VALUING BONDS
BONDS ARE MORE ABOUT NOT BEING WRONG
AND STOCKS ARE MORE ABOUT BEING RIGHT-
Bond Characteristics
Bonds are debt obligations of issuers (borrowers) to bondholders
(creditors)
◦ Face or par value is the principal repaid at maturity, typically Rs.1000
◦ The coupon rate determines the interest payment (“coupon payments”)
paid semiannually
◦ The indenture is the contract between the issuer and the bondholder that
specifies the coupon rate, maturity date, and par value
3–2
Using the Present Value Formula
to Value Bonds
PV 
C1
(1  r )
1

C2
(1  r )
2
 ... 
1,000  C N
(1  r )
N
3–3
Using the Present Value Formula
to Value Bonds
Example
◦ Indusind Bank issues a 5 year bond which pays Rs.50 every December 31st for five
years. At maturity it pays the principal amount of Rs.1,000 and retires the bond.
The yield is 13.08 per annum.
50
50
50
50
1050
𝑃𝑉 =
+
+
+
+
2
3
4
1.1308 (1.1308)
(1.1308)
(1.1308)
(1.1308)5
716.36
3–4
Using the Present Value Formula to
Value Bonds
Example: France
◦ In December 2018 you purchase 100 euros of bonds in France which pay a 5%
coupon every year. If the bond matures in 2023 and the YTM is 3.0%, what is the
value of the bond?
5
5
5
5
105.0
PV 




1.024 1.024 2 1.024 3 1.024 4 1.024 5
 €112.11
3–5
Using the Present Value Formula
to Value Bonds
Another Example: Japan
◦ In July 2020 you purchase 200 yen of bonds in Japan which pay an 8% coupon every
year. If the bond matures in 2025 and the YTM is 4.5%, what is the value of the
bond?
16
16
16
16
216
PV 




1.045 1.0452 1.0453 1.0454 1.0455
 ¥243.57
3–6
Using the Present Value Formula
to Value Bonds
Example: India
◦ In June 2020 you purchase a ten-year Indian government security. The G-Sec has
an annual coupon rate of 7.16%, paid semiannually. If investors demand a 3.605%
semiannual return (7.21% APR), what is the price of the G-Sec?
𝑃𝑉
3.58
3.58
3.58
3.58
=
+
+
+
2
3
1.03605 (1.03605)
(1.03605)
(1.03605)4
103.58
+ ⋯..
(1.03605)20
99.65
3–7
How Bond Prices Vary with
Interest Rates
Example, Continued: India
◦ Take the same ten-and-half year Indian government security. If investors
demand a 6.0% semiannual return, what is the new price of the G-Sec?
𝑃𝑉
3.58
3.58
3.58
3.58
=
+
+
+
2
3
1.03605 (1.03605)
(1.03605)
(1.03605)4
103.58
+ ⋯..
(1.03605)20
108.63
3–8
How Bond Prices Vary with
Interest Rates
BOND PRICE
115.00
110.00
105.00
100.00
95.00
90.00
85.00
80.00
Interest rate, %
3–9
Maturity and Prices
3–10
Debt and Interest Rates
Nominal r = Real r + expected inflation (approximation)
Real r theoretically somewhat stable
Inflation is a large variable
◦ Term structure of interest rates shows cost of debt
3–11
Debt and Interest Rates
Debt and Interest Formula:
1 rnominal  (1 rreal )  (1 i)
3–12
The Risk of Default
Corporate Bonds and Default Risk
◦Payments promised to bondholders
represent best-case scenario
◦Most bonds’ safety judged by bond ratings
3–13
The Risk of Default
Sovereign Bonds and Default Risk
◦Sovereign debt is generally less risky than
corporate debt
◦Inflationary policies can reduce real value
of debts
3–14
The Risk of Default
Sovereign Bonds and Default Risk
◦ Foreign Currency Debt
◦ Default occurs when foreign government borrows dollars
◦ If crisis occurs, governments may run out of taxing capacity and default
◦ Affects bond prices, yield to maturity
3–15
The Risk of Default
Sovereign Bonds and Default Risk
◦Own Currency Debt
◦ Less risky than foreign currency debt
◦ Governments can print money to repay bonds
3–16
The Risk of Default
Sovereign Bonds and Default Risk
◦Eurozone Debt
◦ Can’t print money to service domestic debts
◦ Money supply controlled by European Central
Bank
3–17
18
3–18