## Transcribed Text

Exercise: Problem 2 from ordinary exam January, 8 2018 (weight: 30%)
Problem 2 (30%)
Table 2.1 contains information about five bonds, that are traded on a given
financial market. All five bonds have exactly one year until next term (term =
payment dates).
Table 2.1: Information on bonds
Bond
Type of bond
Ma-
Annual
Number
Annual
Price
turity
coupon
of
pay-
effec-
(DKK)
rate
ments
tive rate
(terms)
per year
L
Linear
3 years
2%
1
?
?
Cp.
Coupon
3 years
2,5%
1
?
?
A
Annuity
3 years
1,5%
1
?
?
Zcb
Zero-coupon
3 years
1
?
?
P
Perpetuity
8
1,5%
1
?
92
Problem 2.1
Calculate the cash flow (per DKK 100 in face value1) for each of the five bonds.
Below, in table 2.2, the annual zero-coupon yields yi(t), t=1, 2, 3. 4, 5 is stated.
Table 2.2: Zero-coupon yields
t (year)
1
2
3
4
5
yi(t)
0,00290
0,00790
0,01150
0,01380
0,01550
Problem 2.2
Illustrate the yield curve on a graph with a time horizon of 5 years using the discount
factor and the zero-coupon yields as the depend variable respectively.
Problem 2.3
Calculate the discount factorsÂ˛ d(t), t = 1, 2. 3, 4, 5 years on the given financial market.
Problem 2.4
Determine the price of bond L, Cp., A and Zcb per DKK 100 in face value.
Face value is also called the principal of the bond or the nominal value of the bond
2 We define d(t) as the price of a zero-coupon default-free bond with face value of DKK and a maturity oft
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Problem 2.5
Determine the annual effective rate (AER) in percentage for each of the five bonds.
The Jensen Family has a nice house, but they miss an isolated garage for their car,
bikes and garden tools. Therefore, the family has decided to get a loan to finance the
establishment of a garage. The establishment of the garage will cost DKK 275.000. The
family's bank adviser says they can get a bond loan to finance the garage. The maturity
of the loan will be 5 years with annual terms. The annual coupon rate of the loan is
1,5% and the loan is an annuity.
Problem 2.6
Determine the face value of the loan, if the net proceeds must be DKK 275.000. Calcu-
late the price of the bond per DKK 100 in face value.
On another financial market, an annuity bond with an annual coupon rate of 2,5% is
traded. The bond has quarterly terms and the last term is the 31/3-2025. Thus, the
bond has terms in the end of each quarter.
Note: It can be assumed the length of a term is 90 days
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