Question

4.

(a) Fill in the table and determine the price and duration of a bond with a maturity of 4 years, $100 face value, paying a 8% coupon annually, and trading at a yield to maturity of 9%? Fill in the cells of the table (28 marks)

T (Year)	Cashflow	Discount factor	PV	Proportion of total PV	T x Proportion of total PV
		SUM		SUM

Price            =

Duration         =

(b) Use the duration of the bond that you have calculated in 4(a) to predict the change in the bond price if interest rates rise by 100 basis points. (6 marks)

Answer 1

4.a) The table below has computed price and maturity:

T (Year)	Cashflow	Discount factor	PV	The proportion of total PV	T x Proportion of total PV
0	0	1	0	0	0
1	8	0.917431193	7.339449541	0.075851884	0.075851884
2	8	0.841679993	6.733439946	0.069588884	0.139177769
3	8	0.77218348	6.17746784	0.063843013	0.19152904
4	108	0.708425211	76.5099228	0.790716218	3.162864874
SUM			96.76028012	1	3.569423566

The price and duration are:

Price	96.76028012
Duration	3.569423566

b) The fall in the price of the bond if interest rates rise by 100 basis points or 1 percentage point is 3.569423566. This is because interest rates and prices of bonds are negatively related.