Answer:
Value of the bonds at issuance:
$131,395,438.89
As this ishigher than face value, there is a premium for 31,395,438.89 dollars
Explanation:
Effective market rate:
To determinatethe price of the bonds we should discount the future coupon payment and maturity at the market rate:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon payment:
100,000,000 x 4% = $4,000,000.00
time 15 years x 2 payment per year = 30 payment
market rate: 0.025
[tex]4000000 \times \frac{1-(1+0.025)^{-30} }{0.025} = PV\\[/tex]
Presnet Value of the coupon payment $83,721,170.3710
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 100,000,000.00
time 30.00
rate 0.025
[tex]\frac{100000000}{(1 + 0.025)^{30} } = PV[/tex]
PV 47,674,268.52
Present value of the bonds today:
coupon $83,721,170.3710
maturity $47,674,268.5181
Total $131,395,438.8891
