Question

Assume that you wish to purchase a bond with a 17-year maturity, an annual coupon rate of 11.5%, a face value of $1,000, and semiannual interest payments. If you require a 9.5% return on this investment, what is the maximum price you should be willing to pay for the bond?  INCLUDE 2 DECIMAL PLACES WITH YOUR ANSWER.  YOU MUST SHOW ALL WORK (INCLUDING FINANCIAL CALCULATOR KEYSTROKES USED TO SOLVE FOR ANSWER) TO RECEIVE CREDIT.

Answer 1

Formula for bond price is:

Bond price = C x 1 – (1+r)-n/r + F/(1+r) n

F = Face value = $ 1,000

Coupon rate = 11.5 %

n = Number periods to maturity = 17 years x 2 = 34 periods

C = Periodic coupon payment = Face value x Coupon rate/Annual coupon frequency

                                                    = $ 1,000 x 0.115/2 =$ 1,000 x 0.0575 = $ 57.5

r = Rate of return = 0.095 %/2 = 0.0475 semi annually

Bond price = $ 57.5 x [1 – (1+0.0475)-34]/ 0.0475 + $ 1,000/ (1+0.0475) -34

                   = $ 57.5 x [1 – (1.0475)-34]/ 0.0475 + $ 1,000 x (1.0475) -34

                   = $ 57.5 x [(1 – 0.206425299935195)/0.0475] + $ 1,000 x 0.206425299935195

                   = $ 57.5 x (0.094049355/0.0475) + $ 206.425299935195

                   = $ 57.5 x 0.793574700064805 + $ 206.425299935195

                   = $ 57.5 x 16.706835790838 + $ 206.425299935195

                   = $ 960.643057973185 + $ 206.425299935195

                   = $ 1,167.06835790838 or $ 1,167.07

In a financial calculator,

17 x 2 = 34   N

9.5 ÷ 2 = 4.75   I/Y

1000 x 0.115 ÷ 2 = 57.5 PMT

1000 FV

CPT PV

Which will display as -1167.07