Question

A 20-year bond with a face value of $1,000 will mature in 8 years. The bond pays semi-annual coupons at 5% p.a. compounding half-yearly. Mia wants to purchase the bond at a price which gives her a yield to maturity of 6% p.a. compounding half-yearly. Calculate the maximum price Mia should pay for the bond. (Round your answer to the nearest cent).

Answer 1

Calculation of the maximum price Mia should pay for the bond:

Formula,

Bond price = (Interest x [1- (1 + YTM)^-n] / YTM) + (Face value / (1+ YTM)^n)

where,

Interest = Coupon rate / 2 x Face value 

              = 5% / 2  x $1000

              = $25

n = year to maturity*2 = 8*2 = 16

YTM = Yield to maturity / 2 = 6%/2 = 3%

 

Solve,

Bond price  = ($25 x [1 - (1+ 0.03)^-16] / 0.03) + ($1000x [1 / (1+ 0.03)^16])

                   = ($25 x [1- 1/(1.03)^16] / 0.03) + ($1000x [1/(1.03)^16])

                   = ($25 x [1- 0.623167] / 0.03) + $1000 x 0.623167

                   = ($25 x 0.376833 / 0.03) + $623.167

                   = $314.028 + $623.167

                   = $937.19

 

So, the maximum price Mia should pay for the bond is $937.19.

So, the maximum price Mia should pay for the bond is $937.19.