Question

A $ 100 000, 8% bond redeemable at par with quarterly coupons is purchased to yield 6.5% compounded quarterly. Find the premium or discount and the purchase price if the bond is purchased (a) fifteen years before maturity; (b) five years before maturity.

Answer 1

Bond Price = C * ( 1 - ( 1+R)^-N) / R + FV / (1+R)^N

Where, C = Coupon Payment

R = Yield per period

N = Number of periods

FV = Face Value

Part A) Bond price before 15 years to maturity

Number of periods = 15 * 4 [ Years before maturity * Number of compounding in a year]

= 60

Yield Per period = 6.5%/4

= 1.625%

Coupon payment = Face value * Coupon rate * ( 1 / Number of periods(

= 100000 * 8% * ( 1/4)

= $2000

Bond Price = 2000 * ( 1 - ( 1 + (6.5%/4)^-15*4)/(6.5%/4) + 100000 / ( 1+6.5%/4)^15*4

= 2000 * ( 1 - 1.01625^-60)/0.01625 + (100000 / 1.01625^60)

= 2000 * 38.1439965036 + 38016.0056817

Bond Price = 114304.00

Premium = Bond Price - Face value

=  114304.00 - 100000

= 14304.00

B) Price of Bond 5 years before maturity

Number of periods = 5 * 4 [ Years * Number of compunding in a year]

= 20

Bond Price = 2000 * ( 1 - ( 1 + (6.5%/4)^-5*4)/(6.5%/4) + 100000 / ( 1+6.5%/4)^5*4

= 2000 * ( 1 - (1.01625^-20)/0.01625 +( 100000 / 1.01625^20)

= 2000 * ( 1 - 0.7244173245) / 0.01625 + 72441.7324505

= 2000 * 16.958933876 + 72441.7324505

Bond price = 106359.60

Premium = Bond Price - Face value

=106359.60  - 100000

= 6359.60