Answer to Question #108333 in Financial Math for Suver

Question

A loan stock is issued on 1st January 2014 with coupons at 9% per annum payable quarterly in arrears. The loan stock is repayable on either the 10th or 12th anniversary of issue at 115%, at the option of the borrower.
(a) Calculate the issue price per £100 nominal which would provide the purchaser subject to 25% tax on income with a net effective yield of at least 6% per annum. (5 marks)
(b) Using the assumptions as in (a) above, calculate the ex-dividend price 2 months after the issue date. (3 marks)
(Total 8 marks)

Answer 1

a)$PV=\frac{K}{(1+r)^n}+\frac{H}{(1+r)^n}=\frac{9}{(1+0.06)^{12}}+\frac{109}{(1+0.06)^{12}}=4.47+54.17=58.64$

$58.64\times0.25+58.64=73.3$

b)$PV=\frac{K}{(1+r)^n}+\frac{H}{(1+r)^n}=\frac{9}{(1+0.005)^{0.1667}}+\frac{109}{(1+0.005)^{0.1667}}=8.99+108.91=117.90$

$r=\frac{r}{12}=0.005$

$n=\frac{n}{12}=\frac{2}{12}=0.1667$

$117.90\times0.25+117.90=147.38$