Tutorial 8

Question 1

Answer the following questions.
1) On 1 January 2010 an investor purchases £1,000 nominal of a stock that pays coupons on 30
June and 31 December at a rate of 8% pa and is redeemable at par on 31 December 2020. The
investor is liable for income tax at a rate of 20% on each 1 October (commencing in 2011) in
respect of coupons received during the previous calendar year. If the investors net redemption yield is 6%, calculate the price paid for the holding. (hint consider tax and coupon
separately).

ii) Calculate the yield if price was £1,200

Answer 1

P = 80a11¬(2) + 1000v^11 – 16v^(9/12)a11¬
i(2) =2(1.06^(1/2)-1) =0.059126

P = 80(1-1.06^-11)/0.059126 + 1000(1.06^-11) – 16(1.06^-0.75)(1-1.06^-11)/0.06

£1,046.27
Calculate the yield if price was £1,200

Try i=5% (i(2) = 0.04939)

P = 80(1-1.05^-11)/0.04939 + 1000(1.05^-11) – 16(1.05^-0.75)(1-1.05^-11)/0.05 = £1,129.27

Try i=4% (i(2) = 0.03961)

P = 80(1-1.04^-11)/0.03961 + 1000(1.04^-11) – 16(1.04^-0.75)(1-1.04^-11)/0.04 = £1,221.21

0.04 + (1200-1221.21)/(1129.27-1221.21)x(0.05-0.04) = 0.0423 or 4.23%

Question 2

2) An investor is considering purchasing 100 ordinary shares in a company that pay dividends
annually. The next dividend is due in 9 months and is expected to be 10p per share. The 2nd
dividend is expected to be 6% higher than the 1st and then dividends are expected to increase at 4% pa compound. i =7%
Calculate the PV of the dividend stream

Will appear on final exam!

Answer 2

10v^0.75+ 10x1.06v^1.75 + 10x1.06x1.04v^2.75 + 10x1.06x1.04^2v^3.75 + …….

10[v^0.75+ 1.06v^1.75 + 1.06x1.04v^2.75 + 1.06x1.04^2v^3.75 +……]

10[v^0.75+ 1.06v^1.75 + 1.06v^1.75(1.04v + 1.04^2v^2 +……]

10[v^0.75+ 1.06v^1.75 + 1.06v^1.75a∞¬ @i’] i’ = 1.07/1.04- 1 = 0.028846

10[v^0.75+ 1.06v^1.75 + 1.06v^1.75(1/0.028846)]

£345.36

Question 3

3) An investor purchases £10,000 nominal of a five-year fixed-interest bond redeemable at par.
Coupons of 8% pa are payable six-monthly in arrears. If the investor is subject to income tax of 25% and capital gains tax at 20%, calculate the price they should pay to obtain a net yield
of 10% pa effective.

Answer 3

i(2) =2(1.10^(1/2)-1) =0.097618
i(2) @ 0.097618 > (1-t,1)D/R
i(2) @ 0.097618 > (1-0.25)800/10000 = i(2) @ 0.097618 > 0.06 so have CG
P = (1-0.25)800a5¬(2) + 10000v^5 – 0.2(10000-P)v^5@10%
P = 600a5¬(2)+ 8000v^5 + 0.2Pv^5 @ 10%
P(1– 0.2v^5) = 600a5¬(2) + 8000v^5
P = [600x3.8833 + 8000(1.1)^-5]/ (1– 0.2(1.1)^-5)
P = £8332.06