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.
Romeo Industries, the ever-maligned chair exporter, wants to sell a 4-year $5,000.00 bond. The stated rate is 6.00% and the market rate is 4.00%.
- The present value factor for an ordinary annuity at 6.00% for 4 years is 3.47.
- The present value factor for an ordinary annuity at 4.00% for 4 years is 3.63.
Will this bond sell at a discount or a premium - and by how much?
Answer:
- The bond will sell at a premium of $362.99.
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
$4,274.02 = $5,000.00 / ((1 + 0.04) ^ 4) - 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
$300 = $5,000.00 * (1 + 0.06) - Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS = PAYMENT * PRESENT VALUE FACTOR AT MARKET RATE - Plugging in the numbers, we get
$1,088.97 = $300 * 3.63 - 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
$5,362.99 = $4,274.02 + 1,088.97 - 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:
$362.99 = $5,362.99 - 5,000.00