Answer:
The bond will sell at a discount of $16,948.41.
Explanation
First, get the present value of the principal.
PRESENT VALUE OF PRINCIPAL =
BOND FACE VALUE / ((
1 +
MARKET INTEREST RATE) ^
YEARS)
$59,103.18 = $93,000.00 / ((1 + 0.12) ^ 4)
Next, get the dollar value of an end-of-period payment.
PAYMENT =
BOND FACE VALUE * (
1 +
STATED INTEREST RATE)
$5,580 = $93,000.00 * (1 + 0.06)
Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS =
PAYMENT *
PRESENT VALUE FACTOR AT MARKET RATE$16,948.41 = $5,580 * 3.04
Next, add the present value of the principal to the present value of all of the interst payments.
PRESENT VALUE OF BOND =
PRESENT VALUE OF PRINCIPAL +
PRESENT VALUE OF INTEREST PAYMENTS$76,051.59 = $59,103.18 + 16,948.41
Finally, Find the difference between the present value of the bond, and its initial cost. If the present value is higher, then people will pay a
premium for it. Otherwise, people will demand a
discount.
DIFFERENCE =
PRESENT VALUE OF BOND -
BOND FACE$-16,948.41 = $76,051.59 - 93,000.00