INTRODUCTION TO BUSINESS
FINANCE (FIN201)
Valuation of Bonds
Lecture 10:
Valuation of Bonds
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KEY FEATURES OF BONDS INCLUDE…
Par value: face amount; paid at maturity. Assume $1,000.
Valuation of Bonds
Coupon interest rate: stated interest rate. Multiply by par
value to get dollar interest payment. Generally fixed.
Maturity: years until bond must be repaid. Declines over time.
Issue date: date when bond was issued.
Market Interest Rate: rate which the investors in market
require at a particular time point.
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THERE ARE DIFFERENT TYPES OF BONDS…
Zero coupon bonds carry no periodic payment and are originally sold at
a discount.
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Government bonds are issued by the government and corporate bonds
are issued by public companies.
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Callable Bonds allows the issuer to repay the investors’ principal early.
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Putable bonds allow the investors to pre-maturely redeem the
outstanding bonds.
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Floating-rate bonds do not have a fixed coupon rate.
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Senior bonds are given preference in the payment of interest and
principle.
Valuation of Bonds
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EXAMPLE OF FIXED-RATE CORPORATE
BOND…
Valuation of Bonds
During 2011, Engro Corporation issued the 1st and
2nd TFCs (Engro Rupiya Certificates) of PKR 4bn and
PKR 3bn respectively, both having a tenor of 3 years
and carrying fixed profit rate of 14.5% p.a., paid
semi-annually. Their principal repayment will be in
bullet form during 2014 or early through put option
available to all investors. The issues initially were
rated AA by PACRA. The rating was revised to A+
(downgraded) in September 2012.
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EXAMPLE OF FLOATING RATE CORPORATE
BOND…
Valuation of Bonds
Askari Bank issued two unsecured subordinated TFCs
of PKR 1.5 billion each for a tenor of 8 years in
February 2005 and October 2005. The profit payments
were made semi-annually in arrears, based on 6-month
KIBOR plus 150 bps. The principal was redeemed in a
bullet payment at the maturity of each instrument in
February and October 2013.
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VALUE OF FINANCIAL SECURITIES IS EQUAL
TO THE PV OF EXPECTED FUTURE CASH
FLOWS…

Estimate future cash flows: size (how
much) and timing (when)

Discount future cash flows at an
appropriate discount rate
Valuation of Bonds
To value bonds and stocks we need to:
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CASH FLOW FROM A BOND
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An annuity (the coupon payments).
A lump sum (the face or par value to be
received in the future).
Valuation of Bonds
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CONSISTS OF…
Value of Bond = PMT(PVIFAi%, n)+ FV(PVIFi%, n)
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Find the value of a 5-year 10% annual coupon bond
issued on January 1, 2005, when kd = 10%???
Valuation of Bonds
When the required rate of return (kd) equals the
coupon rate, the bond value (or price) equals
the par value. If kd remains constant, the value
of the bond will remain same as the par value
as maturity approaches.
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Valuation of Bonds
On January 1, 2006, the required return in market
increases to 12%, calculate the value of the bond issued
on January 1, 2005 with a 5-year maturity at the time of
issuance and a coupon of 10%???
When the market’s required rate of return (kd) is
greater than the coupon rate, the bond value (or
price) is lesser than the par value and the bond
sells at a discount. If kd remains constant, the
value of a discount bond will increase to its par
value as maturity approaches.
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When the market’s required rate of return (kd) is
lesser than the coupon rate, the bond value (or
price) is greater than the par value and the bond
sells at a premium. If kd remains constant, the
value of a premium bond will decrease to its par
value as maturity approaches.
Valuation of Bonds
Now assume that on January 1, 2006, the required
return in market decreases to 8%, calculate the value of
the bond issued on January 1, 2005 with a 5-year
maturity (at the time of issuance) and a coupon of
10%???
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BOND PRICES
AND MARKET INTEREST RATES
MOVE IN OPPOSITE DIRECTIONS…
When coupon rate > YTM,
price > par value (premium bond)
Valuation of Bonds
When coupon rate = YTM,
price = par value
When coupon rate < YTM,
price < par value (discount bond)
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VALUE OF A BOND
MOVES TOWARDS PAR AS
THE MATURITY APPROACHES…
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At maturity, the value of any bond must equal its par
value.
Over time, the value of a premium bond will decrease
to its par value.
Over time, the value of a discount bond will increase to
its par value.
A par value bond will stay at its par value.
Valuation of Bonds
If kd remains constant:
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