Question

. Leggio Corporation issued 25-year, 7.25% semiannual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds has dropped to 7%. What is the new price of the bonds, given that they now have 24 years to maturity? (4 points)

Answer 1

Answer : Calculation of Price of Bond :

Value of Bond = (Coupon * PVAF @ r% for n years) + (Face Value * PVF @ r% for nth years)

Coupon = 1000 * 7.25% = 72.5 / 2 = 36.25 (Divided by 2 as semiannual coupon payment)

r is the yield to maturity i.e 7% / 2 = 3.5% (Divided by 2 as semiannual coupon payment)

n is the number of years remaining to maturity i.e 24 * 2 = 48 (Multiplied by 2 as semiannual coupon payment)

Value of Bond = (36.25 * PVAF @ 3.5% for 48 years) + (1000 * PVF @ 3.5% for 48th years)

= (36.25 * 23.0912442483) + (1000 * 0.19180645101)

= 837.057604 + 191.80645101

= $1,028.86

Note :

PVF can be calculated using [1 / (1 + 0.035)^48 ] = 0.19180645101

PVAF can be calculated as {[1 - (1 + 0.035)^(-48) ] / 0.035} = 23.0912442483