Final answer:
The present value of a bond is calculated by discounting the future cash flows (interest and principal) at the given discount rate. For a two-year bond at 8% discount rate, the PV formula is applied separately on interest payments and the sum of interest plus principal for the second year. If rates rise to 11%, these calculations are adjusted according to the new rate.
Step-by-step explanation:
Calculating Present Value of a Bond
To determine the present value of a bond, you must discount the future cash flows (interest and principal payments) back to their present value by using the relevant discount rate. For the simple two-year bond mentioned, it yields $240 in interest each year, and the principal of $3,000 is paid back at the end of the second year. Using a discount rate of 8%, the present value of the bond can be calculated using the present value formula for each cash flow.
Present Value Calculations
When the discount rate is 8%, the present value (PV) of the first year's interest payment is:
PV = $240 / (1 + 0.08)
For the second year’s interest and principal payment, you must account for two years of discounting:
PV = ($240 + $3,000) / (1 + 0.08)^2
If interest rates rise, and the new discount rate is 11%, the calculations would change accordingly:
First year's interest:
PV = $240 / (1 + 0.11)
Second year’s interest and principal:
PV = ($240 + $3,000) / (1 + 0.11)^2
Book Value and Annual Cost of Debt
To calculate the annual cost of the bond debt, you combine the interest payments and the payments to the sinking fund. The book value of the debt after 10 years takes into account the total accumulated amount in the sinking fund used to retire the debt, along with any remaining face value.