Question

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?   

1. Show your work.
2. Draw a cash flow diagram for each problem.
3. Write out all formulas.

Answer 1

(P/A, i%,n) = ((1 + i)^n-1)/(i(1 + i)^n)

(P/F, i%,n) = (1 + i)^-n

Coupon payment = 0.015*10000 = 150 per quarter

i = 16% / 4 = 4% per quarter

t = 15*4 = 60 quarters

Price of one bond = 150*(P/A,4%,60) + 10000*(P/F,4%,60)

= 150*(((1 + 0.04)^60-1)/(0.04*(1 + 0.04)^60)) + 10000*((1 + 0.04)^-60)

= 150*(((1.04)^60-1)/(0.04*(1.04)^60)) + 10000*((1.04)^-60)

= 150*22.623490 + 10000*0.095060

= 4344.12

CFD