Final answer:
The value of the bond is calculated using the present value formulas for annuities and a lump sum, discounting the annual coupon payments and par value at the required return rate over the bonds remaining life.
Step-by-step explanation:
To determine the value of a bond that has a coupon rate higher than the required return, we calculate its Present Value (PV) using the formula for the present value of an annuity and the present value of a lump sum. In this case, the bond has an annual coupon payment of 14% of the par value ($21,000), resulting in annual payments of $2,940. The calculation of the bond's value involves discounting these payments and the par value at the required return rate of 6% over the remaining 11-year period.
Present Value of Annuity (PVA) of coupon payments: PVA = PMT * [(1 - (1 + r)^(-n)) / r]
Present Value (PV) of par value: PV = F / (1 + r)^n
Where: PMT = annual coupon payment ($2,940), r = required return (6% or 0.06), n = number of years to maturity (11), F = par value of the bond ($21,000).
Using these formulas, we get:
PVA = $2,940 * [(1 - (1 + 0.06)^(-11)) / 0.06]
PV of par value = $21,000 / (1 + 0.06)^11
Therefore, the value of the bond to an investor requiring a 6% return is the sum of the PVA of the coupon payments and the PV of the par value.
The present value of the coupon payments is calculated, and then the present value of the par value is added to yield the total current value of the bond. When summed, these figures give the bond's value to an investor requiring a 6% return.