Question

Given the following information, what is the percentage change in the price of the bonds if interest rates suddenly rise by 2%?

(Please show your work as I am attempting to work out similar problems in excel.)

Wing Air Inc.
Coupon rate	7%
Settlement date	1/1/2000
Maturity date	1/1/2002
Face value	1,000
# of coupons per year	2
Airfoil, Inc.
Coupon rate	7%
Settlement date	1/1/2000
Maturity date	1/1/2015
Face value	1,000
# of coupons per year	2
Change in interest rate	2%

Answer 1

Assume that the bonds are selling at par. Thus, the initial selling price of the bond = $1,000

For the bonds sold at Par Value, yield to maturity (YTM) is equal to its coupon rate.

The interest rate is increased by 2% from 7% to 9%.

Bond’s price can be calculated as follows:

Bond price (P) = C* [1- 1/ (1+i) ^n] /i + FV / (1+i) ^n

Where,

where, C = Coupon payment

FV = Par value or face value of bond

n = Number of periods

i = Yield-to-maturity

For Wing Air Inc. Bond:

Since coupon payments are made on a semi-annual basis therefore coupon payment = 7%/2 of $1000 = $35

n = number of periods = 4 (2*2 for semiannual payments of up to maturity which is 2 years)

i = yield to maturity (YTM) = 9%/2 on semiannual basis = 4.5%

Therefore,

P = $35 * [1 – 1 / (1+4.5%) ^4] /4.5% + $1000 / (1+4.5%) ^4

= $125.56 + $838.56

= $964.12

Percentage change in price Wing Air Inc. Bond = (new price of bond – Initial price)/ Initial price

= ($964.12 - $1000)/$1000 = - 0.0359 or -3.59%

For Airfoil Inc. Bond:

Number of years = 15 years

Number of periods (n) = 15*2 = 30

i = yield to maturity (YTM) = 9%/2 on semiannual basis = 4.5%

Since coupon payments are made on a semi-annual basis therefore coupon payment = 7%/2 of $1000 = $35

Therefore, Price of the bond P = $35 * [1 – 1 / (1+4.5%) ^30] /4.5% + $1000 / (1+4.5%) ^30

= $570.11 + $267.00

= $837.11

Percentage change in price of Airfoil Inc. Bond = (new price of bond – Initial price)/ Initial price

= ($837.11 - $1000)/$1000 = - 0.1629 or -16.29%

Thus, the percentage change in the bond's price of Airfoil Company is more than the Wing Air Inc.

This is based upon the principle that the change in the interest rate would lead to more percentage change in the price for the bonds with longer maturity.

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