Question

On June 30, 2021, Singleton Computers issued 8% stated rate bonds with a face amount of $100 million. The bonds mature on June 30, 2036 (15 years). The market rate of interest for similar bond issues was 5% (2.5% semiannual rate). Interest is paid semiannually (4.0%) on June 30 and December 31, beginning on December 31, 2021.

Answer 1

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

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

$4000000 \times \frac{1-(1+0.025)^{-30} }{0.025} = PV$

Presnet Value of the coupon payment $83,721,170.3710

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   100,000,000.00

time   30.00

rate  0.025

$\frac{100000000}{(1 + 0.025)^{30} } = PV$  

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