Grasshopper Inc issued 20 years, noncallable, 7.8% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity?
multiple choice answers to the question
a. 1,114.94
b. 1,165.62
c. 1.507.70
d. 1.266.98
e. 1,064.26
what is the correct answer
To calculate the current price of the bonds, you need to use the present value formula, which takes into account the coupon payments and the face value of the bond.
The formula to calculate the present value of a bond is:
PV = C * (1 - (1 + r)^-n) / r + F / (1 + r)^n
Where:
PV = Present value (current price of the bond)
C = Coupon payment per period
r = Interest rate per period
n = Number of periods
F = Face value of the bond
In this case, the coupon payment per period is $1,000 * 7.8% = $78, the interest rate per period is 5.5%, the number of periods is 19 years, and the face value of the bond is $1,000.
Substituting these values into the formula:
PV = $78 * (1 - (1 + 0.055)^-19) / 0.055 + $1,000 / (1 + 0.055)^19
Using a calculator or spreadsheet to evaluate this expression:
PV = $78 * (1 - 0.223135) / 0.055 + $1,000 / 1.1616
PV = $78 * 0.776865 / 0.055 + $861.79
PV = $1,017.29 + $861.79
PV = $1,879.08
Therefore, the current price of the bonds, with 19 years remaining to maturity, is approximately $1,879.08.