Question

a. An investor buys a 5 % annual coupon payment bond with three years to maturity. The bond has a yield-to-maturity of 9%. The par value is $1000. i. Determine the market price of the bond. (2 marks) ii. Calculate the bond's duration. (3 marks) b.A bond portfolio consists of the following three annual coupon payment bonds. Prices are per 100 of par value. Modified Duration Yield-to- Coupon (%) Bond Maturity Market (years) Price Maturity (%) (years) 5.23 7.98 Value 5.95 3.00 171,000 161,800 150,000 85.50 6 5.99 6.00 3.40 6.00 80.90 10 9.71 100.00 15 C i. Determine the weight of each bond in the bond portfolio. (3 marks) ii. Calculate the bond portfolio's modified duration. (2 marks)

Answer 1

Solution:

a)

I) The market price of the bond is the present value of the bond.

We have the par value =1000 , 5% annual coupon , YTM= 9% and 3 years to maturity

FV =1000 , N = 3 , PMT = 50 , YTM = 9% and PV =?

Inputting all the values in TVM row of our BA II plus calculator we can find the present value or the market price of the bond.

PV = 898.748 or the market price of the bond.

ii) Duration -> weighted average of the number of years until each of the bonds promised cash flows is to be paid.

YTM = 9%

We know , Present value = Future Value / (1+YTM) ^ n

Calculating Duration

Sno	Cash Flows	Present Value	Weights
1	Coupon1 = 5% * 1000 = 50	PV1 = 50 / (1+9%)^1 = 50/1.09 = 45.87	w1 = 45.87/898.7466=.05103
2	C2 = 5% * 1000 = 50	PV2 = 50 /(1+9%)^2 = 50/(1.09)^2 = 42.083	w2 = 42.083/898.7466 = .04682
3	C3 + Fv = 50 + 1000 = 1050	PV3 = 1050/(1+9%)^3 = 1050/(1.09)^3 = 810.792	w3 = 810.792/ 898.7466 = .90213
Total		898.7466	1

t1 =1 (1 year) , t2 = 2 , t3 =3

We know that the bond's duration is : D = w1 * t1 + w2 * t2 + w3 * t3

= .05103*1 + .04682 * 2 + .90213 * 3

= .05103 + .093650 + 2.7064 = 2.8510 years.