How do you determine the value of a 1,000 bond with a 7 percent coupon rate maturing in 20 tears for an investor whose required rate of return is 8 percent?
Please show formula and result
To determine the value of a bond, you can use the formula for present value of a bond:
PV = C * (1 - (1 + r)^(-n)) / r + F / (1 + r)^n
Where:
PV = Present value or value of the bond
C = Coupon payment per period (in this case, per year)
r = Required rate of return (in decimal form)
n = Number of periods (in this case, number of years)
F = Face value or maturity value of the bond
In this case, we have the following information:
C = $1,000 * 7% = $70 (coupon payment per year)
r = 8% = 0.08 (required rate of return)
n = 20 (number of years)
F = $1,000 (face value)
Substituting these values into the formula:
PV = $70 * (1 - (1 + 0.08)^(-20)) / 0.08 + $1,000 / (1 + 0.08)^20
Calculating this formula will give us the value of the bond.
Using a financial calculator or spreadsheet software, the value of the bond is approximately $1,130.59.