Issuance of bonds (at a premium or discount)


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Issuance of bonds (at a premium or discount)



Present value concept:

  • Present value concept:

    • Present value of $1 is the value today of $1 to be received at some future date, given a specific interest rate.
  • Example:

    • 1. What is the present value of $100 to be received a year from now given an annual market interest rate of 10%?
  • P.V.  (1+10%) = $100

      • P.V. = $100/1.1
      • = $100  0.9091
      • = $90.91


2. What is the present value of $100 to be received two years from now given an annual interest rate of 10%?

  • 2. What is the present value of $100 to be received two years from now given an annual interest rate of 10%?

  • P.V  (1+10%)  (1+10%) = $100

    • P.V  (1+10%)2 = $100
    • P.V.  1.21 = $100
    • P.V. = $100 / 1.21
    • = $100  0.8264
    • = $82.64


Receiving (or paying)a constant amount of money at the end of each period (equal time internal) for a given number of periods

  • Receiving (or paying)a constant amount of money at the end of each period (equal time internal) for a given number of periods



1. Using the example above given a10% Interest rate:

  • 1. Using the example above given a10% Interest rate:

  • P.V. of the first $100 = $100  0.9091 = $90.91

  • P.V. of the second $100 = $100  0.8264 = $82.64

  • P.V. of the third $100 = $100  0.7513 = $75.13

  • P.V. of the fourth $100 = $100  0.6830 = $68.30

  • P.V. of the fifth $100 = $100  0.6209 = $62.09

  • Total 3.7907 $379.07



The P.V. of $100 annuity receiving every year for the following 5 years, starting a year from now =>

  • The P.V. of $100 annuity receiving every year for the following 5 years, starting a year from now =>

  • $100 * 3.7907 = $379.07

  • The P.V. of this annuity can be obtained from an annuity table under 10%, 5 periods.



2. What is the P.V. of $300 annuity receiving every 6 months for the following 30 months, starting 6 months from now ? The annual interest rate is 12%.

  • 2. What is the P.V. of $300 annuity receiving every 6 months for the following 30 months, starting 6 months from now ? The annual interest rate is 12%.



Bonds are securities issued by a corporation to borrow money from the public (many lenders).

  • Bonds are securities issued by a corporation to borrow money from the public (many lenders).

  • This is a source to raise funds.

  • The corporation will receive cash when bonds are issued.



The face value of the bonds must be repaid to the bondholders on the maturity date of the bonds.

  • The face value of the bonds must be repaid to the bondholders on the maturity date of the bonds.

  • Also, the bond issuers will pay interests to the bondholders periodically (i.e., semi-annually).



Long-Term Liability: if bonds mature in more than one year.

  • Long-Term Liability: if bonds mature in more than one year.

  • Short-Term Liability: if bonds mature in less than one year



Bond Indenture is an agreement between the bond issuer and investors stating the following:

  • Bond Indenture is an agreement between the bond issuer and investors stating the following:

    • Interest rate of bonds;
    • Interest Payment dates;
    • The maturity date of bonds;
    • The type of bonds: callable, convertible,..
  • The indenture is held by a trustee appointed by the issuing firm to represent the rights of the bondholders.



Bond Covenant is a contractual provision in a bond indenture (source: financial dictionary).

  • Bond Covenant is a contractual provision in a bond indenture (source: financial dictionary).

  • Financial covenant: requiring issuers to maintain financial ratios such as debt/equity ratio and the interest coverage ratio at a certain level.

  • Non-financial covenant: requiring the disclosure of certain financial information.



1. Receive the approval from the stockholders and regulatory authorities (i.e., the SEC).

  • 1. Receive the approval from the stockholders and regulatory authorities (i.e., the SEC).

  • 2. Print bond certificates and write indenture (to set the terms of bond issue such as the stated interest rate, the interest payment date and the maturity date…)



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