Question

Borland, Inc. issues 25-year semi-annual bonds that have a face value of $1,000 and a coupon rate of 7.5%. The current market price for the bonds is $950.00.   If your required rate of return is 8.5%, what is the value of one of these bonds to you? (Your answer should be with +/- $0.02 of the following answers.)

Group of answer choices

$977.95

$978.09

$950

$897.03

Answer 1

Answer : Correct Option is 897.03

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

Coupon = 1000 * 7.5% = 75 / 2 = 37.5 (Divided by 2 as semiannual coupon payment)

r is the yield to maturity i.e 8.5% / 2 = 4.25% (Divided by 2 as semiannual coupon payment)

n is the number of years to maturity i.e 25 * 2 = 50 (Multiplied by 2 as semiannual coupon payment)

Value of Bond = (37.5 * PVAF @ 4.25% for 50 years) + (1000 * PVF @ 4.25% for 50th years)

= (37.5 * 20.5930613039) + (1000 * 0.12479489423)

= 772.239798896 + 124.79489423

= $897.03

Note :

PVF can be calculated using [1 / (1 + 0.0425)^50 ] = 0.12479489423

PVAF can be calculated as {[1 - (1 + 0.0425)^50 ] / 0.0425} = 20.5930613039