travelling at directions travelling at directions travelling at directions SECTI
ID: 2787971 • Letter: T
Question
travelling at directions travelling at directions travelling at directions SECTION B (Total 40 marks) Answer 2 of the following 3 questions. Question4 A current spot rate curve is given in the following table: Years 2 Spot Rate (%) 7.0 7.6 8.3 9.0 4 Table 04 Consider an 8 % coupon bond with 4 years to maturity. Assume that the face values of the bonds is $1,000. (a) Identify the current price of the bond (4 marks) (b) Identify the next year's 2-year spot rate s,' (4 marks) (c) Identify the discount factors d2,3 and das. (10 marks) d) Examine the price of the bond two year from now. (2 marks uestion 5Explanation / Answer
a) Current Bond Price can be calculated using PV function on a calculator or excel
Insert N = 4, PMT = 8% x 1000 = 80, FV = 1000, I/Y = 9% => Compute PV = $967.60
b) 2-year spot rate one-year from now can be calculated using expectation theory
(1 + s3)^3 = (1 + s1)^1 x (1 + s1,2)^2
=> (1 + 8.3%)^3 = (1 + 7%) x (1 + s1,2)^2
=> s1,2 = 8.96% is the next year's 2-year spot rate
3) We need to calculate the rates s2,3 and s2,4 in order to calculate the discount factors
(1 + s3)^3 = (1 + s2)^2 x (1 + s2,3)
=> (1 + 8.3%)^3 = (1 + 7.6%)^2 x (1 + s2,3)
=> s2,3 = 9.71%
=> d2,3 = 1 / (1 + 9.71%) = 0.9115
Similarly (1 + s4)^4 = (1 + s2)^2 x (1 + s2,4)^2
=> s2,4 = 10.42%
=> d2,4 = 1 / (1 + 10.42%)^2 = 0.9202
d) Two years from now, bond price
= 80 x 0.9115 + (1000 + 80) x 0.9202
= $958.73
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