Tutorial assignment: week 5 2022
Answer guide
1. Consider a bond market where the demand for a particular bond is given by the equation
Bd =2360−0.8 P
where Bd is the number of bonds demanded and P is the price of the bond.
Suppose the supply of this bond is fixed at 1400.
(a) Calculate the price of the bond
In equilibrium,
d s
B =B
Hence,
2360−0.8 P=1400
P=1200
(b) Suppose the bond is a consol with an annual coupon of 45. What is the yield on this
security?
The formula for the price of a consol is
C
P=
i
So,
45
i=
1200
Thus the yield is 3.75%
2. Suppose there is a one-year discount bond trading in the Australian market with a face
value of $1000 and supply and demand curves given by the following equations:
d
B =1240−0.6 P
Bs=1.4 P−720
where P is the price of the bond, Bd and Bs represent the number of bonds supplied or demanded.
, Calculate the following (half mark each):
(a) The equilibrium price of the bond
In equilibrium,
d s
B =B
Hence,
1240−0.6 P=1.4 P−720
2 P=1960
P=980
(b) The yield to maturity
Since this is a one-year discount bond,
CF
P=
( 1+i )
CF 1000
1+i= =
P 980
Hence,
i=2.04 %
(c) The number of bonds supplied and demanded
Bd =1240−0.6 ( 980 )=652
s
B =1.4 ( 980 )−720=652
Note that supply and demand are equalised at the equilibrium price.
(d) The yield to maturity if this had been a two-year bond rather than one-year.
If this were a two-year security the appropriate formula would have been:
CF
P=
( 1+i )2
2 CF 1000
(1+i) = =
P 980
1+i=
√ 1000
980
Answer guide
1. Consider a bond market where the demand for a particular bond is given by the equation
Bd =2360−0.8 P
where Bd is the number of bonds demanded and P is the price of the bond.
Suppose the supply of this bond is fixed at 1400.
(a) Calculate the price of the bond
In equilibrium,
d s
B =B
Hence,
2360−0.8 P=1400
P=1200
(b) Suppose the bond is a consol with an annual coupon of 45. What is the yield on this
security?
The formula for the price of a consol is
C
P=
i
So,
45
i=
1200
Thus the yield is 3.75%
2. Suppose there is a one-year discount bond trading in the Australian market with a face
value of $1000 and supply and demand curves given by the following equations:
d
B =1240−0.6 P
Bs=1.4 P−720
where P is the price of the bond, Bd and Bs represent the number of bonds supplied or demanded.
, Calculate the following (half mark each):
(a) The equilibrium price of the bond
In equilibrium,
d s
B =B
Hence,
1240−0.6 P=1.4 P−720
2 P=1960
P=980
(b) The yield to maturity
Since this is a one-year discount bond,
CF
P=
( 1+i )
CF 1000
1+i= =
P 980
Hence,
i=2.04 %
(c) The number of bonds supplied and demanded
Bd =1240−0.6 ( 980 )=652
s
B =1.4 ( 980 )−720=652
Note that supply and demand are equalised at the equilibrium price.
(d) The yield to maturity if this had been a two-year bond rather than one-year.
If this were a two-year security the appropriate formula would have been:
CF
P=
( 1+i )2
2 CF 1000
(1+i) = =
P 980
1+i=
√ 1000
980
