Final answer:
The current value of a 10-year $100,000 bond with a 10% coupon rate, when the market yield is 12%, is calculated by discounting its semi-annual interest payments and the principal repayment at the bond's maturity by the market's semi-annual interest rate.
Step-by-step explanation:
To compute the value today of a 10-year $100,000 10% bond that pays interest every six months when the market yield rate is 12%, we follow these steps:
- Calculate the bond's semi-annual interest payment: Interest Payment = $100,000 x 10% / 2 = $5,000.
- Determine the number of semi-annual periods: N = 10 years x 2 = 20 periods.
- Convert the market yield rate to a semi-annual rate: semi-annual market rate = 12% / 2 = 6%.
- Calculate the present value of the interest payments using the present value of an annuity formula: PV of interest payments = $5,000 x [(1 - (1 + 0.06)^-20) / 0.06].
- Calculate the present value of the principal repayment at maturity: PV of principal = $100,000 / (1 + 0.06)^20.
- Sum the present values of interest payments and principal repayment to find the current price of the bond.
The calculations show that the bond's price will be less than its face value when the market interest rate is higher than the bond's coupon rate. The present value of the bond's future cash flows is discounted at the market interest rate, which reflects the opportunity cost of investing in the bond compared to other investments.