Question
a) An investor is considering purchasing a fixed interest bond at issue which pays half-yearly coupons at a rate of 6% per annum. The bond will be redeemed at ￡105 per f100 nominal in 10 years' time. The investor is subject to income tax at 20% and capital gains tax at 25% Calculate the price per ￡100 nominal if the investor is to obtain a net real yield of 5% per annum. [6 Marks]
Solution
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Resposta
To calculate the price per £100 nominal, we need to find the present value of the bond's cash flows, which include the coupon payments and the redemption value, discounted at the net real yield.Given information:- Coupon rate: 6% per annum, paid half-yearly- Redemption value: £105 per £100 nominal- Income tax: 20%- Capital gains tax: 25%- Net real yield: 5% per annumStep 1: Calculate the after-tax coupon payment.After-tax coupon payment = Coupon payment * (1 - Income tax rate)After-tax coupon payment = (£6 / 2) * (1 - 0.20) = £2.40 per half-yearStep 2: Calculate the present value of the coupon payments.Since the coupons are paid half-yearly, we need to discount the coupon payments semi-annually.Discount rate = 1 + Net real yield / 2 = 1 + 0.05 / 2 = 1.025Present value of coupon payments = £2.40 * (1 - (1 + 0.025)^(-20)) / 0.025 = £31.11Step 3: Calculate the present value of the redemption value.Present value of redemption value = £105 / (1 + 0.025)^20 = £46.88Step 4: Calculate the price per £100 nominal.Price per £100 nominal = Present value of coupon payments + Present value of redemption valuePrice per £100 nominal = £31.11 + £46.88 = £77.99Therefore, the price per £100 nominal if the investor is to obtain a net real yield of 5% per annum is approximately £77.99.