Question

An analyst is evaluating two bonds, Bond Q and Bond P. The effective maturity of both bonds is 4 years. The face value of both bonds is $1000 and the yield to maturity for the bonds is 8%. Bond Q is a zero coupon bond whereas Bond P pays a 10% annual coupon.
a) Assuming that the yield to maturity of each bond remains at 8% over the next 4 years, calculate the price of both bonds for every year i.e. price at n=4, price at n=3, price at n=2. Price at n= 1, and price at n=0.
b) Plot the time path of prices for each bond (on same scale/graph).

Answer 1

Price of bond P at time t = PV of all coupons left at time t+ PV of Face Value at time t

Bond P
Time	Cash flow	PV @ time 0	PV at time 1	PV at time 2	PV at time 3	Price
0						1066.2
1	100	92.6				1051.5
2	100	85.7	92.6			1035.7
3	100	79.4	85.7	92.6		1018.5
4	1100	808.5	873.2	943.1	1018.5	1000

Price of Zero-coupon bond at time t = PV of the face value at time t

Bond Q
Time	Price
0	854.8
1	889.0
2	924.6
3	961.5
4	1000

Graph

We have time on the x-axis and price on the y-axis