	PV(1+r)^n
	1359.27	1000(1+r)^10
	(1+r)^10	1359.27/1000
	(1+r)^10	1.3593
	(1+r)	1.0312
	r      =	3.12%	Per period
	r   =	6.24%	Per Annum

Realised YTM = 6.24%

d.

Step -1
Period	Event	Cashflow	Maturity Value	Amount
1	Coupon	$           34.00	1.01	$      34.34
2	Coupon	$           34.00	1.02	$      34.68
3	Coupon	$           34.00	1.03	$      35.03
4	Coupon	$           34.00	1.04	$      35.38
5	Coupon	$           34.00	1.05	$      35.73
6	Coupon	$           34.00	1.06	$      36.09
6	Redemption	$     1,050.00	1.00	$ 1,050.00
			Total	$1,261.26
Step-2
	Year	Cashflow
	0	$    -1,000.00
	10	$     1,261.26
Step-3
	Calculation of Realized YTM
	FV      =	PV(1+r)^n
	1261.26	1000(1+r)^6
	(1+r)^6	1261.26/1000
	(1+r)^6	1.26126
	(1+r)	1.03944
	r      =	3.94%	Per period
	r   =	7.89%	Per Annum

Realised YTM = 7.89%

e.

			Bond Price if YTM is 5%	Bond Price if YTM is 4.75%
Period	Event	Cashflow	PVF @2.5%(Semiannually)	Amount	PVF @2.375%	Amount
1	Coupon	$      34.00	0.9756	$      33.17	0.9768	$      33.21
2	Coupon	$      34.00	0.9518	$      32.36	0.9541	$      32.44
3	Coupon	$      34.00	0.9286	$      31.57	0.9320	$      31.69
4	Coupon	$      34.00	0.9060	$      30.80	0.9104	$      30.95
5	Coupon	$      34.00	0.8839	$      30.05	0.8893	$      30.23
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