1. (a) The 1-year forward rates for transactions beginning at times t=0,1,2 are f_(t) where: f_(0)=0.06,f_(1)=0.065,f_(2)=0.07 Calculate the par yield for a 3-year bond [3 marks] (b) A fixed interest stock with a coupon of 8% per annum payable half yearly in arrears can be redeemed at the option of the lender (ie the investor) at any time between 10 and 15 years from the date of issue. What price should an investor subject to tax at 25% on income, who wishes to obtain a net yield of at least 7% per annum, pay for KSh.100 nominal of this stock? [3 marks]

(a) To calculate the par yield for a 3-year bond, we need to find the average of the 1-year forward rates for transactions beginning at times $t=0,1,2$. The par yield is the yield that makes the present value of the bond's cash flows equal to its price.<br /><br />The formula for the par yield is:<br /><br />Par yield = (f0 + f1 + f2) / 3<br /><br />Substituting the given values:<br /><br />Par yield = (0.06 + 0.065 + 0.07) / 3<br />Par yield = 0.068333<br /><br />Therefore, the par yield for a 3-year bond is approximately 0.0683 or 6.83%.<br /><br />(b) To determine the price an investor should pay for the stock, we need to calculate the present value of the coupon payments and the redemption value, discounted at the required rate of return.<br /><br />Given information:<br />- Coupon rate: 8% per annum, payable half-yearly in arrears<br />- Redemption period: 10 to 15 years<br />- Tax rate: 25%<br />- Net yield required: 7% per annum<br />- Nominal value: KSh. 100<br /><br />First, let's calculate the required rate of return after tax:<br /><br />Required rate of return = Net yield / (1 - Tax rate)<br />Required rate of return = 0.07 / (1 - 0.25)<br />Required rate of return = 0.0933 or 9.33%<br /><br />Next, we need to find the present value of the coupon payments and the redemption value. Since the coupon payments are payable half-yearly, we will discount them semi-annually.<br /><br />Let's assume the redemption period is 15 years. The number of semi-annual periods is 30 (15 years * 2).<br /><br />Now, we can calculate the present value of the coupon payments and the redemption value using the required rate of return.<br /><br />Present value of coupon payments = Coupon payment * [1 - (1 + Required rate of return / 2)^(-2 * Number of years)]<br />Present value of coupon payments = 0.08 * 100 * [1 - (1 + 0.0933 / 2)^(-2 * 15)]<br />Present value of coupon payments = 0.08 * 100 * [1 - (1.04665)^(-30)]<br />Present value of coupon payments = 0.08 * 100 * [1 - 0.297]<br />Present value of coupon payments = 0.08 * 100 * 0.703<br />Present value of coupon payments = 56.24<br /><br />Present value of redemption value = Redemption value / (1 + Required rate of return / 2)^(-2 * Number of years)<br />Present value of redemption value = 100 / (1 + 0.0933 / 2)^(-2 * 15)<br />Present value of redemption value = 100 / (1.04665)^(-30)<br />Present value of redemption value = 100 / 0.297<br />Present value of redemption value = 336.67<br /><br />Now, we can calculate the price the investor should pay for the stock:<br /><br />Price = Present value of coupon payments + Present value of redemption value<br />Price = 56.24 + 336.67<br />Price = 392.91<br /><br />Therefore, an investor subject to a tax rate of 25% on income, who wishes to obtain a net yield of at least 7% per annum, should pay approximately KSh. 392.91 for KSh. 100 nominal of this stock.