(c) A ten-year bond with half yearly coupons of 8% pa has just been issued with a redemption yield of 12% pa effective. It is redeemable at par. What price would an investor paying 20% tax on income pay for the bond? Tax payments are due three months after each coupon is received. [4 marks]

To solve this problem, we need to calculate the price of the bond for an investor who pays a 20% tax on income. The bond has a redemption yield of 12% per annum effective, which means that the bond will be redeemed at par value. The bond has a coupon rate of 8% per annum, which means that the bond will pay semi-annual coupons of per semi-annual period.First, let's calculate the present value of the coupon payments. Since the coupons are paid semi-annually, we need to discount them to the present value using the redemption yield of 12% per annum effective. The redemption yield is equivalent to a semi-annual yield of .The present value of the coupon payments can be calculated using the following formula: where is the coupon payment, is the semi-annual yield, and is the number of semi-annual periods. Next, let's calculate the present value of the redemption value. Since the bond is redeemable at par, the redemption value is equal to the face value of the bond, which is PV_{\text{redemption}} = F / (1 + r)^n F PV_{\text{redemption}} = 100 / (1 + 0.06)^{10} PV_{\text{redemption}} = 100 / (1.06)^{10} PV_{\text{redemption}} = 100 / 1.7908 PV_{\text{redemption}} = 55.88 P_{\text{investor}} = PV_{\text{coupons}} \times (1 - \text{tax rate}) + PV_{\text{redemption}} \times (1 - \text{tax rate}) P_{\text{investor}} = 0.28907 \times (1 - 0.20) + 55.88 \times (1 - 0.20) P_{\text{investor}} = 0.28907 \times 0.80 + 55.88 \times 0.80 P_{\text{investor}} = 0.23128 + 44.70 P_{\text{investor}} = 44.93 44.93 for the bond.