Question $4-1$

On January $1,2022,$ Piper Co$.$ issued ten$-$year bonds with a face value of $1,000,000$ and a stated annual interest rate of $10\%,$ payable semiannually on June $30$ and December $31.$ The bonds were sold to yield $12\%($effective annual interest rate$).$ Present value factors are:

Present value of $1$ for $10$ periods at $10\%$

$386$

Present value of $1$ for $10$ periods at $12\%$

$\mathrm{.}322$

Present value of $1$ for $20$ periods at $5\%$

$\mathrm{.}377$

Present value of $1$ for $20$ periods at $6\%\mathrm{.}312$

Present value of ordinary annuity for $10$ periods at $10\%$

$6\mathrm{.}145$

Present value of ordinary annuity for $10$ periods at $12\%$

$5\mathrm{.}650$

Present value of ordinary annuity for $20$ periods at $5\%$

$12\mathrm{.}462$

Present value of ordinary annuity for $20$ periods at $6\%11\mathrm{.}470$

Required:

$($a$)$ Calculate the issue price of the bonds. Are the bonds issued at a discount, or at a premium?

$($b$)$ Assume that Piper has a fiscal year ending on December $31,$ determine the total interest expense relating to this bond charged to the income statement of $2022$ and the bonds payable balance after Piper makes the coupon payment on December $31,2022.$