Question

Hamilton Steel Company has a convertible bond outstanding, trading in the marketplace at $920. The par value is $1,000, the coupon rate is 8 percent, and the bond matures in 20 years. The conversion price is $45 and the company's common stock is selling for $40 per share. Interest is paid semiannually. Use Appendix B and Appendix D. If the interest rates on similar bonds, which are not convertible, go up from 10 to 12 percent, what will the new pure bond value be for Hamilton Steel Company bonds? (Use semiannual analysis.) (Do not round intermediate calculations. Round "PV Factor" to 3 decimal places. Round the final answer to 2 decimal places.) Bond value $

Answer 1

The new value of the Hamilton Steel Company bond when the market interest rate increases to 12% can only be calculated using the present value formulas for the semiannual interest payments and the face value, discounted at the new yield, with the present value factors given in Appendix B and Appendix D.

Step-by-step explanation:

When interest rates increase for similar non-convertible bonds, the value of existing bonds with lower interest rates will decline. The Hamilton Steel Company bond has a coupon rate of 8%, which would generate $80 annually ($1,000 x 8%) or $40 semiannually. Given that interest rates have increased to 12%, investors will require this bond to also yield 12% to compensate for the increased market rates. Therefore, the bond's value has to be discounted at the new market yield of 12%.

To calculate the new present value of the bond's cash flows, we can use the present value formula for an annuity to discount the semiannual interest payments, and the present value formula for a lump sum to discount the face value repayment:

PV of interest payments: (PVIFA12%/2, 40 periods) * $40
PV of face value: (PVIF12%/2, 40 periods) * $1,000

As these calculations are specific to the bond and market conditions, they cannot be accurately completed without information provided in Appendix B and Appendix D, which typically contain present value factors for various rates and periods. Assuming we've obtained the PV factors, the final bond price will be the sum of the present values of the interest payments and the face value.