Bonds – Premiums and Discounts

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  • #201171
    pickanicken
    Participant

    I’m not sure why, but I can’t wrap my head around when a bond is sold at a premium vs a discount.

    This is how I perceive a transaction (please correct me):

    A company is issuing 500 10%, 5 year, $1,000 bonds. The market rate is 7%.

    When I read this I immediately think this is recorded as as selling at a discount for the company because the company will be paying 10% interest while the market is 7%. Meaning in order to sell this bond the company is willing to pay more interest to the purchaser of the bond.

    From my reading, I understand that I have this backwards. The bond is selling at a premium. The reading explains that the company is receiving more than the face amount of the bond, but I don’t understand how they could be receiving more than the face amount when they are paying more interest then the market rate? Now I am getting even more confused. HELP!

    REG - 81
    BEC - 83
    AUD - 86
    FAR - 78 (Done!)

Viewing 4 replies - 1 through 4 (of 4 total)
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  • #771174
    Spartans92
    Participant

    Think of it this way. If you are an investor and you are willing to pay 10% instead of 7% (what the market offers) you are paying more to hope for a higher return. Since you are paying more than what you get from the market this will be a premium. I don't know if this help at all. Or try working out the JE which helps tremendously.

    Apply this to the discount. if Market Rate was 10% vs stated rate of 7% I am paying much less than what the market offers. Hence, I will get a lower return.

    BEC - 76
    REG- 67, 85
    AUD-63, 74, 80!!
    FAR-65, 62, 57, 79

    3 down 1 more to go. BEC is on the Line 🙁

    BEC- PASS

    #771175
    tuanxn
    Participant

    You're thinking about it from the perspective of the seller, when you should be looking at it from the perspective of the buyer.

    The buyer will be buying the bond at a premium since he will likely pay more of the bond since it pays higher than the going rate in the market. The contrary will occur with a discount.

    #771176
    pickanicken
    Participant

    Just to be clear…

    I am a company selling a bond. I sell a bond for 1,000,000 and agree to pay the buyer of the bond interest of 8%.

    I am a buyer of a bond. I give 1,000,000 for a bond. I receive interest payments from the seller until the bond matures.

    If the interest rate offered by the company is greater than the rate I can receive in the market, I am willing to pay more for the bond. Hence, I am willing to pay a premium.

    Conversely, if the interest rate offered by the company is less, then I would want to pay less for the bond.

    Right?

    I think part of what I still don't understand then is why the cash proceeds of the bond are calculated the way that they are?
    When sold at a premium we are calculating cash proceeds based on sum of the present value of the face amount and the present value of the interest payments based on the market rate. How is that a representation of the cash proceeds?

    REG - 81
    BEC - 83
    AUD - 86
    FAR - 78 (Done!)

    #771177
    tuanxn
    Participant

    You got the first part right 🙂

    For the second part:
    Remember that if the market rate was the stated rate, then the bond would sell at par (face value).

    Since the bond's stated rate is above the market rate, we would sell the bond above par (face value)

    How does that work?

    Well technically, if the stated rate equaled the market rate, then the present value of the face amount + the present value of the total interests payments would equal the face amount (in present value terms).

    Since the stated rate is greater than the market rate, the interest payments will be greater than they would be if the stated rate equaled the market rate. Therefore, when we discount the total interest payments using the market rate and add that to the present value of the face amount, the sum will be GREATER than the face amount.

    Let's use your original example and restate it with the market rate equating the stated rate

    A company is issuing 10%, 5 year, $1,000 bonds. The market rate is 10%.

    Present Value of $1000 at 10% for 5 years is $620.92 ($1000 x 0.62092)
       I used the table for present value of 1 and looked at the coefficient for 10% at 5 years (.62092)
    Present Value of the total interest payments are $379.08 ($100 x 3.7908)
       Interest payments at $100 per year (10% x $1000)
       I used the table for present value of an ordinary annuity of 1 and looked at the coefficient for 10% at 5 years (3.7908)
    Therefore the present value of the future cash flows are $1000 ($620.92 + $379.08), which is the face value of the bond

    Now, let's use your original example with a stated rate that is greater than the market rate:

    A company is issuing 10%, 5 year, $1,000 bonds. The market rate is 7%.

    Present Value of $1000 at 7% for 5 years is $712.99 ($1000 x 0.71299)
       I used the table for present value of 1 and looked at the coefficient for 7% at 5 years (.71299)
    Present Value of the total interest payments are $410.02 ($100 x 4.10020)
       Interest payments at $100 per year (10% x $1000)
       I used the table for present value of an ordinary annuity of 1 and looked at the coefficient for 7% at 5 years (4.10020)
    The present value of the future cash flows is $1123.01, which is what the bond should sell for. As you can see, the bond's present value is greater than the face value of the bond; so it should sell for a premium.

    Hope that helped!

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