Question

On January 1, 2021, Frontier World issues $39.9 million of 7% bonds, due in 10 years, with interest payable semiannually on June 30 and December 31 each year.

If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1).

• Do not round interest rate factors.
• Enter your answers in dollars not in millions.
• Round "Market interest rate" to 1 decimal place.
• Round your final answers to the nearest whole dollar.

I have the numbers calculated out (please verify), but how do I get the issue price? Was there a table I need to use?

Face Amount:                                39,900,000

Interest Payment:                           1,396,500

Periods to maturity:                       20

Market Interest Rate:                    3%

Issue price: ????

The bonds will issue at: (Discount, Premium, or Face Amount?)

Answer 1

Number of periods = 10 * 2 = 20 (since semi annual)

Interest rate = 7/2 = 3.5% (since semi annual)

Discount rate = 6/2 = 3% (since semi annual)

Issue price ={ Face value * PVAF(3%,20th yr) }+ { Interest * PVAF(3%,20 yrs)

Issue price ={ 39.9 * 0.5537) + { 1.3965 * 14.8775 }

Issue price = 42.87 million

Bond will be issued at premium because issue price is in excess of par value.

Note:

PVAF (3%,20th yr) = Look at the annuity table at 3% and 20 th yr.

PVAF (3%,20 yrs) = Look at the cumulative table or take the sum of present values of 20 yrs.