1. A company issues a loan stock which pays coupons at a rate of 6% per annum half-yearly in arrears. The stock is to be redeemed at 103% after 25 years.

(a)    i.  Calculate the price per f100 nominal at issue which would provide a gross redemption yield of 3% per annum convertible half yearly.

ii.  Calculate the price per f100 nominal three months after issue which would provide a gross redemption yield of 3% per annum convertible half-yearly.

[3] An investor, who is liable to income tax at 30% and capital gains tax at 40%, bought the stock at issue at a price which gave him a net redemption yield of 10% per annum effective.

(b)  Calculate the price the investor paid.                                                                                        [4] [Total 7]

2. A bank has just granted a loan of f10,000 to a business to be repaid in ten equal instalments, annually in arrears. The rate of interest is 4% per annum effective.

(a)    i.  Calculate the amount of the annual repayment.

ii.  Calculate the duration (discounted mean term) of the repayments.

[5] The bank wishes to immunise itself from changes in interest rates in relation to this particular asset. For this purpose, the bank has issued two zero-coupon bonds. The first bond is of nominal amount S5,000 and has a term to redemption of two years.

(b) Determine the nominal amount of the second zero-coupon bond and its term to redemption such that the present value and durations of the assets and liabilities are equal.                    [6]

Immediately upon the loan being granted, the bank agrees to a request to change the terms of the loan. The loan is now to be repaid monthly in arrears over 25 years and the rate of interest remains unchanged.

(c)    i.  Calculate the revised monthly instalment.

ii. Explain, without further calculation, the main risk to the bank of a change in interest rates.

iii. Determine the interest and capital portions of the 121st repayment under this new arrange-

ment.

3.   (a) Describe what is meant by the term “ex-dividend”.

[8] [Total 19]

[1]

An individual purchased 10,000 shares on 1 December 2017. Dividends are payable on 1 January and 1 July each year, and are assumed to be payable in perpetuity. The next dividend, due on 1 January 2018, is S0.07 per share.

The two dividend payments in any calendar year are expected to be the same, but the div- idend payment is expected to increase at the end of each year at a rate of 2% per annum compound.

Assume that the share is ex-dividend on  1 December 2017 and use an effective rate of in- terest of 7% per annum.

(b)  Calculate the present value of the investment at the date of purchase.                                    [5] [Total 6]

4.  On 1 April 2018 a government issued a 10-year bond redeemable at f105 per f100 nominal and paying coupons at the rate of 3% per annum half-yearly in arrear. The price of the bond was f102 per f100 nominal.

An investor subject to income tax of 25% and capital gains tax of 35% purchased f10,000 nom- inal of the bond at issue.

The investor assumes that inflation will be constant over the term of the bond at a rate of 2% per annum.

(a)  Calculate the net effective real redemption yield which the investor expects to earn on the investment.                                                                                                                                  [6]

(b) Explain how your answer to part (a) would change if inflation were less than 2% per annum

throughout the term.                                                                                                                  [2] [Total 8]

5. Two bonds paying annual coupons of 6% in arrear and redeemable at par have terms to maturity of exactly one year and two years.

The gross redemption yield from the 1-year bond is 5.2% per annum effective. The gross redemption yield from the 2-year bond is 6.1% per annum effective. The 3-year par yield is 6.6% per annum.

Calculate the following as a percentage to three decimal places:

(a) the annual effective spot yields for each of the three years

(b) the annual effective one-year forward rates for each of the three years

[8] [4]

[Total 12]

6. An n-year decreasing annuity is payable annually in arrear where the payment at the end of the first year is n, the payment at the end of the second year is (n – 1), and so on until the final payment at the end of year n is 1.

(a)  Show that the present value of this annuity is 

[3]

A loan is to be repaid over 25 years by means of annual instalments payable in arrear.

The amount of the first instalment is f8,000 and each subsequent instalment reduces by f200.