Question

You have choice of purchasing two mortgage backed securities: a convention bond and a zero coupon bond. Both bonds have a $10,000 par value. The conventional bond pays interest semi-annually and has a 8.75 percent coupon. The second bond is a zero coupon structure. You require a 10.50% return. What are the bond prices?

Answer 1

The years to maturity is not mentioned. Typically mortgages are 30 years in duration. Assuming that, present value of these bonds can be calculated using PV function on a calculator

For conventional bond, insert N = 30 x 2 = 60, PMT = 8.75% x 10,000 / 2 = 437.50, FV = 10,000 and I/Y = 10.5%/2

=> Compute PV = $8,410.69 is the bond price of conventional bond

For zero coupon, PMT = 0, rest everything remains the same.

=> Compute PV = $464.17 is the bond price of zero coupon bond.