Exercise: Problem 2 from ordinary exam January, 8 2018 (weight: 30%...

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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 factors² 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 Page of 2 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 Page of 2

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