Question

A bond has 2 year to maturity, 6% coupon, 8% yield and pays annually. The current price of the bond is $964.3347. If yield increases by 25 basis points, calculate the new bond price using the time value of money formulas (i.e., bond formula). 972.12 970.53 963.99 959.95 None of the above

Answer 1

value of bond = [present value of annuity * bond interest] + [present value factor * bond face value]

here,

present value of annuity = [1-(1+r)^(-n)] / r

here,

r = 8%+0.25% increase in yield =>8.25% =>0.0825.

n = 2

=>[1- (1.0825)^(-2)]/0.0825

=>1.77717

bond interest = $1,000 * 6% =>$60.

present value factor = 1/(1+r)^n

=>1/(1.0825)^2

=>0.8533834.

face value = $1,000

now,

value of bond = [1.77717*$60] + [0.8533834*$1,000]

=>106.63+853.38

=>959.93 which is similar to 959.95..........(minor differences will arise due to rounding off of time value factors).