Question

Coke-Colas bond is issued, has par of $1000 and matures in 6 years. It pays annual coupons of $50 each. Annual interest rates are now 3%.

A. What is the value of the bond

B. Premium bond or discount bond

C. What is the Macauley’s Duration of the Bond

D. You immunize this Bond, which you have booked as a liability, and you were going to use 1-year Zeroes and Perpetuities to match interest-rate change sensitivity risk, how much of each would you buy?

Show formulas!

Answer 1

Answers for A and C are in the excel screenshots below. B - The bond is a premium bond.

D. Let x be the weight of ZCBs and (1- x) is the weight of perpetuities.

Duration of ZCB = 1

Duration of perpetuity can be found using (1+Y/Y) = (1000*1.03)/0.03

We are using (1000*1.03)/0.03 to understand the duration of perpetuity.

To immunize the bond we will add up the duration of ZCB and perpetuity to get the duration of bond.

Equation:

1x+(1-x)*(1000*1.03/0.03) = 5.37.

1x+(1-x)*34333.33 = 5.37

1x+34333.33 - 34333.33x = 5.37

- 34332.33x = 5.37 - 34333.33

x = -34327.96/ - 34332.33 = 0.99

1- x = 0.01

So 99 % should be invested in ZCBs and 1% in perpetuities.