Question 5 14 Marks A bond X matures in exactly 10 years, at time 10, The coupon

Question

Question 5 14 Marks A bond X matures in exactly 10 years, at time 10, The coupon borne is 16% pa., payable annually; and the next coupon is payable in just under a year's time. There are presently 10,000 bonds of type X outstanding, each of $100 face value. (a) Discounting cash flows at an effective interest rate of 12% pa., calculate the (6 marks) (b) Your fund was the issuer of Bond X, and the corresponding asset income is A (i) Calculate A and T so that the present values and durations of the assets (ii) Comment briefly on whether or not your fund is immunised at time 0 duration of bond X at time 0 at time T. There are no other assets and liabilities in your fund. and liabilities of your fund are equal, as at time 0. against small changes in interest rates. (ii State how the situation regarding immunisation is likely to alter: (A) in 6 months, at time 1/2; and (B) in 18 months, at time 3/2. Explain your reasoning briefly. (8 marks) Data. At an effective interest rate of 12% pa. ???-5.650 Clara 25.904 (14 marks)

Explanation / Answer

Soln ; a) Bond maturity = 10 years, coupon rate = 16%, Face Value = 100 , discount rate = 12%

Let's P be the price of the bond, using discounting method, please refer the table :

We get P = NPV = 122.60

Now, duration of the bond, Macaulay duration can be calculated with summation of Present value of cash flows multiply the year in which they occur divided by the market price of the bond.

D = Sum of (PVi of cash flows *ti)/P , here t = year in which P

Macaulay Duration = 736.44/122.60 = 6 years (approx.)

b) As liability holds for 10 years and value 10,000*100 = 1 million (Bond X issued, at maturity neeed to pay face value).

Now, Asset A has such value that after 10 years the amount should equal to 1 million

As PV of the liabilities should equal to assets PV.

A = PV* 1.1210 = 380.78*10000 = 3807798

A = $3807798, T = 10 years

(ii) As the duration is same at t=0 , hence the fund is immunised against small changes in interest rate.

(iii) After 6 months there would not be any change in immunization, as no payment is made in next 6 months

In case of 18 months one coupon has to be paid , So, duration of the bond X will get changed

i.e. please refer the table for duration:

Duration here changes to 5.67 years , as 1.5 years has already being passed and the values will change.

Year 1 2 3 4 5 6 7 8 9 10 Cash flow 16 16 16 16 16 16 16 16 16 116 Discount factor @12% 0.89 0.80 0.71 0.64 0.57 0.51 0.45 0.40 0.36 0.32 Present Value 14.29 12.76 11.39 10.17 9.08 8.11 7.24 6.46 5.77 37.35 NPV 122.60

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