Question

In January 2013, a country’s government issued an index-linked bond with a 2-year term. Coupons were payable half-yearly in arrears, at a rate of 3% per annum. Interest and capital payments were indexed-linked by reference to the value of an inflation index with a time lag of 6 months.
An investor purchased £100,000 nominal at issue and held it to redemption and was not subject to any tax. The issue price was 96%.
The inflation index was as follows:
Date - Inflation Index
July 2012 - 111.5
January 2013 - 113.1
July 2013 - 116.7
January 2014 - 120.1
July 2014 - 124.2
(a) Calculate the investor’s cash flows from this investment, showing the month in which, each cash flow occurs. (4 marks)
(b) Calculate the investor’s effective yield per annum, to closest 1%. (3 marks)
(Total 7 marks)

Answer 1

a) Сalculate coupon income for the following months:

we clean the nominal at the inflation rate:

$100 000\times1.167=116 700$

$K=N\times\frac{q}{100}\times\frac{T}{B}$

N - nominal

q - current coupon rate (in percent per annum)

T - the number of days from the start of the coupon period to the current date

B - calculation base (730 days).

$Kj2013=N\times\frac{q}{100}\times\frac{T}{B}=116 700\times\frac{3}{100}\times\frac{181}{730}=868.05$

January 2014 - 120.1 

$100 000\times1.201=120100$

$Kj2014=N\times\frac{q}{100}\times\frac{T}{B}=120100\times\frac{3}{100}\times\frac{365}{730}=1801.5$

July 2014 - 124.2 

$100 000\times1.242=124200$

$Kj2014=N\times\frac{q}{100}\times\frac{T}{B}=124200\times\frac{3}{100}\times\frac{546}{730}=2786.84$

Cash flow:

$P=N\times0.96=100 000*0.96=96 000$ , The issue price

Cash flow

July 2013= 116 700+868.05-96 000=21 568.05

January 2014 = 120 100+1 801.05-96 000=25 901.05

July 2014 = 124 200+2786.84-96 000=30 986.84

b)The investor’s effective yield:

$r=\frac{\frac{(N-P)+C}{n}}{\frac{N+P}{n}}=\frac{\frac{(124 200-96 000)+5456.39}{3}}{\frac{124 200+96000}{3}}=0.1528=15.28$