Chapter 3 Valuing Bonds 47
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If you own a bond, you are entitled to a fixed set of cash payoffs. Every year until the
bond matures, you collect regular interest payments. At maturity, when you get the final
interest payment, you also get back the face value of the bond, which is called the bond’s
principal.
A Short Trip to Paris to Value a Government Bond
Why are we going to Paris, apart from the cafés, restaurants, and sophisticated nightlife?
Because we want to start with the simplest type of bond, one that makes payments just once
a year.
French government bonds, known as OATs (short for Obligations Assimilables du Trésor),
pay interest and principal in euros (€). Suppose that in October 2014 you decide to buy € 100
face value of the 4.25% OAT maturing in October 2018. Each year until the bond matures
you are entitled to an interest payment of .0425 × 100 = €4.25. This amount is the bond’s
coupon.^1 When the bond matures in 2018, the government pays you the final €4.25 inter-
est, plus the principal payment of €100. Your first coupon payment is in one year’s time, in
October 2015. So the cash payments from the bond are as follows:
Cash Payments (€)
2015 2016 2017 2018
€4.25 €4.25 €4.25 €104.25What is the present value of these payments? It depends on the opportunity cost of capital,
which in this case equals the rate of return offered by other government debt issues denom-
inated in euros. In October 2014, other medium-term French government bonds offered a
return of just .15%. That is what you were giving up when you bought the 4.25% OATs.
Therefore, to value the 4.25% OATs, you must discount the cash flows at .15%:
PV = ______4.25
1.0015+ _______ 4.25
1.0015^2+ _______4.25
1.0015^3+ _______ 104.25
1.0015^4= €116.34Bond prices are usually expressed as a percentage of face value. Thus the price of your 4.25%
OAT was quoted as 116.34%.
You may have noticed a shortcut way to value this bond. Your OAT amounts to a pack-
age of two investments. The first investment gets the four annual coupon payments of €4.25
each. The second gets the €100 face value at maturity. You can use the annuity formula
from Chapter 2 to value the coupon payments and then add on the present value of the final
payment.
PV(bond) = PV(annuity of coupon payments) + PV(final payment of principal)
= (coupon × 4-year annuity factor) + (final payment × discount factor)= 4.25
[_____^1
.0015− _____________^1
.0015(1.0015)^4
]+ _______10 0
1.0015^4= 16.93 + 99.40 = €116.343–1 Using the Present Value Formula to Value Bonds
(^1) Bonds used to come with coupons attached, which had to be clipped off and presented to the issuer to obtain the interest payments.
This is still the case with bearer bonds, where the only evidence of indebtedness is the bond itself. In many parts of the world bearer
bonds are still issued and are popular with investors who would rather remain anonymous. The alternative is registered bonds, where
the identity of the bond’s owner is recorded and the coupon payments are sent automatically. OATs are registered bonds.