Arjay purchases a bond newly issued by Amalgamated Corporation, for 1,000. The bond pays 60 to its holder at the end of the first few years and pays 1,060 upon its maturity at the end of the 5 years. a. What are the principal amount, the term , the coupon rate, and the coupon payment for Arjay's bond? Instructions: Enter your responses as whole numbers. Principal amount: square Term: square years Coupon rate: square % Coupon payment: square b. After receiving the second coupon payment (at the end of the second year). Arjay decides to sell his bond in the bond market. What price can he expect for his bond if the one-year interest rate at that time is 4 percent?9 percent? 12 percent? Instructions: Enter your responses as whole numbers. Expected price for the bond at: 4 percent: 9 percent: square 12 percent: c. Suppose that after two years, the price of Arjay's bond falls below 1,000 even though the market interest rate equals the coupon rate. One possible reason is that: there is bad news about Amalgamated Corporation leading financial investors to fear that the firm might go bankrupt and not pay off its debt in one year. there is a very good chance that a final payment of more than 1,060 will be made, so financial investors will be willing to pay 1,000 for the bond since they know they can earn 6 percent. bad news arrives about Amalgamated Corporation, leading financial investors to strongly believe that the firm would promptly pay off its debt in one year. there is good news about Amalgamated Corporation leading financial investors to demand more of the company's bonds.

a. Let's identify the components of Arjay's bond:<br /><br />- **Principal amount**: This is the initial amount paid for the bond, which is \$1,000.<br /> <br />- **Term**: The bond matures in 5 years.<br /><br />- **Coupon rate**: The coupon rate is calculated as the annual coupon payment divided by the principal amount. Here, the annual coupon payment is \$60, and the principal amount is \$1,000. Therefore, the coupon rate is \((\$60/\$1,000) \times 100\% = 6\%\).<br /><br />- **Coupon payment**: The bond pays \$60 annually.<br /><br />So, the answers are:<br />- Principal amount: \$1,000<br />- Term: 5 years<br />- Coupon rate: 6%<br />- Coupon payment: \$60<br /><br />b. To find the expected price of the bond after receiving the second coupon payment, we need to calculate the present value of the remaining cash flows (three more \$60 payments and the \$1,060 maturity payment) using different interest rates.<br /><br />1. **4 percent interest rate**:<br /> - Present value of remaining coupon payments: <br /> \[<br /> PV = \frac{\$60}{(1+0.04)^1} + \frac{\$60}{(1+0.04)^2} + \frac{\$60}{(1+0.04)^3}<br /> \]<br /> - Present value of maturity payment:<br /> \[<br /> PV = \frac{\$1,060}{(1+0.04)^3}<br /> \]<br /> - Total present value = Sum of all present values above.<br /><br />2. **9 percent interest rate**:<br /> - Present value of remaining coupon payments:<br /> \[<br /> PV = \frac{\$60}{(1+0.09)^1} + \frac{\$60}{(1+0.09)^2} + \frac{\$60}{(1+0.09)^3}<br /> \]<br /> - Present value of maturity payment:<br /> \[<br /> PV = \frac{\$1,060}{(1+0.09)^3}<br /> \]<br /> - Total present value = Sum of all present values above.<br /><br />3. **12 percent interest rate**:<br /> - Present value of remaining coupon payments:<br /> \[<br /> PV = \frac{\$60}{(1+0.12)^1} + \frac{\$60}{(1+0.12)^2} + \frac{\$60}{(1+0.12)^3}<br /> \]<br /> - Present value of maturity payment:<br /> \[<br /> PV = \frac{\$1,060}{(1+0.12)^3}<br /> \]<br /> - Total present value = Sum of all present values above.<br /><br />Calculating these values:<br /><br />- **4 percent**: <br /> \[<br /> PV = \frac{60}{1.04} + \frac{60}{1.0816} + \frac{60}{1.124864} + \frac{1060}{1.124864} \approx 57.69 + 55.77 + 53.63 + 942.48 = 1,109.57<br /> \]<br /><br />- **9 percent**: <br /> \[<br /> PV = \frac{60}{1.09} + \frac{60}{1.1881} + \frac{60}{1.295029} + \frac{1060}{1.295029} \approx 55.05 + 50.51 + 46.32 + 818.61 = 970.49<br /> \]<br /><br />- **12 percent**: <br /> \[<br /> PV = \frac{60}{1.12} + \frac{60}{1.2544} + \frac{60}{1.404928} + \frac{1060}{1.404928} \approx 53.57 + 47.85 + 42.73 + 754.15 = 898.30<br /> \]<br /><br />Expected prices:<br />- 4 percent: \$1,110<br />- 9 percent: \$970<br />- 12 percent: \$898<br /><br />c. If the price of Arjay's bond falls below \$1,000 even though the market interest rate equals the coupon rate, one possible reason could be:<br /><br />- There is bad news about Amalgamated Corporation, leading financial investors to fear that the firm might go bankrupt and not pay off its debt in one year.<br /><br />This scenario would cause the bond's price to drop due to increased perceived risk.