Let's solve the problem step by step as requested. --- ### **Step 1: Calculate the Value of the Bond (Before Conversion)** **Given Data:** - Number of bonds: 1,000 - Par value per bond: $1,000 - Annual coupon payment: $80 - Years to maturity: 20 - Market interest rate: 8% **Bond Value Calculation:** The bond pays annual coupons, and the market rate equals the coupon rate (8%). So, the bond will sell at **par value**. \[ \text{Bond Value} = \text{Coupon PV} + \text{Par Value PV} \] But when \( \text{Coupon Rate} = \text{Market Rate} \), \[ \text{Bond Value} = \text{Par Value} = \$1,000 \] **Explanation:** Since the coupon rate equals the market rate, the bond's value is its par value, $1,000. --- ### **Step 2: Calculate the Value if Converted (Conversion Value)** **Given Data:** - Each bond can be converted into 50 shares. - Current stock price: $20 **Conversion Value Calculation:** \[ \text{Conversion Value per Bond} = \text{Number of Shares} \times \text{Stock Price} \] \[ = 50 \times \$20 = \$1,000 \] **Explanation:** If the bond is converted, it provides 50 shares valued at $20 each, totaling $1,000. --- ## **Final Answer** - **Value as a bond:** $1,000 - **Value if converted:** $1,000 **Conclusion:** In this scenario, both the straight bond value and the conversion value are the same: $1,000.

# Step-by-Step Solution Let's solve the problem step by step. --- ## **Step 1: Calculate the Value of the Bond (Before Conversion)** ### **Given Data:** - **Number of bonds:** 1,000 - **Par value per bond:** $1,000 - **Annual coupon payment:** $80 - **Years to maturity:** 20 - **Market interest rate:** 8% ### **Bond Value Calculation:** The bond pays annual coupons, and since the market rate equals the coupon rate (8%), the bond will sell at **par value**. \[ \text{Bond Value} = \text{Coupon PV} + \text{Par Value PV} \] In this case, when the coupon rate equals the market rate: \[ \text{Bond Value} = \text{Par Value} = \$1,000 \] ### **Explanation:** Since the coupon rate (8%) equals the market rate (8%), the bond's value is its par value, which is $1,000. --- ## **Step 2: Calculate the Value if Converted (Conversion Value)** ### **Given Data:** - **Number of shares per bond upon conversion:** 50 - **Current stock price:** $20 ### **Conversion Value Calculation:** To find the conversion value: \[ \text{Conversion Value per Bond} = \text{Number of Shares} \times \text{Stock Price} \] Calculating this gives: \[ = 50 \times \$20 = \$1,000 \] ### **Explanation:** If the bond is converted, it gives 50 shares valued at $20 each, resulting in a total conversion value of $1,000. --- ## **Final Answer** - **Value as a bond:** $1,000 - **Value if converted:** $1,000 ### **Conclusion:** In this scenario, both the straight bond value and the conversion value are the same: **$1,000**.