Final answer:
The present value of a Liberty, Inc. bond to an investor with a required return of 12.5% is computed using the discounted cash flow method, which involves calculating the present value of annuity (coupon payments) and the present value of a lump sum (face value at maturity) with the given coupon rate, face value, time to maturity, and required return.
Step-by-step explanation:
To calculate the value of a bond to an investor with a required return of 12.5%, we have to discount the future cash flows of the bond to their present value. For a bond with a coupon rate of 8% and a face value of $1,000 that matures in 15 years, the investor will receive annual interest payments of 8% of $1,000, which is $80, plus the face value of the bond at maturity. Using the discounted cash flow (DCF) method, the value of each of these cash flows is calculated using the required return of 12.5% as the discount rate.
Calculating the Present Value of Annuity (Coupon Payments)
Present Value of Annuity (PVA) = C * [(1 - (1 + r)^-n) / r]
Where:
C = Annual Coupon Payment ($80)
r = Investor's Required Return (12.5% or 0.125)
n = Number of Years to Maturity (15)
PVA = $80 * [(1 - (1 + 0.125)^-15) / 0.125]
Calculating the Present Value of a Lump Sum (Face Value at Maturity)
Present Value of a Lump Sum (PVLS) = F / (1 + r)^n
Where:
F = Face Value of the Bond ($1,000)
PVLS = $1,000 / (1 + 0.125)^15
The total present value of the bond is the sum of PVA and PVLS. After calculating these figures, we can determine which of the provided answer choices matches our calculation.