Question

There is a bond with FV = 1000, coupon rate of 10% paid annually and 5 year maturity. At year 0, YTM = 8%.

Given constant YTM, what is the bond price at time 1?

What is capital gain yield and current yield?

What are the prices of the bond in year 2, 3, 4, and 5?

If at year 1, YTM becomes 12%, what is a bond price in year 1?

Answer 1

Calculation of Bond Price at time 1

Price = cash flow_t / (1 + YTM)^t

Cash flow = 1000 x 10% = 100

Year	Cash flow	PV Factor@ 8%	Value
1	100	0.9259	92.59
2	100	0.8573	85.73
3	100	0.7938	79.38
4	100	0.7350	73.50
5	100	0.6806	68.06
5	1000	0.6806	680.60
		Price	1079,86

Capital gain yield = Current price - original price / original price X 100

= (1079.86 -1000) / 1000 x 100 = 7.986 %

Current Yield = Annual cash flow / Market price = 100 /1079.86 = 0.0926 = 9.26%

Prices of Bond at Year 2

Year	Cash flow	PV Factor @ 8%	Value
1	100	0.9259	92.59
2	100	0.8573	85.73
3	100	0.7938	79.38
4	100	0.735	73.50
4	1000	0.735	735.00
		Price	1066.2

Price of Bond at Year 3

Year	Cash flow	PV Factor @ 8%	Value
1	100	0.9259	92.59
2	100	0.8573	85.73
3	100	0.7938	79.38
3	1000	0.7938	793.80
		Price	1051.5

Price of Bond at Year 4

Year	Cash flow	PV Factor @ 8%	Value
1	100	0.9259	92.59
2	100	0.8573	85.73
2	1000	0.8573	857.30
		Price	1035.62

Price of Bond at Year 5

Year	Cash flow	PV Factor @ 8%	Value
1	100	0.9259	92.59
1	1000	0.9259	925.90
		Price	1018.49

Price of Bond in Year 1 if YTM is 12%

Year	Cash flow	PV Factor @ 12%	Value
1	100	0.8929	89.29
2	100	0.7972	79.72
3	100	0.7117	71.17
4	100	0.6355	63.55
5	100	0.5674	56.74
5	1000	0.5674	567.43
		Price	927.90