Question

A) The price of which of the following will be more sensitive to changes in interest rates. Explain your answer. Proper explanation / calculations required

Bond  X. 2-year 15% coupon bond with a face value of $1000 that pays semi-annual coupons and is trading at a yield of 26%

Or

Bond Y. A Zero-Coupon Bond that has a maturity of 18 months

B)  What is the price of the Bond X . above ?

C) Would your answer to part A change if bond X were trading at par?

YES: yield is at 26%

Answer 1

A)

For the purpose of deciding sensitivity we should find out the Duration of Both the bond.

Duration of Bond Y will be 18 Months only Because it is a zero coupon bond

Duration of Bond X can be calculated as follows

Periods(X) Cashflows PV of Cashflows(W)@ 26/2 = 13% Product (W*X)

1 75 66.37 66.37

2 75 58.74 117.48

3 75 51.98 155.94

4 75 + 1000 107.33 429.32

Now D =  

= 769.11 / 284.42

Bond X = 2.70 Years

and Bond Y = 1.5 Years

So Higher the Duration Higher the Sensitivity to chnage in Interest Rate

B)

Price of The Bond X is Present Value of Coupon amount and Redemption amount.

Price = Coupon PVAF (13%, 4 ) + Redemption PVIF (13%, 4 )

Therefor = 75 ( 2.9745 ) + 1000 ( 0.6133 )

= 223.09 + 613.32

= 836.40 Appx.

C)

No Answer to Part A won't change as it's duration will be 2 Years and it will still be higher than the Bond Y.