Question

3) Basic County Independent School District is building a new school. The cost of the school is $40,000,000. To raise the capital necessary to build the school, the school district will be selling bonds with a face value of $10,000 which will mature in 15 years. The bond interest rate is 6% per year, payable quarterly. If you wanted to earn an interest rate of 16% per year, compounded quarterly, what would you be willing to pay for the bond?

Show your work

Draw a cash flow diagram for each problem.

Write out all formulas

Answer 1

Quarterly bond interest = 10,000 x (6%/4) = 150

Quarterly (nominal) interest rate = 16% / 4 = 4%

Number of quarters = 15 x 4 = 60

(I) Cash flow diagram (values in $)

+3yy. 53 เS 0 150 150 136 10,130 1 ! 0 3 6 0

(II) Bond price ($) = PV of bond interest payments + PV of face value

= 150 x P/A(4%, 60) + 10,000 x P/F(4%, 60)

= 150 x 22.6235** + 10,000 x 0.0951**

= 3,393.53 + 951

= 4,344.53

**P/A(4%, 60) = [1 - (1.04)^-60] / 0.04 = (1 - 0.0951) / 0.04 = 0.9049 / 0.04 = 22.6235

**P/F(4%, 60) = (1.04)^-60 = 0.0951