Question

The Mayflower Corporation has two different bonds currently outstanding. Bond A has a face value of $50,000 and matures in 5 years. The bond makes no payments for the first 2 years, then pays $2,000 every 6 months over the next 3 years until maturity. Bond B also has a face value of $50,000 and matures in 5 years; it makes $750 of coupon payment every 6 months over the life of the bond. If the annual required rate of return for both of these bonds is 10%, what is the value of Bond A? Bond B?

I need help with equations

Answer 1

Computation of Bond Price Today

1) Bond A.

Since cashflows are generating after 2 years we will have to calculate price of the bond at the end of second year and find present value of bond price today to get the answer.

Bond Price is the Present Value of all Future CashFlows

At the end of Year 2

We have

Future Periodic Payment (I)= $2000 every 6 months

Interest Rate = 10%/2 = 5% for 6months

Redemption Amount (F)= $50000

Period (n) = 3years * 2 = 6 periods

Price at the end of Year 2 (P₂) = I*PVAF(5%,6) + F *PVIF(5%,6)

                                                      = 2000 * PVIF(5%,6) + $50000 (5%,6)

                                                      = $10151.38 + $37310.77

                                                       = $47462.15

Price of the Bond A Today = $ 47462.15 * PVIF (10%,2)

                                            = $39224.92

2) Bond B:

Coupon Amount (I) = 750 every 6 months

Interest Rate (r) = 10%/2 = 5% for 6months

Redemption Amount (F)= $50000

Period (n) = 5years * 2 = 10 periods

Price of the Bond B Today = I *PVAF(5%,10) + F *PVIF(5%,10)

                                             = $750 *PVAF(5%,10) + $50000 *PVIF(5%,10)       

                                             = $ 5791.30 + $30695.66

                                              = $ 36486.96