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5. Bond Valuation - good
Microeconomics (EC1103)
University of Central Punjab
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Chapter 5
Bond Valuation
As all other securities stated, bonds are also securities, which are used by companies, municipalities, states and governments to finance a variety of projects and activities. Bonds are defined as:
_<It is a debt investment in which an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate.= _
Basic Terms of Bonds
In this chapter, we will understand the valuation of bonds. To fully understand this valuation, following terms must be discussed.
Par or Face Value
It is the stated value of any security, and in this case, a bond. It is the amount that is paid to the bondholders at maturity. It also generally represents the amount of money borrowed by the bond issuer. For most of the bonds, its face value is $1000.
Coupon Rate
The coupon rate determines periodic coupon or interest payments. It is generally fixed and expressed as a percentage of the bond9s face value. Most bonds pay interest semiannually.
Coupon Payments
Coupon payments are the periodic interest payments from a bond issuer to a bondholder. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months. The annual coupon payment is calculated as following:
_Annual Coupon Payment = Coupon rate*Bond9s face value _
Maturity Date
A bond almost always has a stated maturity date, which is the time when a company is obligated to pay bondholder the face value of the bond. The last coupon payment is also paid on the maturity date.
Required Return
The rate of return investors currently require on a bond.
Prize Bonds
Prize bonds are a form of investment, which are different than the real financial bonds we study in business finance. State Bank of Pakistan (SBP) oversees the prize bond issuance and prize nomination and distribution.
Prize bonds are one tool for government to collect money from the public. They receive money from you and give you a paper, called a prize bond, which can be traded in the market. The returns on the prize bonds are in the form of prizes distributed by the government. They do not guarantee any fix return and can be sold in the market for the same price originally paid. The only form of investment return on the prize bond is a chance to win prize, each period the prizes are drawn.
Zero Coupon Bonds
Zero coupon bond is a bond that does not pay coupon payments and instead pays one lump sum at maturity. The amount paid at maturity is called the face value. So this type of debt security provides compensation to investors in the form of price appreciation. Now a question arises: Why buy a bond which pays no interest? Obviously, the buyers do receive a return. The return is the gradual increase of the value of that bond than its original value and the holder of a zero coupon bond only receives the face value of the bond at maturity. The present value of such bond is calculated as:
ßÝ=
ÝÝ
(ß+þ)ÿ
Where: FV= Face Value i= Required return n= Time period
**Example 1 **
Oriflame Inc. has issued a zero coupon bond having a 100year maturity and a face value of PKR1000. If your required return is 12%, calculate its present value.
PV=(!!!"""!.!")!" = PKR 322
**Example 2 **
X & Y Inc. issues a bond having a par value of PKR 1000 with 10% coupon semi0annual and nine years to maturity. The coupon rate has interest payments of PKR 50 every 60months. Assuming your required rate of return on the bond is 8%, find the value of this bond.
Here, I = 100/2 = 50, i = 8%/2 = 4%, n = 9*2 = 18, FV = 1000
PV=
50
( 1 + 0. 04 )!+
50
( 1 + 0. 04 )!+ï+
50
1 + 0. 04 !"+
1 , 000
( 1 + 0. 04 )!"
PV = PKR 1,126
Perpetual Bonds
The easiest way to understand the value of bonds is with a unique class of bonds that never matures. These are indeed the rare bonds, but it illustrates valuation technique in a very simple form. Its present value is calculated as:
PV =
Ü
þ
Where: I= Fixed annual payment i= Investor9s required rate of return
**Example 5 **
Hadi wants to buy a perpetual bond that pays $50 a year forever. His required rate of return for this type of bond is 12%. What maximum amount should he be willing to pay for this bond?
PV= !!".!"=PKR 416. 67
5. Bond Valuation - good
Course: Microeconomics (EC1103)
University: University of Central Punjab
