Bonds at a Premium or Discount
Lesson:
It takes a lot of time to get a bond ready to be issued. Because of that, it's nearly impossible to know what interest rate a bond should offer.
Often the market interest rate is higher or lower than it was when the bond offering was originally planned.
For this reason, bonds are often sold at a:
- Premium - A bond is sold for more than its face value when the market rate is lower.
- Discount - A bond is sold for less than its face value when the market rate is higher.
Often bonds will be assigned a number representing how much of a percent discount or premium its price.
For instance, a bond at 90 is sold at a 10% discount, and a bond at 110 is sold a 10 percent premium.
Buyers and sellers in the bond market need to be able to calculate what a premium or discount should look like in order to make a deal attractive to both parties.
Kilo Industries, the ancient shoelace exporter, wants to sell a 7-year $100,000.00 bond. The stated rate is 11.00% and the market rate is 3.00%.
- The present value factor for an ordinary annuity at 3.00% for 7 years is 6.23.
- The present value factor for an ordinary annuity at 11.00% for 7 years is 4.71.
Will this bond sell at a discount or a premium - and by how much?
Answer:
- The bond will sell at a premium of $49,842.26.
Explanation:
- First, remember the formula to find the present value of the principal.
PRESENT VALUE OF PRINCIPAL = BOND FACE VALUE / ((1 + MARKET INTEREST RATE) ^ YEARS) - Now let's plug in the numbers
$81,309.15 = $100,000.00 / ((1 + 0.03) ^ 7) - Next, remember the dollar value of an end-of-period payment.
PAYMENT = BOND FACE VALUE * (1 + STATED INTEREST RATE) - Let's turn the variables into numbers
$11,000 = $100,000.00 * (1 + 0.11) - Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS = PAYMENT * PRESENT VALUE FACTOR AT MARKET RATE - Plugging in the numbers, we get
$68,533.11 = $11,000 * 6.23 - 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 - Plugging in the numbers, we get
$149,842.26 = $81,309.15 + 68,533.11 - 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 - And we see the following:
$49,842.26 = $149,842.26 - 100,000.00