Question 3 13 MarksS The government in Zealandia issued an index linked 3 year b

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Question 3 13 MarksS The government in Zealandia issued an index linked 3 year bond on 1 January 2016 with a nominal coupon rate of 3% p.a., payable annually. Coupons are payable on 31 December each year, and redemption is at par in nominal terms on 31 December 2018 Par value of each bond is $100 in nominal terms; and the issue price was $95 All payments made on the bond are indexed to increase with inflation lagged by a year. Recent rates of inflation, either actual or forecast, are shown in the following table year inflation rate | 2% | 3% | 4% | 3% Thus the coupon payable on 31 December 2016 was $3 x 1.02, that on 31 December 2017 is to be $3 x 1.02 x 1.03, etc. You may assume that the forecast rates of inflation in the table are accurate (i) Write down the equation of value for the real yield (allowing for inflation) for an individual purchasing one of these bonds when they were issued You may assume that the individual intends to keep the bond until matu- (a) ri (ii) Linearly interpolating in this equation between 3% and 4% (effective an- nual rates), estimate the real yield obtained by this individual (9 marks) (b) You intend to purchase one of these bonds on 1 July 2017 for a price of P. Without carrying out any further calculations, write down an equation of value for the real yield that you will obtain on this bond, given that you intend to keep the bond until maturity You may assume that the inflation rate between 1 July and 31 December 2017 is 290 per 6 months (4 marks) (13 marks)

Explanation / Answer

A(i) 31-12-2016 3*1.02= 3.06 31-12-2017 3*1.02*1.03= 3.1518 31-12-2018 3*1.02*1.03*1.04= 3.277872 31-12-2018 3*1.02*1.03*1.04*1.03= 112.5403 A(ii) Year Cash flow Pv @ 3% PV of cash flow Year Cash flow Pv @ 4% PV of cash flow 31-12-2016 3.06 0.970874 2.970874 31-12-2016 3.06 0.961538 2.942308 31-12-2017 3.1518 0.942596 2.970874 31-12-2017 3.1518 0.924556 2.914016 31-12-2018 3.277872 0.915142 2.999717 31-12-2018 3.277872 0.888996 2.914016 31-12-2018 112.540272 0.915142 102.9903 31-12-2018 112.5403 0.888996 100.0479 111.9318 108.8182 Linear interpolating = 102.941 Real yield= 2.941048 % Answer b 31-12-2017 1.607418 31-12-2018 3.277872 31-12-2018 112.5403

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