Question

On December 31, 2021, Interlink Communications issued 6% stated rate bonds with a face amount of $100 million. The bonds mature on December 31, 2051. Interest is payable annually on each December 31, beginning in 2022. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the table values provided.)

Determine the price of the bonds on December 31, 2021, assuming that the market rate of interest for similar bonds was 7%. (Round your final answers to the nearest whole dollar amount.)

Table values are based on:
n =?
i =?

Cash Flow Amount Present value
Interest
Principle
Price of bonds

Answer 1

The bonds were issued at $87,590,959

Step-by-step explanation:

The bonds will be issued at the present value of the coupon and maturity discounted by the market rate

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 6,000,000.000 ( 100 million x 6%)

time 30 (2051 - 2021)

market rate 7% = 7/100 = 0.07

`6000000 * (1-(1+0.07)^(-30) )/(0.07) = PV\\`

PV $74,454,247.1010

PV of the maturity

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 100,000,000.00

time 30.00

rate 0.07

`(100000000)/((1 + 0.07)^(30) ) = PV`

PV 13,136,711.72

Total current value of the bonds:

PV coupon $ 74,454,247.1010

PV maturity $ 13,136, 711.7155

Total $87,590,958.8165