ANSWERS are: change in S = -5%, change in D = -16%, for rate decrease change in

ID: 2652943 • Letter: A

Question

ANSWERS are: change in S = -5%, change in D = -16%, for rate decrease change in S = 5% and change in D = 21%! Not sure how to do this!

C. Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent,

C.1 what is the percentage change in the price of Bond Sam?

C.2. Of Bond Dave?

C.3. If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then?

C.4. Of Bond Dave?

Explanation / Answer

Solution:

1. Percentage change in the price of Sam -

It is assumed the par value of thr bond to be $ 100 of both Sam and Dove for making calculation easy.

= ( 4.5 * PVAF(5.5 %, 6 years) )+ Redeemable value * PVIF(5.5 %, 6 years)

= ( 4.5 * 4.9955) + ( 100 * 7252)

= $ 95

( 4.5 * PVAF(5.5 %, 40 years) )+ Redeemable value * PVIF( 5.5 %, 40 years)

= ( 4.5 * 16.04162) + ( 100 * .1175)

= $ 83.9= $ 84

= ( New Price -Old price / Old price) * 100

= 95 - 100 * 100 = - 5 %

= (New Price - Old price / Old price) * 100

= 84 - 100/ 100 * 100 = - 16 %

= ( 4.5 * 5.3286 ) + ( 100 * 0.8135 )

= $ 104.5 = $ 105

= ( 4.5 * 21.3551 ) + ( 100 * 0.2526 )

= $ 121.33

$ 105 - 100 / 100 * 100

= 5 %

= $ 121.33 - 100 / 100 * 100

= 21.33 % = 21 %

Using formulas

Price of Bond = ( Annual interest * PVAF( at interest rate, for number of years)) )+ ( redeemable value of bond * PVIF( at interest rate, for number of years) )

When at par, interest rate or 9 % or say 4.5 % half yearly

At 2 % increase, it is 11 % or say 5.5 % semi annually

At 2 % fall, it is 7 % or say 3.5 % semi annually.

Particulars Sam Dove Curent price of the Bond = ( 4.5 * PVAF(4.5 %, 6 years) )+ Redeemable value * PVIF( 4.5 %, 6 years) = $ 100 ( 4.5 * PVAF(4.5 %, 40 years) )+ Redeemable value * PVIF( 4.5 %, 40 years) = $ 100 After 2 % increase, price of bond